非等温非牛顿黏弹性高分子熔体流动本构行为数值模拟和实验研究
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摘要
高分子成型加工过程中所涉及的应力场、压力场、温度场和化学反应效应不仅决定制品的外观、形状和质量,而且对分子链结构、超分子结构和织态结构的形成和演变具有极其重要的影响。成型加工中由流动而诱发的高分子结晶及其取向可显著提高制品的力学和光学性能。但另一方面,加工过程中时常出现的不稳定流动状态,将导致挤出物表面呈鲨鱼皮状或熔体破裂、共挤出物界面不稳定、注射制品表面有虎皮纹等影响最终制品性能和外观,因而是亟需解决的产品质量问题。研究高分子材料成型加工中的流动过程,不仅对优化工艺条件、模具结构、挤出口模、机头结构,甚至对挤出机或注射成型机的螺杆等结构设计、对节约能耗、降低成本、提高产品竞争力都起着至关重要的作用。因此,对高分子黏弹性流体流动的模拟和分析具有重要的工程实际意义。
一般,高分子加工过程是在三维非等温情况下进行的,并且材料在一些高应变和高应变率区域受到拉伸和剪切的双重作用,呈现复杂的流变行为和高度的非线性特征。另外,流动分析中经常遇到具有尖角的模具或口模,这些几何奇异点容易导致高分子流体产生应力奇异行为,从而诱发不稳定流动；同时,一些加工过程,例如注塑充填过程中还要考虑材料自由面或多组分界面的追踪,这些都会给数值模拟黏弹性流动带来很大的挑战。对成型加工过程中高分子流变行为的模拟研究,可为优化工艺条件、提高产品性能和更好理解高分子流体动力学提供科学依据,从而在高聚物结构—加工—产品三者之间起到桥梁作用,为高分子熔体加工的多尺度或跨尺度模拟,产品的高性能化奠定基础。
本研究用基于有限增量微积分(FIC)过程的压力稳定化迭代分步算法和DEVSS/SU方法,采用近年发展的能够较好描述支化高分子熔体的本构模型(XPP模型、PTT-XPP模型、MDCPP模型以及作者提出的S-MDCPP模型)模拟了高分子加工过程中常遇到的收缩流和挤出胀大流问题,以及非等温非牛顿黏性流体注塑充填过程中熔体的流动行为等,分析了数值模拟这些工程问题所涉及的难点,提出了解决对策,为进一步发展高效、健壮的数值算法提供新的思路。同时,基于数值结果分析了挤出胀大流动中存在的不稳定流动状态,为解决类似产品质量问题提供科学依据和对策。
为了能准确描述成型加工中高分子熔体复杂的流变行为,本研究系统总结和分析了非牛顿黏性本构模型和黏弹性本构模型,指出了它们的局限性和不足；同时重点考察了近年由Pom-Pom分子理论发展的一些新的本构模型,如Pom-Pom模型、XPP模型、修正的XPP模型,PTT-XPP模型和DCPP模型。从数值模拟和试验研究的文献报道看,这些新的本构模型在一定程度上体现了高分子的拓扑结构,能较好地反映真实支化高分子熔体的复杂流变行为,但尚存在一些如解的唯一性和收敛性等数值求解困难和正确再现流变学现象的缺陷。因此,本文进一步提出了一个新的能方便地在现有程序框架中实现的本构模型—S-MDCPP模型,该模型克服了现有XPP、修正的XPP、DCPP等模型的一些缺点,如解的不唯一性、过度剪切变稀行为等。该模型的预测能力通过平面4：1收缩流标准问题进行了考核,发现其具有良好的数值稳定性：并且能够捕捉在高剪切和高拉仲速率下的真实流变行为,而XPP和PTT-XPP模型只能分别较好地捕捉在高剪切或高拉伸速率下的流变行为。此外,用S-MDCPP模型模拟了支化高分子熔体的挤出胀大行为,发现口模出口附近的剪切应力和主链拉伸最大,并从大分子滑移和松弛机理上揭示了可能引起挤出不稳定流动的现象。
采用被许多学者认为能较好描述支化高分子熔体流动特性的XPP模型模拟了高分子加工过程中常遇到的收缩流问题,并详细讨论了不同Weissenberg数和XPP模型中不同材料参数对收缩流场的影响,可视化地给出了不同支化程度的高分子熔体在收缩流场中的拉伸分布情况。此外,还应用PTT模型模拟了高分子熔体的挤出胀大行为,数值结果与相关文献的试验结果吻合较好,从而验证了本文所采用算法的有效性和可靠性；并进一步讨论和分析了挤出过程中可能引起不稳定流动的原因,为深刻理解挤出过程中畸形挤出物的形成机理提供了有益的帮助。
最后,分别采用修正的Cross-Arrhenius模型和Moldflow二阶黏度模型描述LLDPE熔体的流变行为,模拟了该熔体在非等温情况下的注塑充填流动过程；并设计了相应的注塑短射试验。由任意的拉格朗日—欧拉(ALE)有限元方法模拟非等温情况下非牛顿黏性流体的充填结果与注塑短射试验结果比较看,发现本文采用ALE方法追踪自由面的形状和位置与试验结果比较一致。充填结束时,模拟预测的充填时间与试验结果吻合较好。此外,还给出了不同充填量时流场中的速度、压力和温度分布以及不同横截面上的水平速度和温度分布；并得到了充填结束时,熔体碰壁后的速度分布。不同横截面上的速度和温度分布与相关文献对非牛顿黏性流体非等温流动研究得出的结果一致。这些依据表明本文所采用的ALE有限元方法能准确、可靠地追踪充填过程中的自由面位置和形状,为将来把该方法拓展到三维注塑充填分析奠定了基础。
The stress, pressure and temperature fields as well as the effect of chemical reaction in polymer processes not only affect the appearance, shape and quality of final products, but also have great influences on the structures of molecule chain, supermolecule, the texture structure and their evolutions. The flow-induced crystallization and its orientation in polymer processing may improve the mechanical and optical properties of products. On the other hand, the flow instabilities which often occur in polymer processing will result in the deterioration of finished products in their properties and appearance, such as the sharkskin, melt fracture, the interface instability observed in coextrusion flows, the tiger strips on the surface of injection molding products, etc. and become crucial issues to be solved in order to ensure the product qualities. The studies of polymeric flow in polymer processing are not only related to the optimizations of processing conditions, die or mould, extrusion channel, along with the structure design of screw of extruder or injection molding machine, but also play important roles in reducing the energy consuming and the cost of production, so as to improve the competition ability of production. In one word, it is of importance to perform numerical simulation and analysis of polymer viscoelastic flow in the polymer industrial practice.
In general, polymer processes exhibit complex rheological behavior and strong nonlinear characteristics, they are often in three dimension non-isothermal cases and the materials undergo elongation and shear deformations in high strain and strain rate areas. It is noted that the sharp corner of die or mould can often induce stress singularity and lead to flow instabilities. In addition, to trace moving free surfaces or moving interfaces among different melted components in some polymer processes, for example the injection mould filling process, particularly for viscoelastic flows, will bring great challenges to the numerical simulations. The modeling of macromolecule rheological behavior in polymer processing will provide the scientific bases for deep understanding the dynamics of polymeric fluid flows, optimizing technological conditions and improving the qualities of the polymer products. Hence, it bridges among the structure of the polymer, processing and product quality, and establishes a sound foundation for high-performance polymer products based on micromechanically-based and multiscale numerical simulations.
The pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) procedure, and the discrete elastic viscous stress splitting (DEVSS) using the inconsistent streamline-upwind (SU) method are applied in the present investigation. The XPP, PTT-XPP, MDCPP models recently developed and widely used for modeling viscoelastic behaviors of polymer melts and the S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model proposed by the author are adopted for constitutive modeling of the contraction viscoelastic flow and extrusion swell flow in the present work. In addition, the non-isothermal non-Newtonian fluid in mold filling process is investigated. The typical difficulties encountered in modeling these engineering projects are discussed and some schemes are put forward, so as to develop the efficient and robust algorithms. Furthermore, according to the numerical results, the extrusion swell flow instabilities are analyzed in order to provide the scientific bases to solve the problems of product quality.
To accurately describe the complex rheological behavior of polymer melts during the processing, the constitutive models of the generalized Newtonian and viscoelastic fluids are summarized and investigated in the present work. Meanwhile, the shortcomings and limitations of these models are identified. Particularly, some new constitutive equations recently derived from the Pom-Pom molecular theory, such as the Pom-Pom model, XPP, modified XPP, PTT-XPP and DCPP models are introduced and investigated in detail. From the numerical and experimental results reported in the literature for these new models, one will find that they may reflect the actual topological structure of branched polymer and reproduce well the complex rheological behavior of realistic branched polymer melts. However, they still, more or less, suffer from the difficulties in the uniqueness and convergence of the numerical solution procedure and the defects in the correctly reproducing the rheological phenomena in the numerical simulation. Hence, a new constitutive model, S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model, which is conveniently implemented in the framework of the existing computer codes used for the simulation is developed in this study. The S-MDCPP model eliminates some shortcomings of the existing XPP, modified XPP and DCPP models, such as the multi-solution problem, excessive shear-thinning behavior, and so forth. The capability of this model in the numerical prediction is also investigated by means of the benchmark test problem of the planar 4:1 contraction flow. It is noted that the present model demonstrates good numerical stability and is capable of capturing real rheological behaviors under both high shear and elongational rates while the XPP and PTT-XPP models can only well capture those rheological behaviors in high shear or elongational rates respectively. Additionally, the extrusion swell flow of branched polymer melts is numerically simulated by using the S-MDCPP model. It is found that the maximum shear stress and stretch of backbone occur at the places near the die exit. In addition, the extrusion instability is explained and discussed from the macromolecule slip and stress relaxation mechanisms points of view.
The XPP model, which is recognized to be able to well describe the flow characters of the branched polymer melts, is adopted to numerically simulate the planar contraction flow often encountered in the polymer processing in the present study.The influences of Weissenberg number and the material parameters of the XPP model on the flow characters exhibited in the contraction flow are discussed, and the distributions of the backbone stretch of branched polymer with different end arms are visualized. Moreover, the extrusion swell behavior of the polymer melts modeled by the PTT constitutive equation is simulated and the obtained numerical results are in good agreement with the experimental ones reported in the literature. Thus, the reliability of the algorithms adopted in this investigation is validated. Furthermore, the causes of the flow instability occurred in the extrusion processing are explicated for better understanding to the mechanism of occurrence of abnormal extruded products.
Finally, the linear low density polyethylene (LLDPE) melts are described by the modified Cross-Arrhenius model and the Moldflow second order model, respectively, and the non-isothermal injection mold filling flows are simulated. Additionally, the injection short shots are performed so as to verify the locations and shape of the melts front obtained by the arbitrary Lagrangian-Eulerian (ALE) finite element simulation for the non-isothermal filling process. It is shown that the predicted locations and shape of the melts front are in good agreement with the experiment, and the time spent to complete the filling and predicted by the ALE finite element method is consistent with the experimental result. Moreover, the distributions of the horizontal velocity, pressure and temperature at different filling stages as well as the distributions of the horizontal velocity and temperature at various cross sections are given, which agree well with the results reported in the literatures. The distribution of the horizontal velocity at the time when the melts front completely reaches the wall of the mould cavity, i.e. at the end of the filling, is also given. The numerical results validate the reliability, accuracy and robustness of the ALE-based finite element algorithm employed in the present work, particularly in tracing the moving free surface for the injection filling process, and provide a sound base for further development of the present work to the three dimension injection molding process.
一般,高分子加工过程是在三维非等温情况下进行的,并且材料在一些高应变和高应变率区域受到拉伸和剪切的双重作用,呈现复杂的流变行为和高度的非线性特征。另外,流动分析中经常遇到具有尖角的模具或口模,这些几何奇异点容易导致高分子流体产生应力奇异行为,从而诱发不稳定流动；同时,一些加工过程,例如注塑充填过程中还要考虑材料自由面或多组分界面的追踪,这些都会给数值模拟黏弹性流动带来很大的挑战。对成型加工过程中高分子流变行为的模拟研究,可为优化工艺条件、提高产品性能和更好理解高分子流体动力学提供科学依据,从而在高聚物结构—加工—产品三者之间起到桥梁作用,为高分子熔体加工的多尺度或跨尺度模拟,产品的高性能化奠定基础。
本研究用基于有限增量微积分(FIC)过程的压力稳定化迭代分步算法和DEVSS/SU方法,采用近年发展的能够较好描述支化高分子熔体的本构模型(XPP模型、PTT-XPP模型、MDCPP模型以及作者提出的S-MDCPP模型)模拟了高分子加工过程中常遇到的收缩流和挤出胀大流问题,以及非等温非牛顿黏性流体注塑充填过程中熔体的流动行为等,分析了数值模拟这些工程问题所涉及的难点,提出了解决对策,为进一步发展高效、健壮的数值算法提供新的思路。同时,基于数值结果分析了挤出胀大流动中存在的不稳定流动状态,为解决类似产品质量问题提供科学依据和对策。
为了能准确描述成型加工中高分子熔体复杂的流变行为,本研究系统总结和分析了非牛顿黏性本构模型和黏弹性本构模型,指出了它们的局限性和不足；同时重点考察了近年由Pom-Pom分子理论发展的一些新的本构模型,如Pom-Pom模型、XPP模型、修正的XPP模型,PTT-XPP模型和DCPP模型。从数值模拟和试验研究的文献报道看,这些新的本构模型在一定程度上体现了高分子的拓扑结构,能较好地反映真实支化高分子熔体的复杂流变行为,但尚存在一些如解的唯一性和收敛性等数值求解困难和正确再现流变学现象的缺陷。因此,本文进一步提出了一个新的能方便地在现有程序框架中实现的本构模型—S-MDCPP模型,该模型克服了现有XPP、修正的XPP、DCPP等模型的一些缺点,如解的不唯一性、过度剪切变稀行为等。该模型的预测能力通过平面4：1收缩流标准问题进行了考核,发现其具有良好的数值稳定性：并且能够捕捉在高剪切和高拉仲速率下的真实流变行为,而XPP和PTT-XPP模型只能分别较好地捕捉在高剪切或高拉伸速率下的流变行为。此外,用S-MDCPP模型模拟了支化高分子熔体的挤出胀大行为,发现口模出口附近的剪切应力和主链拉伸最大,并从大分子滑移和松弛机理上揭示了可能引起挤出不稳定流动的现象。
采用被许多学者认为能较好描述支化高分子熔体流动特性的XPP模型模拟了高分子加工过程中常遇到的收缩流问题,并详细讨论了不同Weissenberg数和XPP模型中不同材料参数对收缩流场的影响,可视化地给出了不同支化程度的高分子熔体在收缩流场中的拉伸分布情况。此外,还应用PTT模型模拟了高分子熔体的挤出胀大行为,数值结果与相关文献的试验结果吻合较好,从而验证了本文所采用算法的有效性和可靠性；并进一步讨论和分析了挤出过程中可能引起不稳定流动的原因,为深刻理解挤出过程中畸形挤出物的形成机理提供了有益的帮助。
最后,分别采用修正的Cross-Arrhenius模型和Moldflow二阶黏度模型描述LLDPE熔体的流变行为,模拟了该熔体在非等温情况下的注塑充填流动过程；并设计了相应的注塑短射试验。由任意的拉格朗日—欧拉(ALE)有限元方法模拟非等温情况下非牛顿黏性流体的充填结果与注塑短射试验结果比较看,发现本文采用ALE方法追踪自由面的形状和位置与试验结果比较一致。充填结束时,模拟预测的充填时间与试验结果吻合较好。此外,还给出了不同充填量时流场中的速度、压力和温度分布以及不同横截面上的水平速度和温度分布；并得到了充填结束时,熔体碰壁后的速度分布。不同横截面上的速度和温度分布与相关文献对非牛顿黏性流体非等温流动研究得出的结果一致。这些依据表明本文所采用的ALE有限元方法能准确、可靠地追踪充填过程中的自由面位置和形状,为将来把该方法拓展到三维注塑充填分析奠定了基础。
The stress, pressure and temperature fields as well as the effect of chemical reaction in polymer processes not only affect the appearance, shape and quality of final products, but also have great influences on the structures of molecule chain, supermolecule, the texture structure and their evolutions. The flow-induced crystallization and its orientation in polymer processing may improve the mechanical and optical properties of products. On the other hand, the flow instabilities which often occur in polymer processing will result in the deterioration of finished products in their properties and appearance, such as the sharkskin, melt fracture, the interface instability observed in coextrusion flows, the tiger strips on the surface of injection molding products, etc. and become crucial issues to be solved in order to ensure the product qualities. The studies of polymeric flow in polymer processing are not only related to the optimizations of processing conditions, die or mould, extrusion channel, along with the structure design of screw of extruder or injection molding machine, but also play important roles in reducing the energy consuming and the cost of production, so as to improve the competition ability of production. In one word, it is of importance to perform numerical simulation and analysis of polymer viscoelastic flow in the polymer industrial practice.
In general, polymer processes exhibit complex rheological behavior and strong nonlinear characteristics, they are often in three dimension non-isothermal cases and the materials undergo elongation and shear deformations in high strain and strain rate areas. It is noted that the sharp corner of die or mould can often induce stress singularity and lead to flow instabilities. In addition, to trace moving free surfaces or moving interfaces among different melted components in some polymer processes, for example the injection mould filling process, particularly for viscoelastic flows, will bring great challenges to the numerical simulations. The modeling of macromolecule rheological behavior in polymer processing will provide the scientific bases for deep understanding the dynamics of polymeric fluid flows, optimizing technological conditions and improving the qualities of the polymer products. Hence, it bridges among the structure of the polymer, processing and product quality, and establishes a sound foundation for high-performance polymer products based on micromechanically-based and multiscale numerical simulations.
The pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) procedure, and the discrete elastic viscous stress splitting (DEVSS) using the inconsistent streamline-upwind (SU) method are applied in the present investigation. The XPP, PTT-XPP, MDCPP models recently developed and widely used for modeling viscoelastic behaviors of polymer melts and the S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model proposed by the author are adopted for constitutive modeling of the contraction viscoelastic flow and extrusion swell flow in the present work. In addition, the non-isothermal non-Newtonian fluid in mold filling process is investigated. The typical difficulties encountered in modeling these engineering projects are discussed and some schemes are put forward, so as to develop the efficient and robust algorithms. Furthermore, according to the numerical results, the extrusion swell flow instabilities are analyzed in order to provide the scientific bases to solve the problems of product quality.
To accurately describe the complex rheological behavior of polymer melts during the processing, the constitutive models of the generalized Newtonian and viscoelastic fluids are summarized and investigated in the present work. Meanwhile, the shortcomings and limitations of these models are identified. Particularly, some new constitutive equations recently derived from the Pom-Pom molecular theory, such as the Pom-Pom model, XPP, modified XPP, PTT-XPP and DCPP models are introduced and investigated in detail. From the numerical and experimental results reported in the literature for these new models, one will find that they may reflect the actual topological structure of branched polymer and reproduce well the complex rheological behavior of realistic branched polymer melts. However, they still, more or less, suffer from the difficulties in the uniqueness and convergence of the numerical solution procedure and the defects in the correctly reproducing the rheological phenomena in the numerical simulation. Hence, a new constitutive model, S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model, which is conveniently implemented in the framework of the existing computer codes used for the simulation is developed in this study. The S-MDCPP model eliminates some shortcomings of the existing XPP, modified XPP and DCPP models, such as the multi-solution problem, excessive shear-thinning behavior, and so forth. The capability of this model in the numerical prediction is also investigated by means of the benchmark test problem of the planar 4:1 contraction flow. It is noted that the present model demonstrates good numerical stability and is capable of capturing real rheological behaviors under both high shear and elongational rates while the XPP and PTT-XPP models can only well capture those rheological behaviors in high shear or elongational rates respectively. Additionally, the extrusion swell flow of branched polymer melts is numerically simulated by using the S-MDCPP model. It is found that the maximum shear stress and stretch of backbone occur at the places near the die exit. In addition, the extrusion instability is explained and discussed from the macromolecule slip and stress relaxation mechanisms points of view.
The XPP model, which is recognized to be able to well describe the flow characters of the branched polymer melts, is adopted to numerically simulate the planar contraction flow often encountered in the polymer processing in the present study.The influences of Weissenberg number and the material parameters of the XPP model on the flow characters exhibited in the contraction flow are discussed, and the distributions of the backbone stretch of branched polymer with different end arms are visualized. Moreover, the extrusion swell behavior of the polymer melts modeled by the PTT constitutive equation is simulated and the obtained numerical results are in good agreement with the experimental ones reported in the literature. Thus, the reliability of the algorithms adopted in this investigation is validated. Furthermore, the causes of the flow instability occurred in the extrusion processing are explicated for better understanding to the mechanism of occurrence of abnormal extruded products.
Finally, the linear low density polyethylene (LLDPE) melts are described by the modified Cross-Arrhenius model and the Moldflow second order model, respectively, and the non-isothermal injection mold filling flows are simulated. Additionally, the injection short shots are performed so as to verify the locations and shape of the melts front obtained by the arbitrary Lagrangian-Eulerian (ALE) finite element simulation for the non-isothermal filling process. It is shown that the predicted locations and shape of the melts front are in good agreement with the experiment, and the time spent to complete the filling and predicted by the ALE finite element method is consistent with the experimental result. Moreover, the distributions of the horizontal velocity, pressure and temperature at different filling stages as well as the distributions of the horizontal velocity and temperature at various cross sections are given, which agree well with the results reported in the literatures. The distribution of the horizontal velocity at the time when the melts front completely reaches the wall of the mould cavity, i.e. at the end of the filling, is also given. The numerical results validate the reliability, accuracy and robustness of the ALE-based finite element algorithm employed in the present work, particularly in tracing the moving free surface for the injection filling process, and provide a sound base for further development of the present work to the three dimension injection molding process.
引文
[1]Goodship V, Kirwan K. Goodhead T C, et al. Interfacial instabilities in multimaterial co-injection mouldings Part 2-Interfacial mixing in transparent mouldings[J]. Plastics, Rubber and Composites,2003, 32(3):98-103.
[2]Hatzikiriakos S G, Migler K B.Polymer Processing Instabilities:Control and Understanding[M]. New York:Marcel Dekker,2005.
[3]Zatloukal M. Martyn M T, Coates P D, et al. Modelling of viscoelastic coextrusion flows in multi-manifold flat dies[J]. Plastics, Rubbers and Composites,2004,33(7):305-309.
[4]Marchal T. Challenges of modelling the extrusion process[J]. Plastics. Rubber and Composites,2005, 34(5-6):265-270.
[5]Jaluria Y. Fluid Flow Phenomena in Materials Processing—The 2000 Freeman Scholar Lecture[J]. Journal of Fluids Engineering,2001,123:173-210.
[6]Tadmor Z, Gogos C G.Principles of polymer processing[M]. New Jersey:John Wiley & Sons,2006.
[7]Debbaut B. Rheology:from process to simulation[J]. Plastics, Rubber and Composites,2008,37(2-4): 166-173.
[8]廖正品.中国塑料工业(2008)[J].中国塑料,2009,23(5)：1-11.
[9]http://info.21cp.net/Info/Topic/201009/373096.htm.
[10]Walters K, Webster M F. The distinctive CFD challenges of computational rheology[J]. International Journal for Numerical Methods in Fluids,2003,43:577-596.
[11]Renardy M. Current issues in non-Newtonian flows:a mathematical perspective[J]. Journal of Non-Newtonian Fluid Mechanics.2000,90:243-259.
[12]de Gennes P G. Reptation of a polymer chain in the presence of fixed obstacles[J]. Journal of Chemical Physics,1971,5(2):572-579.
[13]Doi M, Edwards S F.The theory of polymer dynamics[M]. New York:Oxford University Press,1986.
[14]Laso M, Ottinger H C. Calculation of viscoelastic flow using molecular models:the CONNFFESSIT approach[J]. Journal of Non-Newtonian Fluid Mechanics,1993, (47):1-20.
[15]Keunings R. A survey of computational rheology [C]. ⅩⅢth International Congress on Rheology, Cambridge, UK,2000.
[16]McLeish T C B, Milner S T. Entangled Dynamics and Melt Flow of Branched Polymers[M]. Advances in Polymer Science. Berlin:Springer,1999,195-254.
[17]Tchesnokova M A, Molenaara J, Slotc J J M, et al. A constitutive model with moderate chain stretch for linear polymer melts[J]. Journal of Non-Newtonian Fluid Mechanics,2004, (123):185-199.
[18]McLeish T C B, Larson R G. Molecular constitutive equations for a class of branched polymers:The pom-pom polymer[J]. Journal of Rheology,1998,42(1):81-110.
[19]Verbeeten W M H, Peters G W M, Baaijens F P T. Differential constitutive equations for polymer melts:The extended Pom-Pom model [J]. Journal of Rheology,2001,45(4):823-844.
[20]Verbeeten W M H, Peters G W M, Baaijens F P T. Viscoelastic Analysis of Complex Polymer Melt Flows using the eXtended Pom-Pom model[J]. Journal of Non-Newtonian Fluid Mechanics,2002,108: 301-326.
[21]Clemeur N, Rutgers R P G, Debbaut B. On the evaluation of some differential formulations for the Pom-Pom constitutive model[J]. Rheologica Acta,2003,42(3):217-231.
[22]Clemeur N, Debbaut B. A pragmatic approach for deriving constitutive equations endowed with pom-pom attributes[J]. Rheologica Acta,2007,46:1187-1196.
[23]Tanner R I, Nasseri S. Simple constitutive models for linear and branched polymers[J]. Journal of Non-Newtonian Fluid Mechanics,2003,116:1-17.
[24]吴其晔,巫静安.高分子材料流变学[M].北京：高等教育出版社,2002.
[25]Schoonen J F M. Determination of Rheological Constitutive Equations using Complex Flows[D]: [Dissertation]. Eindhoven:Eindhoven University of Technology,1998.
[26]Collis M W, Lele A K, Mackley M R, et al. Constriction flows of monodisperse linear entangled polymers:Multiscale modeling and flow visualization J]. Journal of Rheology.2005,49(2):501-522.
[27]Verbeeten W M H, Peters G W M, Baaijens F P T. Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model[J]. Journal of Non-Newtonian Fluid Mechanics,2004, 117:73-84.
[28]Clemeur N, Rutgers R P G, Debbaut B. Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model[J]. Journal of Non-Newtonian Fluid Mechanics,2004,117:193-209.
[29]Whiteside B R, Spares R, Brown E C, et al. Optical imaging metrology for micromoulding cavity flows and products[J]. Plastics, Rubber and Composites,2008,37(2-4):57-66.
[30]Soulages J, Oliveira M S N, Sousa P C, et al. Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels[J]. Journal of Non-Newtonian Fluid Mechanics,2009,163(1-3):9-24.
[31]Bent J, Hutchings L R, Richards R W, et al. Neutron-Mapping Polymer Flow:Scattering, Flow Visualization,and Molecular Theory[J]. Science,2003.301:1691-1695.
[32]Tadmor Z. The evolution of polymer processing into macromolecular engineering and science[J]. Plastics, Rubbers and Composites,2004,33(1):3-4.
[33]Polynkin A, Pittman J F T, Sienz J. Industrial applications of gas assisted injection moulding: numerical prediction and experimental trials[J]. Plastics, Rubber and Composites,2005,34(5-6):236-246.
[34]Johnson L, Olley P, Coates P D. Gas assisted injection moulding Finite element modelling and experimental validation[J]. Plastics, Rubber and Composites,2000,29(1):31-37.
[35]Liu S-J, Chen W-K. Experimental investigation and numerical simulation of cooling process in water assisted injection moulded parts[J]. Plastics, Rubbers and Composites,2004,33(6):260-266.
[36]Zhao J, Mayes R H, Chen G, et al. Polymer micromould design and micromoulding process[J]. Plastics, Rubber and Composites,2003,32(6):240-247.
[37]韩哲文.高分子科学教程[M].上海：华东理工大学出版社,2008.
[38]马德柱,何平笙,徐种德,等.高聚物的结构与性能[M].北京：科学出版社,1995.
[39]何曼君,张红东,陈维孝,等.高分子物理[M].上海：复旦大学出版社,2006.
[40]许元泽.高分子结构流变学[M].成都：四川教育出版社,1988.
[41]北川浩,铃木谦一郎.鹿政理译.吸附的基础与设计[M].北京：化学工业出版社,1983.
[42]Achilleos E, Georgiou G C. On numerical Simulations of Polymer Extrusion Instabilities[J]. Applied Rheology,2002(12):88-104.
[43]Georgiou G C, Vlassopoulos D. On the stability of the simple shear flow of a Johnson-Segalman fluid[J]. Journal of Non-Newtonian Fluid Mechanics,1998,75:77-97.
[44]Han C D.Rheology and Processing of Polymeric Materials[M]. New York:Oxford University Press, 2007.
[45]Bird R B, Armstrong R C, Hassager O.Dynamics of Polymeric Liquids[M]. Fluid Mechanics. New York:John Wiley & Sons,1987.
[46]Luo X-L. Numerical simulation of Weissenberg phenomena-the rod-climbing of viscoelastic fluids[J]. Computer Methods in Applied Mechanics and Engineering,1999,180:393-412.
[47]Tanner R I. Engineering Rheology[M]. New York:Oxford University Press,2000.
[48]Brochard F, de Gennes P G. Shear-dependent slippage at a polymer/solid interface[J]. Langmuir,1992, 8:3033-3037.
[49]Wang S Q. Molecular Transitions and Dynamics at Polymer/Wall Interfaces:Origins of Flow Instabilities and Wall Slip[M]. Advances in Polymer Science. Berlin:Springer-Verlag,1999.
[50]Wang S Q, Drda P. Molecular instabilities in capillary flow of polymer melts:interfacial stick-slip transition, wall slip and extrudate distortion[J]. Macromolecular Chemistry and Physics,1997.198: 673-701.
[51]Drda P P, Wang S Q. Stick-slip transition at polymer melt/solid interfaces[J]. Physical Review Letters, 1995,75(14):2698-2701.
[52]廖华勇,范毓润.聚合物熔体壁面滑移的流变研究[J].高等学校化学学报.2006,27(9)：1755-1761.
[53]吴其晔,巫静安,温学明,等.聚乙烯熔体的挤出畸变与非线性粘弹性的关系[J].中国塑料,2004,18(7)：40-44.
[54]Nassehi V.Practical Aspects of Finite Element Modelling of Polymer Processing[M]. New York:John Wiley & Sons,2002.
[55]Li X K, Duan Q L, Han X H, et al. Adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method for injection molding process[J]. International Journal for Numerical Methods in Engineering,2008,73(8):1153-1180.
[56]http://www.mate.tue.nl/-hulsen.
[57]Moldflow软件培训资料.上海：Moldflow公司,2007.
[58]Baaijens F P T, Hulsen M A, Anderson P D. The Use of Mixed Finite Element Methods for Viscoelastic Fluid Flow Analysis[M]. In:Stein E, Borst R e d. Hughes T J R (eds) Encyclopedia Of Computational Mechanics. New York:John Wiley & Sons,2004;481-498.
[59]Kotelyanskii M, Theodorou D N. Simulation Methods for Polymers. New York:Marcel Dekker,2004.
[60]Burmenko I. Brownian Dynamics Simulations of Fine-Scale Molecular Models[D]:[Dissertation]. Massachusetts Institute of Technology,2005.
[61]Bajaj M, Bhat P P, Prakash J R, et al. Multiscale simulation of viscoelastic free surface flows[J]. Journal of Non-Newtonian Fluid Mechanics.2006,140:87-107.
[62]Halin P, Lielens R, Keunings R, et al. The Lagrangian partical method for macroscopic and micro-macro viscoelastic flow computations[J]. Journal of Non-Newtonian Fluid Mechanics,1998,79: 387-403.
[63]张小华,欧阳洁,孔倩.聚合物流动的多尺度模拟[J].化工学报,2007,58(8)：1897-1904.
[64]Laso M, Picasso M, Ottinger H C.2-D Time-Dependent Viscoelastic Flow Calculations Using CONNFFESSIT[J]. AIChE Journal,1997,43(4):877-892.
[65]Feigl K, Laso M, Ottinger H C. CONNFFESSIT Approach for Solving a Two-Dimensional Viscoelastic Fluid Problem[J]. Macromolecules,1995,28(9):3261-3274.
[66]Hulsen M A, van Heel A P G, van den Brule B H A A. Simulation of viscoelastic flows using Brownian configuration fields[J]. Journal of Non-Newtonian Fluid Mechanics,1997, (70):79-101.
[67]Bajaj M, Bhat P P, Prakash J R, et al. Micro-Macro simulation of viscoelastic free surface flows using the Brownian configuration fields method[C]. Proceeding ⅩⅣth International Congress on Rheology, Seoul, Korea,2004.
[68]Ramirez J, Laso M. Size reduction methods for the implicit time-dependent simulation of micro-macro viscoelastic flow problems[J]. Journal of Non-Newtonian Fluid Mechanics,2005,127: 41-49.
[69]Peters E A J F, van Heel A P G, Hulsen M A, et al. Generalization of the deformation field method to simulate advanced reptation models in complex flow[J]. Journal of Rheology,2000,44(4):811-829.
[70]Gallez X, Halin P, Lielens G, et al. The adaptive Lagrangian particle method for macroscopic and micro-macro computations of time-dependent viscoelastic[J]. Computer Methods in Applied Mechanics and Engineering,1999,180:345-364.
[71]Zhou Q, Akhavan R. A comparison of FENE and FENE-P dumbbell and chain models in turbulent flow[J]. Journal of Non-Newtonian Fluid Mechanics,2003,109:115-155.
[72]Herrchen M, Ottinger H C. A detailed comparison of various FENE dumbbell models[J]. Journal of Non-Newtonian Fluid Mechanics,1997,68:17-42.
[73]Ghosh I, Joo Y L. McKinley G H, et al. A new model for dilute polymer solutions in flows with strong extensional components [J]. Journal of Rheology,2002,46(5):1057-1089.
[74]Rakshit A, Picu R C. Coarse-grained model of entangled polymer melts in non-equilibrium[J]. Rheologica Acta,2008,47:1039-1048.
[75]Keunings R. A survey of computational rheology[C]. ⅩⅢth International Congress on Rheology, Cambridge, UK,2000.
[76]Ottinger H C, van den Brule B H A A, Hulsen M A. Brownian configuration fields and variance reduced CONNFFESSIT[J]. Journal of Non-Newtonian Fluid Mechanics,1997, (70):255-261.
[77]Li X K, Han X H. An iterative stabilized fractional step algorithm for numerical solution of incompressible N-S equations[J]. International Journal for Numerical Methods in Fluids,2005,49: 395-416.
[78]Onate E. A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation[J]. Computer Methods in Applied Mechanics and Engineering,2000,182:355-370.
[79]Han X H, Li X K. An iterative stabilized CNBS-CG scheme for incompressible non-isothermal non-Newtonian fluid flow[J]. International Journal of Heat and Mass Transfer.2007,50:847-856.
[80]Osswald T A, Hernandez-Ortiz J P.Polymer processing:modeling and simulation[M]. Munich: Hanser,2006.
[81]韩先洪.成型充填过程中非等温非牛顿粘弹性流动数值模拟[D]：[博士论文].大连：大连理工大学.2007.
[82]Bird R B, Wiest. J M. Constitutive equations for polymeric liquids. In Annual review of fluid mechanics[J]. Annual review of fluid mechanics,1995,27:169-193.
[83]古大治.高分子流体动力学[M].现代高分子科学丛书.成都：四川教育出版社,1988.
[84]Thien N P, Tanner R I. A new constitutive equation drived from network theory[J]. Journal of Non-Newtonian Fluid Mechanics,1977,2::353-365.
[85]Giesekus H. A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility[J]. Journal of Non-Newtonian Fluid Mechanics,1982,11: 69-109.
[86]Blackwell R J, McLeish T C B, Harlen O G. Molecular Drag-Strain Coupling in Branched Polymer Melts[J]. Journal of Rheology,2000,44(1):121-136.
[87]Inkson N J, McLeish T C B, Harlen O G, et al. Predicting low density polyethylene melt rheology in elongational and shear flows with"pom-pom" constitutive equations[J]. Journal of Rheology,1999,43(4): 873-896.
[88]Tanner R I. On the congruence of some network and pom-pom models[J]. Korea-Australia Rheology Journal,2006,18(1):9-14.
[89]Larson R G.Constitutive Equations for Polymer Melts and Solutions[M]. Boston:Butterworths,1988.
[90]Wagner M H, Kheirandish S, Koyama K, et al. Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory[J]. Rheologica Acta,2005,44:235-243.
[91]Xue S-C, Tanner R I, Phan-Thien N. Numerical modelling of transient viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,2004,123:33-58.
[92]Bonito A, Picasso M, Laso M. Numerical simulation of 3D viscoelastic flows with free surfaces [J]. Journal of Computational Physics,2006,215:691-716.
[93]Aboubacar M, Aguayo J P, Phillips P M, et al. Modelling pom-pom type models with high-order finite volume schemes[J]. Journal of Non-Newtonian Fluid Mechanics,2005,126:207-220.
[94]Tsukanov I, Shapiro V, Zhang S. A meshfree method for incompressible fluid dynamics problems[J]. International Journal for Numerical Methods in Engineering,2003,58:127-158.
[95]Zhang X K, Kwon K C, Youn S K. Least-squares meshfree method for incompressible Navier-Stokes problems[J]. International Journal for Numerical Methods in Fluids,2004,46:263-288.
[96]Liu G R, Wu Y L, Ding H. Meshfree weak-strong (MWS) form method and its application to incompressible flow problems[J]. International Journal for Numerical Methods in Fluids,2004,46: 1025-1047.
[97]Onate E, Idelsohn S R, Zienkiewicz O C A finite point method in computational mechanics. Applications to convective transport and fluid flow[J]. International Journal for Numerical Methods in Engineering,1996,39:3839-3866.
[98]Nadau L, Sequeira A. Numerical simulations of shear dependent viscoelastic flows with a combined finite element-finite volume method[J]. Computers and Mathematics with Applications,2007,53: 547-568.
[99]Webster M F, Tamaddon-Jahromi H R, Aboubacar M. Transient viscoelastic flows in planar contractions [J]. Journal of Non-Newtonian Fluid Mechanics,2004,118:83-101.
[100]Taliadorou E, Georgiou G C, Alexandrou A N. A two-dimensional numerical study of the stick-slip extrusion instability [J]. Journal of Non-Newtonian Fluid Mechanics,2007,146:30-44.
[101]Zhang L T, Wagner G J, Liu W K. Modelling and simulation of fluid structure interaction by meshfree and FEM[J]. Communications in Numerical Methods in Engineering,2003.19:615-621.
[102]Chung T J.Computational fluid dynamics[M]. Cambridge:Cambridge University Press 2002.
[103]Ferziger J H, Peric M.Computational Methods for Fluid Dynamics[M]. Berlin:Springer,2002.
[104]Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J]. International Journal for Numerical Methods in Engineering,1994,37:229-256.
[105]Belytschko T, Krongauz Y, Organ D, et al. Meshless methods:an overview and recent developments[J]. Computer Methods in Applied Mechanics and Engineering,1996,139:3-47.
[106]Liu G R, Liu M B.Smoothed Particle Hydrodynamics:A Meshfree Particle Method[M]. Singapore: World Scientific,2003.
[107]张雄,刘岩.无网格法[M].北京：清华大学出版社.2004.
[108]Zienkiewicz O C, Heinrich J C, Huyakorn P S, et al. An upwind finite element scheme for two dimensional convective transport equations[J]. International Journal for Numerical Methods in Engineering, 1977,11:131-144.
[109]Nguyen H, Reynen J. A space-time least-squares finite element scheme for advection—diffusion equations[J]. Computer Methods in Applied Mechanics and Engineering,1984,42(3):331-342.
[110]Hughes T J R, Franca L P, Hulbert G M. A new finite element formulation for computational fluid dynamics. Ⅷ. The Galerkin/least-squares method for advection-diffusion equations[J]. Computer Methods in Applied Mechanics and Engineering,1989,73:173-189.
[111]Masud A, Hughes T J R. A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems[J]. Computer Methods in Applied Mechanics and Engineering,1997,146(1-2):91-126.
[112]Shakib F, Hughes T J R. A new finite element formulation for computational fluid dynamics. IX. Fourier analysis of space-time Galerkin/least-squares algorithms[J]. Computer Methods in Applied Mechanics and Engineering,1991,87(1):35-58.
[113]Hughes T J R, Feijoo G R, Mazzei L, et al. The variational multiscale method-a paradigm for computational mechanics[J]. Computer Methods in Applied Mechanics and Engineering,1998,166:3-24.
[114]Brooks A N, Hughes T J R. Streamline upwind/Petrov-Galerkin methods for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering,1982,32:199-259.
[115]Donea J. A Taylor-Galerkin method for convective transport problems[J]. International Journal for Numerical Methods in Fluids,1984,20:101-119.
[116]Donea J, Huerta A.Finite element methods for flow problems[M]. Chichester:John Wiley & Sons, 2003.
[117]Zienkiewicz O C, Taylor R L.The Finite Element Method[M]. Fluid Dynamics. Stoneham: Butterworth Heinemann,2000.
[118]Zienkiewicz O C, Codina R. A general algorithm for compressible and incompressible flow-part Ⅰ: The split, characteristic-based scheme[J]. International Journal for Numerical Methods in Fluids,1995,20: 869-885.
[119]Mutlu I, Townsend P, Webster M F. Simulation of cable-coating viscoelastic flows with coupled and decoupled schemes[J]. Journal of Non-Newtonian Fluid Mechanics,1998,74:1-23.
[120]Nithiarasu P. A fully explicit characteristic based split (CBS) scheme for viscoelastic flow calculations[J]. International Journal for Numerical Methods in Engineering,2004,60:949-978.
[121]Duan Q L, Li X K. An ALE based iterative CBS algorithm for non-isothermal non-Newtonian flow with adaptive coupled finite element and meshfree method[J]. Computer Methods in Applied Mechanics and Engineering,2007,196(49-52):4911-4933.
[122]Chorin A J. A numerical method for solving incompressible viscous flow problems[J]. Journal of Computational Physics,1967,2:12-26.
[123]Temam R. Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaries Ⅱ[J]. Archives for Rational Mechanics and Analysis,1969,33:377-385.
[124]Guermond J-L, Quartapelle L. Calculation of incompressible viscous flow by an unconditionally stable projection FEM[J]. Journal of Computational Physics,1997,132(1):12-33.
[125]Guermond J-L, Quartapelle L. On stability and convergence of projection methods based on pressure Poisson equation[J]. International Journal for Numerical Methods in Fluids,1998,26(9):1039-1053.
[126]Kim J M. Kim C, Kim J H, et al. High-resolution finite element simulation of 4:1 planar contraction flow of viscoelastic fluid[J]. Journal of Non-Newtonian Fluid Mechanics,2005,129:23-37.
[127]韩先洪,李锡夔.高黏性流动有限元模拟的迭代稳定分步算法[J].力学学报,2006,38(1)：16-24.
[128]Laval H, Quartapelle L. A fractional-step Taylor-Galerkin method for unsteady incompressible flow[J]. International Journal for Numerical Methods in Fluids,1990,11:501-513.
[129]Jahromi H R T, Ding D P, Webster M F, et al. A Taylor-Galerkin finite element method for non-Newtonian flows[J]. International Journal for Numerical Methods in Engineering,1992,34: 741-757.
[130]Codina R. Pressure stability in fractional step finite element methods for incompressible flows [J]. Journal of Computational Physics,2001,170:112-140.
[131]Fortin M, Fortin A. A new approach for the fern simulation of viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1989,32:295-310.
[132]Li X K, Duan Q L. Meshfree iterative stabilized Taylor-Galerkin and characteristic-based split (CBS) algorithms for incompressible N-S equations[J]. Computer Methods in Applied Mechanics and Engineering,2006,195:6125-6145.
[133]Baaijens F P T. Mixed finite element methods for viscoelastic flow analysis:A review[J]. Journal of Non-Newtonian Fluid Mechanics,1998.79:361-386.
[134]Brooks A N, Hughes T J R. Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering,1982,32(1-3):199-259.
[135]Marchal J M, Crochet M J. A new mixed finite element for calculating viscoelastic flow[J]. Journal of Non-Newtonian Fluid Mechanics,1987,26:77-114.
[136]Fortin M, Fortin A. A new approach for the fem simulation of viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1989,32:295-310.
[137]King R C, Apelian M R, Armstrong R C, et al. Numerically stable finite element techniques for viscoelastic calculations in smooth and singular domains[J]. Journal of Non-Newtonian Fluid Mechanics, 1988,29:147-216.
[138]Perera M G N, Walters K. Long-range memory effects in flows involving abrupt changes in geometry, Part Ⅰ. Flows associated with L-shaped and T-shaped geometries[J]. Journal of Non-Newtonian Fluid Mechanics,1977.2(2):49-81.
[139]Rajagopalan D, Armstrong R C, Brown R A. Finite element methods for calculation of steady viscoelastic flow using constitutive equations with a Newtonian viscosity[J]. Journal of Non-Newtonian Fluid Mechanics,1990,36(159-192)
[140]Guenette R, Fortin M. A new mixed finite element method for computing viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1995,60:27-52.
[141]Fortin A, Guenette R, Pierre R. On the discrete EVSS method[J]. Computer Methods in Applied Mechanics and Engineering,2000,189:121-139.
[142]Sun J, Smith M D, Armstrong R C, et al. Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method:DAVSS-G/DG[J]. Journal of Non-Newtonian Fluid Mechanics,1999,86:281-307.
[143]Hua X, Ding Z, Lee L J. Simulation of 2D transient viscoelastic flow using the CONNFFESSIT approach[J]. Journal of Non-Newtonian Fluid Mechanics,2005,127:107-122.
[144]Grillet A M, Bogaerds A C B, Peters G W M, et al. Numerical analysis of flow mark surface defects in injection molding flow[J]. Journal of Rheology,2002,46(3):651-669.
[145]Aboubacar M, Webster M F. Development of an optimal hybrid finite volume/element method for viscoelastic flows[J]. International Journal for Numerical Methods in Fluids,2003,41:1147-1172.
[146]Wapperom P, Webster M F. A second-order hybrid finiteelement/volume method for viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1998,79:405-431.
[147]Wapperom P, Webster M F. Simulation for viscoelastic flow by a finite volume/element method[J]. Computer Methods in Applied Mechanics and Engineering,1999,180:281-304.
[148]Belytschko T, Organ D, Krongauz Y. A coupled finite element-element-free Galerkin method[J]. Computational Mechanics,1995,17:186-195.
[149]Peters G W M, Baaijens F P T. Modelling of non-isothermal viscoelastic flows [J]. Journal of Non-Newtonian Fluid Mechanics,1997,68:205-224.
[150]Massarotti N, Nithiarasu P, Zienkiewicz O C. Characteristic-based-split (CBS) algorithm for incompressible flow problems with heat transfer[J]. International Journal of Numerical Methods for Heat& Fluid Flow,1998.8(8):969-990.
[151]Nithiarasu P, Mathur J S, Weatherill N P, et al. Three-dimensional incompressible flow calculations using the characteristic based split (CBS) scheme[J]. International Journal for Numerical Methods in Fluids, 2004,44:1207-1229.
[152]Zienkiewicz O C, Qu S, Taylor R L. The patch test for mixed formulations[J]. International Journal for Numerical Methods in Engineering,1986,23:1873-1883.
[153]Onate E. Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems[J]. Computer Methods in Applied Mechanics and Engineering,1998,151(1-2): 233-265.
[154]Hughes T J R. Multiscale phenomena:Green's functions, the Dirichlet-to-Neumann formulation. subgrid scale models, bubbles and the origins of stabilized methods[J]. Computer Methods in Applied Mechanics and Engineering,1995,127(1-4):387-401.
[155]Hughes T J R, Feijoo G R, Mazzei L, et al. The variational multiscale method-a paradigm for computational mechanics[J]. Computer Methods in Applied Mechanics and Engineering,1998,166(1-2): 3-24.
[156]Hughes T J R, Scovazzi G, Franca L P. Multiscale and stabilized methods[M]. In:Stein E, Borst R, Hughes T J R (eds) Encyclopedia Of Computational Mechanics. Chichester:John Wiley & Sons, 2004;5-60.
[157]Fattal R, Kupferman R. Constitutive laws for the matrix-logarithm of the conformation tensor[J]. Journal of Non-Newtonian Fluid Mechanics,2004,123:281-285.
[158]Afonso A, Oliveira P J, Pinho F T, et al. The log-conformation tensor approach in the finite-volume method frame work[J]. Journal of Non-Newtonian Fluid Mechanics,2009,157:55-65.
[159]Guenette R, Fortin A, Kane A, et al. An adaptive remeshing strategy for viscoelastic fluid flow simulations[J]. Journal of Non-Newtonian Fluid Mechanics,2008.153:34-45.
[160]Coronado O M, Arora D, Behr M, et al. A simple method for simulating general viscoelastic fluid flows with an alternate log-conformation formulation[J]. Journal of Non-Newtonian Fluid Mechanics,2007, 147:189-199.
[161]Sussman M. Puckett E G. A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows[J]. Journal of Computational Physics,2000, (162): 301-337.
[162]Devals C, Heniche M, Bertrand F, et al. A finite element strategy for the solution of interface tracking problems[J]. International Journal for Numerical Methods in Fluids,2005,49:1305-1327.
[163]Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics,1981,39:201-225.
[164]曹伟.王蕊.申长雨.塑料熔体在注塑模中的三维流动分析[J].化工学报,2004.55(9)：78-81.
[165]Luoma J A, Voller V R. An explicit scheme for tracking the filling front during polymer mold filling[J]. Applied Mathematical Modelling,2000,24:575-590.
[166]Osher S, Sethian J A. Fronts propagating with curvature dependent speed:Algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics,1988,79:12-49.
[167]Osher S, Fedkiw P. Level set methods:an overview and some recent results.[J]. Journal of Computational Physics,2001,169:463-502.
[168]Lin C-L, Lee H, Lee T, et al. A level set characteristic Galerkin finite element method for free surface flows[J]. International Journal for Numerical Methods in Fluids,2005,49:521-547.
[169]Holm E J, Langtangen H P. A unified finite element model for the injection molding process[J]. Computer Methods in Applied Mechanics and Engineering,1999,178:413-429.
[170]Yang B X, Ouyang J, Liu C T, et al. Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method[J]. Chinese Journal of Chemical Engineering,2010,18(4): 600-608.
[171]Yang B, Ouyang J, Li Q, et al. Modeling and simulation of the viscoelastic fluid mold filling process by level set method[J]. Journal of Non-Newtonian Fluid Mechanics,2010,165:1275-1293.
[172]Hayashi M, Hatanaka K, Kawahara M. Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods.[J]. International Journal for Numerical Methods in Fluids,1991,13:805-840.
[173]Zhang J, Khayat R E. A Lagrangian boundary element approach to transient three-dimensional free surface flow in thin cavities[J]. International Journal for Numerical Methods in Fluids,2001,37:399-418.
[174]Feng Y T, Perie D. A time-adaptive space-time finite element method for incompressible Lagrangian flows with free surfaces:computational issues[J]. Computer Methods in Applied Mechanics and Engineering,2000,190:499-518.
[175]Khayat R E, Elsin W, Kim K. An adaptive boundary element approach to transient free surface flow as applied to injection molding[J]. International Journal for Numerical Methods in Fluids,2000,33: 847-868.
[176]Khayat R E, Plaskos C, Genouvrier D. An adaptive boundary-element approach for 3D transient free surface cavity flow, as applied to polymer processing[J]. International Journal for Numerical Methods in Engineering,2001,50:1347-1368.
[177]Fang J, Owens R G, Tacher L, et al. A numerical study of the SPH method for simulating transient viscoelastic free surface flows[J]. Journal of Non-Newtonian Fluid Mechanics,2006,139:68-84.
[178]Kulasegaram S, Bonet J, Lewis R W, et al. High pressure die casting simulation using a Lagrangian particle method[J]. Communications in Numerical Methods in Engineering,2003,19:679-687.
[179]Idelsohn S R, Onate E, Pin F D. The particle finite element method:a powerful tool to solve incompressible flows with free-surfaces and breaking waves[J]. International Journal for Numerical Methods in Engineering,2004,61:964-989.
[180]Onate E, Garcia J, Idelsohn S R, et al. Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches[J]. Computer Methods in Applied Mechanics and Engineering,2006,195:3001-3037.
[181]Noh W F. CEL:a time-dependent two-space-dimensional coupled Eulerian-Lagrangian code[J]. Methods in Computational Physics,1964,3:117-179.
[182]Hirt C, Amsden A, Cook J. An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics,1974,14:227-253.
[183]Hughes T J R, Liu W K, Zimmerman T K. Lagrangian-Eulerian finite element formulation for viscous flows[J]. Computer Methods in Applied Mechanics and Engineering,1981,29:329-349.
[184]Belytschko T, Flanagan D P, Kennedy J M. Finite element methods with user-controlled meshes for fluid-structure interaction[J]. Computer Methods in Applied Mechanics and Engineering,1982,30: 669-688.
[185]Liu W K, Chang H, Chen J S, et al. Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua[J]. Computer Methods in Applied Mechanics and Engineering,1988,68:259-310.
[186]Braess H, Wriggers P. Arbitrary Lagrangian Eulerian finite element analysis of free surface flow[J]. Computer Methods in Applied Mechanics and Engineering,2000,190:95-109.
[187]Gadala M S. Recent trends in ALE formulation and its applications in solid mechanics[J]. Computer Methods in Applied Mechanics and Engineering,2004,193:4247-4275.
[188]Lewis R W, Navti S E, Taylor C. A mixed Lagrangian-Eulerian approach to modelling fluid flow during mould filling[J]. International Journal for Numerical Methods in Fluids,1997,25:931-952.
[189]韩先洪,李锡夔.成型充填过程的ALE有限元模拟[J].应用力学学报,2005,22(3)：440-445.
[190]韩先洪,李锡夔.充填过程ALE自由面追踪及网格生成方法[J].大连理工大学学报,2005,45(5)：633-639.
[191]Yamaguchi H, Mishima A, Yasumoto T, et al. An arbitrary Lagrangian-Eulerian approach for simulating stratified viscoelastic fluids[J]. Journal of Non-Newtonian Fluid Mechanics,2000,89:251-272.
[192]Ganvir V, Lele A, Thaokar R, et al. Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156(1-2):21-28.
[193]关振群.宋超.顾元宪.等.有限元网格生成方法研究的新进展[J].计算机辅助设计与图形学学报.2003.15(1-14)
[194]Lewis R W, Navti S E, Taylor C. A mixed Lagrangian-Eulerian approach to modelling fluid flow during mould filling[J]. International Journal for Numerical Methods in Fluids,1997,25:931-952.
[195]Bathe K J.Finite element procedure[M]. New Jersey:Prentice-Hall,1996.
[196]Brezzi F, Fortin M.Mixed and Hybrid Finite Element methods[M]. Series in Computational Mechanics. New York:Springer,1991.
[197]Lee K, Mackley M R. The significance of slip in matching polyethylene processing data with numerical simulation[J]. Journal of Non-Newtonian Fluid Mechanics.2000.94:159-177.
[198]Larson R G.The structure and rheology of complex fluids[M]. New York:Oxford University Press, 1999.
[199]Ferry J D.Viscoelastic properties of polymers[M]. New York:John Wiley & Sons,1986.
[200]周持兴.聚合物流变学实验与应用[M].上海：上海交通大学出版社,2003.
[201]颜家华,彭玉成.聚合物熔体本构关系的研究进展[J].力学进展,1998,28(2)：218-226.
[202]Ottinger H C. Capitalizing on nonequilibrium thermodynamics:branched polymers[C]. Proceedings of the ⅩⅢth International Congress on Rheology, Cambridge, U.K..2000.
[203]Inkson N J, Phillips T N. Unphysical phenomena associated with the extended pom-pom model in steady flow[J]. Journal of Non-Newtonian Fluid Mechanics,2007,145:92-101.
[204]Wang W, Li X K, Han X H. A numerical study of constitutive models endowed with Pom-Pom molecular attributes[J]. Journal of Non-Newtonian Fluid Mechanics.2010,165(21-22):1480-1493.
[205]Rubio P, Bastian H, Wagner. M H. The molecular stress function model for polymer melts with dissipative constraint release[J]. Journal of Rheology,2001
[206]Marrucci G, Greco F, Ianniruberto. G. Integral and differential constitutive equations for entangled polymers with simple versions of CCR and force balance on entanglements.[J]. Rheologica Acta,2001, 40(2):98-103.
[207]Feigl K, Ottinger H C. A new class of stochastic simulation models for polymer stress calculation[J]. Journal of Chemical Physics,1998,109:815-826.
[208]Wagner M H, P. Rubio, Bastian H. The Molecular Stress Function Model for Polydisperse Polymer Melts with Dissipative Convective Constraint ReIease[J]. Journal of Rheology,2001,45:1387-1412.
[209]Wagner M H. Modeling nonlinear rheology of polydisperse polymer melts[J]. International Journal of Applied Mechanics and Engineering,2005,11(2):255-267.
[210]韩式方.非牛顿流体本构方程和计算解析理论[M].北京：科学出版社,2000.
[211]宋名实,杨志洪.高分子熔体和浓溶液流变性能的研究[J].化学物理学报,2000,13(6)：699-720.
[212]朱克勤.非牛顿流体力学研究的若干进展[J].力学与实践,2006,28(4)：1-8.
[213]周持兴.加工流场中高聚物复杂流体内部结构的唯象定律[J].高分子材料科学与工程.1999,15(5)：1-4.
[214]Fan X J. Molecular models and flow calculations. Ⅱ. Simulation of steady planar flow[J]. Acta Mechanic Sinica,1989,5(3):216-226.
[215]范西俊.定常流动中聚合物分子的取向[J].力学学报,1991.23：400-410.
[2]6]方建农.范西俊.聚合物分子模型的Brown动力学模拟[J].力学进展,1999.29(1)：112-120.
[217]王克俭,周持兴.考虑壁面滑移的Z-W流变模型及其应用[J].高分子通报.2003(1)：8-17.
[218]Ngamaramvaranggul V, Webster M F. Viscoelastic simulations of stick-slip and die-swell flows[J]. International Journal for Numerical Methods in Fluids,2001,36:539-595.
[219]Bishko G. McLeish T C B, Harlen O G. Theoretical Molecular Rheology of Branched Polymers in Simple and Complex Flows:The Pom-Pom Model[J]. Physical Review Letters,1997,79(12):2352-2355.
[220]Bishko G B, Harlen O G, McLeish T C B, et al. Numerical simulation of the transient flow of branched polymer melts through a planar contraction using the 'pom-pom' model [J]. Journal of Non-Newtonian Fluid Mechanics,1999,82(2-3):255-273.
[221]Ottinger H C. Thermodynamic admissibility of the pompon model for branched polymers[J]. Rheologica Acta,2001,40:317-321.
[222]Inkson N J, Phillips T N, van Os R G M. Numerical simulation of flow past a cylinder using models of XPP type[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156:7-20.
[223]Baltussen M G H M, Verbeeten W M H, Bogaerds A C B, et al. Anisotropy parameter restrictions for the eXtended Pom-Pom model[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156:7-20.
[224]Aguayo J P, Tamaddon-Jahromi H R, Webster M F. Extensional response of the pom-pom model through planar contraction flows for branched polymer melts[J]. Journal of Non-Newtonian Fluid Mechanics,2006,134:105-126.
[225]Han X H, Li X K. A mixed finite element scheme for modelling of XPP viscoelastic flows[J]. Acta Mechanica Sinica,2008,24(6):671-680.
[226]Li X K, Han X H. Numerical modeling of viscoelastic flows using equal low-order finite elements[J]. Computer Methods in Applied Mechanics and Engineering,2010,199:570-581.
[227]Pivokonsky R, Zatloukalb M, Filip P, et al. Rheological characterization and modeling of linear and branched metallocene polypropylenes prepared by reactive processing[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156:1-6.
[228]Pivokonsky R, Zatloukal M, Filip P. On the predictive/fitting capabilities of the advanced differential constitutive equations for linear polyethylene melts[J]. Journal of Non-Newtonian Fluid Mechanics,2008,150:56-64.
[229]Piau J M, Agassant J F.Rheology for Polymer Melt Processing[M]. Amsterdam:Elsevier,1996.
[230]Baaijens F P T. An iterative solver for the DEVSS/DG method with application to smooth and non-smooth flows of the upper convected Maxwell fluid[J]. Journal of Non-Newtonian Fluid Mechanics. 1998(75):119-138.
[231]Chorin A J. Numerical solution of the Navier-Stokes equations[J]. Mathematics of Computation, 1968,22:742-762.
[232]Temam R. Sur l'approximation de la solution des equations de Navier-Stokes par la me thode des pas fractionnaries Ⅱ[J]. Archives for Rational Mechanics and Analysis,1969,33:377-385.
[233]Comini G, Guidice S D. Finite element solution of incompressible Navier-Stokes equations[J]. Numerical Heat Transfer, Part A,1972,5:463-478.
[234]Donea J, Giuliani S, Laval H, et al. Finite element solution of the unsteady Navier-Stokes equations by a fractional step method[J]. Computer Methods in Applied Mechanics and Engineering,1982,30: 53-73.
[235]Aguayo J P, Phillips P M, Phillips T N, et al. The numerical prediction of planar viscoelastic contraction flows using the pom-pom model and higher-order finite volume schemes[J]. Journal of Computational Physics,2007,220:586-611.
[236]Li X K, Han X H, Pastor M. An iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics[J]. Computer Methods in Applied Mechanics and Engineering,2003, 192:3845-3859.
[237]段庆林.成型充填过程中非等温非牛顿粘性流动的ALE有限元与无网格自适应耦合模拟[D]：[博士学位].大连：大连理工大学,2007.
[238]Alves M A, Oliveira P J. Pinho F T. Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions[J]. Journal of Non-Newtonian Fluid Mechanics,2003,110:45-75.
[239]Tanner R I. A theory of die-swell[J]. Journal of Polymer Science Part A,1970,8:2067-2078.
[240]Crochet M J, Keunings R. Die swell of a Maxwell fluid numerical prediction[J]. Journal of Non-Newtonian Fluid Mechanics,1980,7:199-212.
[241]Crochet M J, Keunings R. Finite element analysis of die swell of a highly elastic fluid[J]. Journal of Non-Newtonian Fluid Mechanics,1982,10:339-356.
[242]杨广军.申长雨,陈静波.聚合物挤出胀大的CAE分析[J].郑州工学院学报.1995.16(4)：38-44.
[243]涂志刚,柳和生,包忠诩.粘弹性聚合物熔体挤出胀大的三维计算机模拟[J].塑料科技.2003.153：15-19.
[244]张敏,孙胜,贾玉玺,等.聚合物共挤出过程的挤出胀大有限元分析[J].高分子材料科学与工程.2006,22(5)：36-40.
[245]Rutgers R P G, Mackley M R. The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE[J]. Journal of Non-Newtonian Fluid Mechanics, 2001,98:185-199.
[246]Beraudo C, Fortin A, Coupez T, et al. A finite element method for computing the flow of multi-mode viscoelastic fluids:comparison with experiments[J]. Journal of Non-Newtonian Fluid Mechanics,1998,75:1-23.
[247]Kalika D S, Denn M M. Wall slip and extrudate distortion in linear low density polyethylene[J]. Journal of Rheology,1987,31:815-834.
[248]Tanner R I. A theory of die-swell revisited[J]. Journal of Non-Newtonian Fluid Mechanics,2005, 129:85-87.
[249]Venet C, Vergnes B. Stress distribution around capillary die exit:an interpretation of the onset of sharkskin defect[J]. Journal of Non-Newtonian Fluid Mechanics,2000,93:117-132.
[250]Zhou H M, Li D Q. A numerical simulation of the filling stage in injection molding based on a surface model[J]. Advances in Polymer Technology,2001,20(2):125-131.
[251]申长雨。陈静波,刘春太,等.注射模充模过程CAE技术Ⅰ理论与算法[J].模具工业,2001(2)：51-56.
[252]耿铁,李德群,周华民,等.注塑充模过程中温度场的全三维数值模拟[J].化工学报,2005,56(9)：1612-1617.
[253]中长雨,王利霞,陈静波,等.注塑成型充填／后充填过程统一的可压缩流动分析[J].计算力学学报,2007,24(2)：159-165.
[254]Zhou H, Li D. Integrated simulation of the injection molding process with stereolithography molds[J]. The International Journal of Advanced Manufacturing Technology,2006,28:53-60.
[255]崔鹍,欧阳洁,郑素佩,等.三维熔体前沿界而的Level Set追踪[J].化工学报,2008,59(12)：3020-3026.
[256]Belytschko T, Liu W K, Moran B. Nonlinear finite elements for continua and structures[M]. New York:John Wiley & Sons,2000.
[257]Huynh B P. A numerical investigation of non-isothermal extrusion through annular dies[J]. International Journal of Engineering Science,1998,36(2):171-188.
[258]Pichelin E, Coupez T. A Taylor discontinuous Galerkin method for the thermal solution in 3D mold filling[J]. Computer Methods in Applied Mechanics and Engineering,1999,178:153-169.
[259]Zdanski P S B, Vaz Jr. M. Non-isothermal polymer melt flow in sudden expansions[J]. Journal of Non-Newtonian Fluid Mechanics,2009,161:42-47.
[2]Hatzikiriakos S G, Migler K B.Polymer Processing Instabilities:Control and Understanding[M]. New York:Marcel Dekker,2005.
[3]Zatloukal M. Martyn M T, Coates P D, et al. Modelling of viscoelastic coextrusion flows in multi-manifold flat dies[J]. Plastics, Rubbers and Composites,2004,33(7):305-309.
[4]Marchal T. Challenges of modelling the extrusion process[J]. Plastics. Rubber and Composites,2005, 34(5-6):265-270.
[5]Jaluria Y. Fluid Flow Phenomena in Materials Processing—The 2000 Freeman Scholar Lecture[J]. Journal of Fluids Engineering,2001,123:173-210.
[6]Tadmor Z, Gogos C G.Principles of polymer processing[M]. New Jersey:John Wiley & Sons,2006.
[7]Debbaut B. Rheology:from process to simulation[J]. Plastics, Rubber and Composites,2008,37(2-4): 166-173.
[8]廖正品.中国塑料工业(2008)[J].中国塑料,2009,23(5)：1-11.
[9]http://info.21cp.net/Info/Topic/201009/373096.htm.
[10]Walters K, Webster M F. The distinctive CFD challenges of computational rheology[J]. International Journal for Numerical Methods in Fluids,2003,43:577-596.
[11]Renardy M. Current issues in non-Newtonian flows:a mathematical perspective[J]. Journal of Non-Newtonian Fluid Mechanics.2000,90:243-259.
[12]de Gennes P G. Reptation of a polymer chain in the presence of fixed obstacles[J]. Journal of Chemical Physics,1971,5(2):572-579.
[13]Doi M, Edwards S F.The theory of polymer dynamics[M]. New York:Oxford University Press,1986.
[14]Laso M, Ottinger H C. Calculation of viscoelastic flow using molecular models:the CONNFFESSIT approach[J]. Journal of Non-Newtonian Fluid Mechanics,1993, (47):1-20.
[15]Keunings R. A survey of computational rheology [C]. ⅩⅢth International Congress on Rheology, Cambridge, UK,2000.
[16]McLeish T C B, Milner S T. Entangled Dynamics and Melt Flow of Branched Polymers[M]. Advances in Polymer Science. Berlin:Springer,1999,195-254.
[17]Tchesnokova M A, Molenaara J, Slotc J J M, et al. A constitutive model with moderate chain stretch for linear polymer melts[J]. Journal of Non-Newtonian Fluid Mechanics,2004, (123):185-199.
[18]McLeish T C B, Larson R G. Molecular constitutive equations for a class of branched polymers:The pom-pom polymer[J]. Journal of Rheology,1998,42(1):81-110.
[19]Verbeeten W M H, Peters G W M, Baaijens F P T. Differential constitutive equations for polymer melts:The extended Pom-Pom model [J]. Journal of Rheology,2001,45(4):823-844.
[20]Verbeeten W M H, Peters G W M, Baaijens F P T. Viscoelastic Analysis of Complex Polymer Melt Flows using the eXtended Pom-Pom model[J]. Journal of Non-Newtonian Fluid Mechanics,2002,108: 301-326.
[21]Clemeur N, Rutgers R P G, Debbaut B. On the evaluation of some differential formulations for the Pom-Pom constitutive model[J]. Rheologica Acta,2003,42(3):217-231.
[22]Clemeur N, Debbaut B. A pragmatic approach for deriving constitutive equations endowed with pom-pom attributes[J]. Rheologica Acta,2007,46:1187-1196.
[23]Tanner R I, Nasseri S. Simple constitutive models for linear and branched polymers[J]. Journal of Non-Newtonian Fluid Mechanics,2003,116:1-17.
[24]吴其晔,巫静安.高分子材料流变学[M].北京：高等教育出版社,2002.
[25]Schoonen J F M. Determination of Rheological Constitutive Equations using Complex Flows[D]: [Dissertation]. Eindhoven:Eindhoven University of Technology,1998.
[26]Collis M W, Lele A K, Mackley M R, et al. Constriction flows of monodisperse linear entangled polymers:Multiscale modeling and flow visualization J]. Journal of Rheology.2005,49(2):501-522.
[27]Verbeeten W M H, Peters G W M, Baaijens F P T. Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model[J]. Journal of Non-Newtonian Fluid Mechanics,2004, 117:73-84.
[28]Clemeur N, Rutgers R P G, Debbaut B. Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model[J]. Journal of Non-Newtonian Fluid Mechanics,2004,117:193-209.
[29]Whiteside B R, Spares R, Brown E C, et al. Optical imaging metrology for micromoulding cavity flows and products[J]. Plastics, Rubber and Composites,2008,37(2-4):57-66.
[30]Soulages J, Oliveira M S N, Sousa P C, et al. Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels[J]. Journal of Non-Newtonian Fluid Mechanics,2009,163(1-3):9-24.
[31]Bent J, Hutchings L R, Richards R W, et al. Neutron-Mapping Polymer Flow:Scattering, Flow Visualization,and Molecular Theory[J]. Science,2003.301:1691-1695.
[32]Tadmor Z. The evolution of polymer processing into macromolecular engineering and science[J]. Plastics, Rubbers and Composites,2004,33(1):3-4.
[33]Polynkin A, Pittman J F T, Sienz J. Industrial applications of gas assisted injection moulding: numerical prediction and experimental trials[J]. Plastics, Rubber and Composites,2005,34(5-6):236-246.
[34]Johnson L, Olley P, Coates P D. Gas assisted injection moulding Finite element modelling and experimental validation[J]. Plastics, Rubber and Composites,2000,29(1):31-37.
[35]Liu S-J, Chen W-K. Experimental investigation and numerical simulation of cooling process in water assisted injection moulded parts[J]. Plastics, Rubbers and Composites,2004,33(6):260-266.
[36]Zhao J, Mayes R H, Chen G, et al. Polymer micromould design and micromoulding process[J]. Plastics, Rubber and Composites,2003,32(6):240-247.
[37]韩哲文.高分子科学教程[M].上海：华东理工大学出版社,2008.
[38]马德柱,何平笙,徐种德,等.高聚物的结构与性能[M].北京：科学出版社,1995.
[39]何曼君,张红东,陈维孝,等.高分子物理[M].上海：复旦大学出版社,2006.
[40]许元泽.高分子结构流变学[M].成都：四川教育出版社,1988.
[41]北川浩,铃木谦一郎.鹿政理译.吸附的基础与设计[M].北京：化学工业出版社,1983.
[42]Achilleos E, Georgiou G C. On numerical Simulations of Polymer Extrusion Instabilities[J]. Applied Rheology,2002(12):88-104.
[43]Georgiou G C, Vlassopoulos D. On the stability of the simple shear flow of a Johnson-Segalman fluid[J]. Journal of Non-Newtonian Fluid Mechanics,1998,75:77-97.
[44]Han C D.Rheology and Processing of Polymeric Materials[M]. New York:Oxford University Press, 2007.
[45]Bird R B, Armstrong R C, Hassager O.Dynamics of Polymeric Liquids[M]. Fluid Mechanics. New York:John Wiley & Sons,1987.
[46]Luo X-L. Numerical simulation of Weissenberg phenomena-the rod-climbing of viscoelastic fluids[J]. Computer Methods in Applied Mechanics and Engineering,1999,180:393-412.
[47]Tanner R I. Engineering Rheology[M]. New York:Oxford University Press,2000.
[48]Brochard F, de Gennes P G. Shear-dependent slippage at a polymer/solid interface[J]. Langmuir,1992, 8:3033-3037.
[49]Wang S Q. Molecular Transitions and Dynamics at Polymer/Wall Interfaces:Origins of Flow Instabilities and Wall Slip[M]. Advances in Polymer Science. Berlin:Springer-Verlag,1999.
[50]Wang S Q, Drda P. Molecular instabilities in capillary flow of polymer melts:interfacial stick-slip transition, wall slip and extrudate distortion[J]. Macromolecular Chemistry and Physics,1997.198: 673-701.
[51]Drda P P, Wang S Q. Stick-slip transition at polymer melt/solid interfaces[J]. Physical Review Letters, 1995,75(14):2698-2701.
[52]廖华勇,范毓润.聚合物熔体壁面滑移的流变研究[J].高等学校化学学报.2006,27(9)：1755-1761.
[53]吴其晔,巫静安,温学明,等.聚乙烯熔体的挤出畸变与非线性粘弹性的关系[J].中国塑料,2004,18(7)：40-44.
[54]Nassehi V.Practical Aspects of Finite Element Modelling of Polymer Processing[M]. New York:John Wiley & Sons,2002.
[55]Li X K, Duan Q L, Han X H, et al. Adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method for injection molding process[J]. International Journal for Numerical Methods in Engineering,2008,73(8):1153-1180.
[56]http://www.mate.tue.nl/-hulsen.
[57]Moldflow软件培训资料.上海：Moldflow公司,2007.
[58]Baaijens F P T, Hulsen M A, Anderson P D. The Use of Mixed Finite Element Methods for Viscoelastic Fluid Flow Analysis[M]. In:Stein E, Borst R e d. Hughes T J R (eds) Encyclopedia Of Computational Mechanics. New York:John Wiley & Sons,2004;481-498.
[59]Kotelyanskii M, Theodorou D N. Simulation Methods for Polymers. New York:Marcel Dekker,2004.
[60]Burmenko I. Brownian Dynamics Simulations of Fine-Scale Molecular Models[D]:[Dissertation]. Massachusetts Institute of Technology,2005.
[61]Bajaj M, Bhat P P, Prakash J R, et al. Multiscale simulation of viscoelastic free surface flows[J]. Journal of Non-Newtonian Fluid Mechanics.2006,140:87-107.
[62]Halin P, Lielens R, Keunings R, et al. The Lagrangian partical method for macroscopic and micro-macro viscoelastic flow computations[J]. Journal of Non-Newtonian Fluid Mechanics,1998,79: 387-403.
[63]张小华,欧阳洁,孔倩.聚合物流动的多尺度模拟[J].化工学报,2007,58(8)：1897-1904.
[64]Laso M, Picasso M, Ottinger H C.2-D Time-Dependent Viscoelastic Flow Calculations Using CONNFFESSIT[J]. AIChE Journal,1997,43(4):877-892.
[65]Feigl K, Laso M, Ottinger H C. CONNFFESSIT Approach for Solving a Two-Dimensional Viscoelastic Fluid Problem[J]. Macromolecules,1995,28(9):3261-3274.
[66]Hulsen M A, van Heel A P G, van den Brule B H A A. Simulation of viscoelastic flows using Brownian configuration fields[J]. Journal of Non-Newtonian Fluid Mechanics,1997, (70):79-101.
[67]Bajaj M, Bhat P P, Prakash J R, et al. Micro-Macro simulation of viscoelastic free surface flows using the Brownian configuration fields method[C]. Proceeding ⅩⅣth International Congress on Rheology, Seoul, Korea,2004.
[68]Ramirez J, Laso M. Size reduction methods for the implicit time-dependent simulation of micro-macro viscoelastic flow problems[J]. Journal of Non-Newtonian Fluid Mechanics,2005,127: 41-49.
[69]Peters E A J F, van Heel A P G, Hulsen M A, et al. Generalization of the deformation field method to simulate advanced reptation models in complex flow[J]. Journal of Rheology,2000,44(4):811-829.
[70]Gallez X, Halin P, Lielens G, et al. The adaptive Lagrangian particle method for macroscopic and micro-macro computations of time-dependent viscoelastic[J]. Computer Methods in Applied Mechanics and Engineering,1999,180:345-364.
[71]Zhou Q, Akhavan R. A comparison of FENE and FENE-P dumbbell and chain models in turbulent flow[J]. Journal of Non-Newtonian Fluid Mechanics,2003,109:115-155.
[72]Herrchen M, Ottinger H C. A detailed comparison of various FENE dumbbell models[J]. Journal of Non-Newtonian Fluid Mechanics,1997,68:17-42.
[73]Ghosh I, Joo Y L. McKinley G H, et al. A new model for dilute polymer solutions in flows with strong extensional components [J]. Journal of Rheology,2002,46(5):1057-1089.
[74]Rakshit A, Picu R C. Coarse-grained model of entangled polymer melts in non-equilibrium[J]. Rheologica Acta,2008,47:1039-1048.
[75]Keunings R. A survey of computational rheology[C]. ⅩⅢth International Congress on Rheology, Cambridge, UK,2000.
[76]Ottinger H C, van den Brule B H A A, Hulsen M A. Brownian configuration fields and variance reduced CONNFFESSIT[J]. Journal of Non-Newtonian Fluid Mechanics,1997, (70):255-261.
[77]Li X K, Han X H. An iterative stabilized fractional step algorithm for numerical solution of incompressible N-S equations[J]. International Journal for Numerical Methods in Fluids,2005,49: 395-416.
[78]Onate E. A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation[J]. Computer Methods in Applied Mechanics and Engineering,2000,182:355-370.
[79]Han X H, Li X K. An iterative stabilized CNBS-CG scheme for incompressible non-isothermal non-Newtonian fluid flow[J]. International Journal of Heat and Mass Transfer.2007,50:847-856.
[80]Osswald T A, Hernandez-Ortiz J P.Polymer processing:modeling and simulation[M]. Munich: Hanser,2006.
[81]韩先洪.成型充填过程中非等温非牛顿粘弹性流动数值模拟[D]：[博士论文].大连：大连理工大学.2007.
[82]Bird R B, Wiest. J M. Constitutive equations for polymeric liquids. In Annual review of fluid mechanics[J]. Annual review of fluid mechanics,1995,27:169-193.
[83]古大治.高分子流体动力学[M].现代高分子科学丛书.成都：四川教育出版社,1988.
[84]Thien N P, Tanner R I. A new constitutive equation drived from network theory[J]. Journal of Non-Newtonian Fluid Mechanics,1977,2::353-365.
[85]Giesekus H. A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility[J]. Journal of Non-Newtonian Fluid Mechanics,1982,11: 69-109.
[86]Blackwell R J, McLeish T C B, Harlen O G. Molecular Drag-Strain Coupling in Branched Polymer Melts[J]. Journal of Rheology,2000,44(1):121-136.
[87]Inkson N J, McLeish T C B, Harlen O G, et al. Predicting low density polyethylene melt rheology in elongational and shear flows with"pom-pom" constitutive equations[J]. Journal of Rheology,1999,43(4): 873-896.
[88]Tanner R I. On the congruence of some network and pom-pom models[J]. Korea-Australia Rheology Journal,2006,18(1):9-14.
[89]Larson R G.Constitutive Equations for Polymer Melts and Solutions[M]. Boston:Butterworths,1988.
[90]Wagner M H, Kheirandish S, Koyama K, et al. Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory[J]. Rheologica Acta,2005,44:235-243.
[91]Xue S-C, Tanner R I, Phan-Thien N. Numerical modelling of transient viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,2004,123:33-58.
[92]Bonito A, Picasso M, Laso M. Numerical simulation of 3D viscoelastic flows with free surfaces [J]. Journal of Computational Physics,2006,215:691-716.
[93]Aboubacar M, Aguayo J P, Phillips P M, et al. Modelling pom-pom type models with high-order finite volume schemes[J]. Journal of Non-Newtonian Fluid Mechanics,2005,126:207-220.
[94]Tsukanov I, Shapiro V, Zhang S. A meshfree method for incompressible fluid dynamics problems[J]. International Journal for Numerical Methods in Engineering,2003,58:127-158.
[95]Zhang X K, Kwon K C, Youn S K. Least-squares meshfree method for incompressible Navier-Stokes problems[J]. International Journal for Numerical Methods in Fluids,2004,46:263-288.
[96]Liu G R, Wu Y L, Ding H. Meshfree weak-strong (MWS) form method and its application to incompressible flow problems[J]. International Journal for Numerical Methods in Fluids,2004,46: 1025-1047.
[97]Onate E, Idelsohn S R, Zienkiewicz O C A finite point method in computational mechanics. Applications to convective transport and fluid flow[J]. International Journal for Numerical Methods in Engineering,1996,39:3839-3866.
[98]Nadau L, Sequeira A. Numerical simulations of shear dependent viscoelastic flows with a combined finite element-finite volume method[J]. Computers and Mathematics with Applications,2007,53: 547-568.
[99]Webster M F, Tamaddon-Jahromi H R, Aboubacar M. Transient viscoelastic flows in planar contractions [J]. Journal of Non-Newtonian Fluid Mechanics,2004,118:83-101.
[100]Taliadorou E, Georgiou G C, Alexandrou A N. A two-dimensional numerical study of the stick-slip extrusion instability [J]. Journal of Non-Newtonian Fluid Mechanics,2007,146:30-44.
[101]Zhang L T, Wagner G J, Liu W K. Modelling and simulation of fluid structure interaction by meshfree and FEM[J]. Communications in Numerical Methods in Engineering,2003.19:615-621.
[102]Chung T J.Computational fluid dynamics[M]. Cambridge:Cambridge University Press 2002.
[103]Ferziger J H, Peric M.Computational Methods for Fluid Dynamics[M]. Berlin:Springer,2002.
[104]Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J]. International Journal for Numerical Methods in Engineering,1994,37:229-256.
[105]Belytschko T, Krongauz Y, Organ D, et al. Meshless methods:an overview and recent developments[J]. Computer Methods in Applied Mechanics and Engineering,1996,139:3-47.
[106]Liu G R, Liu M B.Smoothed Particle Hydrodynamics:A Meshfree Particle Method[M]. Singapore: World Scientific,2003.
[107]张雄,刘岩.无网格法[M].北京：清华大学出版社.2004.
[108]Zienkiewicz O C, Heinrich J C, Huyakorn P S, et al. An upwind finite element scheme for two dimensional convective transport equations[J]. International Journal for Numerical Methods in Engineering, 1977,11:131-144.
[109]Nguyen H, Reynen J. A space-time least-squares finite element scheme for advection—diffusion equations[J]. Computer Methods in Applied Mechanics and Engineering,1984,42(3):331-342.
[110]Hughes T J R, Franca L P, Hulbert G M. A new finite element formulation for computational fluid dynamics. Ⅷ. The Galerkin/least-squares method for advection-diffusion equations[J]. Computer Methods in Applied Mechanics and Engineering,1989,73:173-189.
[111]Masud A, Hughes T J R. A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems[J]. Computer Methods in Applied Mechanics and Engineering,1997,146(1-2):91-126.
[112]Shakib F, Hughes T J R. A new finite element formulation for computational fluid dynamics. IX. Fourier analysis of space-time Galerkin/least-squares algorithms[J]. Computer Methods in Applied Mechanics and Engineering,1991,87(1):35-58.
[113]Hughes T J R, Feijoo G R, Mazzei L, et al. The variational multiscale method-a paradigm for computational mechanics[J]. Computer Methods in Applied Mechanics and Engineering,1998,166:3-24.
[114]Brooks A N, Hughes T J R. Streamline upwind/Petrov-Galerkin methods for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering,1982,32:199-259.
[115]Donea J. A Taylor-Galerkin method for convective transport problems[J]. International Journal for Numerical Methods in Fluids,1984,20:101-119.
[116]Donea J, Huerta A.Finite element methods for flow problems[M]. Chichester:John Wiley & Sons, 2003.
[117]Zienkiewicz O C, Taylor R L.The Finite Element Method[M]. Fluid Dynamics. Stoneham: Butterworth Heinemann,2000.
[118]Zienkiewicz O C, Codina R. A general algorithm for compressible and incompressible flow-part Ⅰ: The split, characteristic-based scheme[J]. International Journal for Numerical Methods in Fluids,1995,20: 869-885.
[119]Mutlu I, Townsend P, Webster M F. Simulation of cable-coating viscoelastic flows with coupled and decoupled schemes[J]. Journal of Non-Newtonian Fluid Mechanics,1998,74:1-23.
[120]Nithiarasu P. A fully explicit characteristic based split (CBS) scheme for viscoelastic flow calculations[J]. International Journal for Numerical Methods in Engineering,2004,60:949-978.
[121]Duan Q L, Li X K. An ALE based iterative CBS algorithm for non-isothermal non-Newtonian flow with adaptive coupled finite element and meshfree method[J]. Computer Methods in Applied Mechanics and Engineering,2007,196(49-52):4911-4933.
[122]Chorin A J. A numerical method for solving incompressible viscous flow problems[J]. Journal of Computational Physics,1967,2:12-26.
[123]Temam R. Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaries Ⅱ[J]. Archives for Rational Mechanics and Analysis,1969,33:377-385.
[124]Guermond J-L, Quartapelle L. Calculation of incompressible viscous flow by an unconditionally stable projection FEM[J]. Journal of Computational Physics,1997,132(1):12-33.
[125]Guermond J-L, Quartapelle L. On stability and convergence of projection methods based on pressure Poisson equation[J]. International Journal for Numerical Methods in Fluids,1998,26(9):1039-1053.
[126]Kim J M. Kim C, Kim J H, et al. High-resolution finite element simulation of 4:1 planar contraction flow of viscoelastic fluid[J]. Journal of Non-Newtonian Fluid Mechanics,2005,129:23-37.
[127]韩先洪,李锡夔.高黏性流动有限元模拟的迭代稳定分步算法[J].力学学报,2006,38(1)：16-24.
[128]Laval H, Quartapelle L. A fractional-step Taylor-Galerkin method for unsteady incompressible flow[J]. International Journal for Numerical Methods in Fluids,1990,11:501-513.
[129]Jahromi H R T, Ding D P, Webster M F, et al. A Taylor-Galerkin finite element method for non-Newtonian flows[J]. International Journal for Numerical Methods in Engineering,1992,34: 741-757.
[130]Codina R. Pressure stability in fractional step finite element methods for incompressible flows [J]. Journal of Computational Physics,2001,170:112-140.
[131]Fortin M, Fortin A. A new approach for the fern simulation of viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1989,32:295-310.
[132]Li X K, Duan Q L. Meshfree iterative stabilized Taylor-Galerkin and characteristic-based split (CBS) algorithms for incompressible N-S equations[J]. Computer Methods in Applied Mechanics and Engineering,2006,195:6125-6145.
[133]Baaijens F P T. Mixed finite element methods for viscoelastic flow analysis:A review[J]. Journal of Non-Newtonian Fluid Mechanics,1998.79:361-386.
[134]Brooks A N, Hughes T J R. Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering,1982,32(1-3):199-259.
[135]Marchal J M, Crochet M J. A new mixed finite element for calculating viscoelastic flow[J]. Journal of Non-Newtonian Fluid Mechanics,1987,26:77-114.
[136]Fortin M, Fortin A. A new approach for the fem simulation of viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1989,32:295-310.
[137]King R C, Apelian M R, Armstrong R C, et al. Numerically stable finite element techniques for viscoelastic calculations in smooth and singular domains[J]. Journal of Non-Newtonian Fluid Mechanics, 1988,29:147-216.
[138]Perera M G N, Walters K. Long-range memory effects in flows involving abrupt changes in geometry, Part Ⅰ. Flows associated with L-shaped and T-shaped geometries[J]. Journal of Non-Newtonian Fluid Mechanics,1977.2(2):49-81.
[139]Rajagopalan D, Armstrong R C, Brown R A. Finite element methods for calculation of steady viscoelastic flow using constitutive equations with a Newtonian viscosity[J]. Journal of Non-Newtonian Fluid Mechanics,1990,36(159-192)
[140]Guenette R, Fortin M. A new mixed finite element method for computing viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1995,60:27-52.
[141]Fortin A, Guenette R, Pierre R. On the discrete EVSS method[J]. Computer Methods in Applied Mechanics and Engineering,2000,189:121-139.
[142]Sun J, Smith M D, Armstrong R C, et al. Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method:DAVSS-G/DG[J]. Journal of Non-Newtonian Fluid Mechanics,1999,86:281-307.
[143]Hua X, Ding Z, Lee L J. Simulation of 2D transient viscoelastic flow using the CONNFFESSIT approach[J]. Journal of Non-Newtonian Fluid Mechanics,2005,127:107-122.
[144]Grillet A M, Bogaerds A C B, Peters G W M, et al. Numerical analysis of flow mark surface defects in injection molding flow[J]. Journal of Rheology,2002,46(3):651-669.
[145]Aboubacar M, Webster M F. Development of an optimal hybrid finite volume/element method for viscoelastic flows[J]. International Journal for Numerical Methods in Fluids,2003,41:1147-1172.
[146]Wapperom P, Webster M F. A second-order hybrid finiteelement/volume method for viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics,1998,79:405-431.
[147]Wapperom P, Webster M F. Simulation for viscoelastic flow by a finite volume/element method[J]. Computer Methods in Applied Mechanics and Engineering,1999,180:281-304.
[148]Belytschko T, Organ D, Krongauz Y. A coupled finite element-element-free Galerkin method[J]. Computational Mechanics,1995,17:186-195.
[149]Peters G W M, Baaijens F P T. Modelling of non-isothermal viscoelastic flows [J]. Journal of Non-Newtonian Fluid Mechanics,1997,68:205-224.
[150]Massarotti N, Nithiarasu P, Zienkiewicz O C. Characteristic-based-split (CBS) algorithm for incompressible flow problems with heat transfer[J]. International Journal of Numerical Methods for Heat& Fluid Flow,1998.8(8):969-990.
[151]Nithiarasu P, Mathur J S, Weatherill N P, et al. Three-dimensional incompressible flow calculations using the characteristic based split (CBS) scheme[J]. International Journal for Numerical Methods in Fluids, 2004,44:1207-1229.
[152]Zienkiewicz O C, Qu S, Taylor R L. The patch test for mixed formulations[J]. International Journal for Numerical Methods in Engineering,1986,23:1873-1883.
[153]Onate E. Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems[J]. Computer Methods in Applied Mechanics and Engineering,1998,151(1-2): 233-265.
[154]Hughes T J R. Multiscale phenomena:Green's functions, the Dirichlet-to-Neumann formulation. subgrid scale models, bubbles and the origins of stabilized methods[J]. Computer Methods in Applied Mechanics and Engineering,1995,127(1-4):387-401.
[155]Hughes T J R, Feijoo G R, Mazzei L, et al. The variational multiscale method-a paradigm for computational mechanics[J]. Computer Methods in Applied Mechanics and Engineering,1998,166(1-2): 3-24.
[156]Hughes T J R, Scovazzi G, Franca L P. Multiscale and stabilized methods[M]. In:Stein E, Borst R, Hughes T J R (eds) Encyclopedia Of Computational Mechanics. Chichester:John Wiley & Sons, 2004;5-60.
[157]Fattal R, Kupferman R. Constitutive laws for the matrix-logarithm of the conformation tensor[J]. Journal of Non-Newtonian Fluid Mechanics,2004,123:281-285.
[158]Afonso A, Oliveira P J, Pinho F T, et al. The log-conformation tensor approach in the finite-volume method frame work[J]. Journal of Non-Newtonian Fluid Mechanics,2009,157:55-65.
[159]Guenette R, Fortin A, Kane A, et al. An adaptive remeshing strategy for viscoelastic fluid flow simulations[J]. Journal of Non-Newtonian Fluid Mechanics,2008.153:34-45.
[160]Coronado O M, Arora D, Behr M, et al. A simple method for simulating general viscoelastic fluid flows with an alternate log-conformation formulation[J]. Journal of Non-Newtonian Fluid Mechanics,2007, 147:189-199.
[161]Sussman M. Puckett E G. A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows[J]. Journal of Computational Physics,2000, (162): 301-337.
[162]Devals C, Heniche M, Bertrand F, et al. A finite element strategy for the solution of interface tracking problems[J]. International Journal for Numerical Methods in Fluids,2005,49:1305-1327.
[163]Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics,1981,39:201-225.
[164]曹伟.王蕊.申长雨.塑料熔体在注塑模中的三维流动分析[J].化工学报,2004.55(9)：78-81.
[165]Luoma J A, Voller V R. An explicit scheme for tracking the filling front during polymer mold filling[J]. Applied Mathematical Modelling,2000,24:575-590.
[166]Osher S, Sethian J A. Fronts propagating with curvature dependent speed:Algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics,1988,79:12-49.
[167]Osher S, Fedkiw P. Level set methods:an overview and some recent results.[J]. Journal of Computational Physics,2001,169:463-502.
[168]Lin C-L, Lee H, Lee T, et al. A level set characteristic Galerkin finite element method for free surface flows[J]. International Journal for Numerical Methods in Fluids,2005,49:521-547.
[169]Holm E J, Langtangen H P. A unified finite element model for the injection molding process[J]. Computer Methods in Applied Mechanics and Engineering,1999,178:413-429.
[170]Yang B X, Ouyang J, Liu C T, et al. Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method[J]. Chinese Journal of Chemical Engineering,2010,18(4): 600-608.
[171]Yang B, Ouyang J, Li Q, et al. Modeling and simulation of the viscoelastic fluid mold filling process by level set method[J]. Journal of Non-Newtonian Fluid Mechanics,2010,165:1275-1293.
[172]Hayashi M, Hatanaka K, Kawahara M. Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods.[J]. International Journal for Numerical Methods in Fluids,1991,13:805-840.
[173]Zhang J, Khayat R E. A Lagrangian boundary element approach to transient three-dimensional free surface flow in thin cavities[J]. International Journal for Numerical Methods in Fluids,2001,37:399-418.
[174]Feng Y T, Perie D. A time-adaptive space-time finite element method for incompressible Lagrangian flows with free surfaces:computational issues[J]. Computer Methods in Applied Mechanics and Engineering,2000,190:499-518.
[175]Khayat R E, Elsin W, Kim K. An adaptive boundary element approach to transient free surface flow as applied to injection molding[J]. International Journal for Numerical Methods in Fluids,2000,33: 847-868.
[176]Khayat R E, Plaskos C, Genouvrier D. An adaptive boundary-element approach for 3D transient free surface cavity flow, as applied to polymer processing[J]. International Journal for Numerical Methods in Engineering,2001,50:1347-1368.
[177]Fang J, Owens R G, Tacher L, et al. A numerical study of the SPH method for simulating transient viscoelastic free surface flows[J]. Journal of Non-Newtonian Fluid Mechanics,2006,139:68-84.
[178]Kulasegaram S, Bonet J, Lewis R W, et al. High pressure die casting simulation using a Lagrangian particle method[J]. Communications in Numerical Methods in Engineering,2003,19:679-687.
[179]Idelsohn S R, Onate E, Pin F D. The particle finite element method:a powerful tool to solve incompressible flows with free-surfaces and breaking waves[J]. International Journal for Numerical Methods in Engineering,2004,61:964-989.
[180]Onate E, Garcia J, Idelsohn S R, et al. Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches[J]. Computer Methods in Applied Mechanics and Engineering,2006,195:3001-3037.
[181]Noh W F. CEL:a time-dependent two-space-dimensional coupled Eulerian-Lagrangian code[J]. Methods in Computational Physics,1964,3:117-179.
[182]Hirt C, Amsden A, Cook J. An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics,1974,14:227-253.
[183]Hughes T J R, Liu W K, Zimmerman T K. Lagrangian-Eulerian finite element formulation for viscous flows[J]. Computer Methods in Applied Mechanics and Engineering,1981,29:329-349.
[184]Belytschko T, Flanagan D P, Kennedy J M. Finite element methods with user-controlled meshes for fluid-structure interaction[J]. Computer Methods in Applied Mechanics and Engineering,1982,30: 669-688.
[185]Liu W K, Chang H, Chen J S, et al. Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua[J]. Computer Methods in Applied Mechanics and Engineering,1988,68:259-310.
[186]Braess H, Wriggers P. Arbitrary Lagrangian Eulerian finite element analysis of free surface flow[J]. Computer Methods in Applied Mechanics and Engineering,2000,190:95-109.
[187]Gadala M S. Recent trends in ALE formulation and its applications in solid mechanics[J]. Computer Methods in Applied Mechanics and Engineering,2004,193:4247-4275.
[188]Lewis R W, Navti S E, Taylor C. A mixed Lagrangian-Eulerian approach to modelling fluid flow during mould filling[J]. International Journal for Numerical Methods in Fluids,1997,25:931-952.
[189]韩先洪,李锡夔.成型充填过程的ALE有限元模拟[J].应用力学学报,2005,22(3)：440-445.
[190]韩先洪,李锡夔.充填过程ALE自由面追踪及网格生成方法[J].大连理工大学学报,2005,45(5)：633-639.
[191]Yamaguchi H, Mishima A, Yasumoto T, et al. An arbitrary Lagrangian-Eulerian approach for simulating stratified viscoelastic fluids[J]. Journal of Non-Newtonian Fluid Mechanics,2000,89:251-272.
[192]Ganvir V, Lele A, Thaokar R, et al. Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156(1-2):21-28.
[193]关振群.宋超.顾元宪.等.有限元网格生成方法研究的新进展[J].计算机辅助设计与图形学学报.2003.15(1-14)
[194]Lewis R W, Navti S E, Taylor C. A mixed Lagrangian-Eulerian approach to modelling fluid flow during mould filling[J]. International Journal for Numerical Methods in Fluids,1997,25:931-952.
[195]Bathe K J.Finite element procedure[M]. New Jersey:Prentice-Hall,1996.
[196]Brezzi F, Fortin M.Mixed and Hybrid Finite Element methods[M]. Series in Computational Mechanics. New York:Springer,1991.
[197]Lee K, Mackley M R. The significance of slip in matching polyethylene processing data with numerical simulation[J]. Journal of Non-Newtonian Fluid Mechanics.2000.94:159-177.
[198]Larson R G.The structure and rheology of complex fluids[M]. New York:Oxford University Press, 1999.
[199]Ferry J D.Viscoelastic properties of polymers[M]. New York:John Wiley & Sons,1986.
[200]周持兴.聚合物流变学实验与应用[M].上海：上海交通大学出版社,2003.
[201]颜家华,彭玉成.聚合物熔体本构关系的研究进展[J].力学进展,1998,28(2)：218-226.
[202]Ottinger H C. Capitalizing on nonequilibrium thermodynamics:branched polymers[C]. Proceedings of the ⅩⅢth International Congress on Rheology, Cambridge, U.K..2000.
[203]Inkson N J, Phillips T N. Unphysical phenomena associated with the extended pom-pom model in steady flow[J]. Journal of Non-Newtonian Fluid Mechanics,2007,145:92-101.
[204]Wang W, Li X K, Han X H. A numerical study of constitutive models endowed with Pom-Pom molecular attributes[J]. Journal of Non-Newtonian Fluid Mechanics.2010,165(21-22):1480-1493.
[205]Rubio P, Bastian H, Wagner. M H. The molecular stress function model for polymer melts with dissipative constraint release[J]. Journal of Rheology,2001
[206]Marrucci G, Greco F, Ianniruberto. G. Integral and differential constitutive equations for entangled polymers with simple versions of CCR and force balance on entanglements.[J]. Rheologica Acta,2001, 40(2):98-103.
[207]Feigl K, Ottinger H C. A new class of stochastic simulation models for polymer stress calculation[J]. Journal of Chemical Physics,1998,109:815-826.
[208]Wagner M H, P. Rubio, Bastian H. The Molecular Stress Function Model for Polydisperse Polymer Melts with Dissipative Convective Constraint ReIease[J]. Journal of Rheology,2001,45:1387-1412.
[209]Wagner M H. Modeling nonlinear rheology of polydisperse polymer melts[J]. International Journal of Applied Mechanics and Engineering,2005,11(2):255-267.
[210]韩式方.非牛顿流体本构方程和计算解析理论[M].北京：科学出版社,2000.
[211]宋名实,杨志洪.高分子熔体和浓溶液流变性能的研究[J].化学物理学报,2000,13(6)：699-720.
[212]朱克勤.非牛顿流体力学研究的若干进展[J].力学与实践,2006,28(4)：1-8.
[213]周持兴.加工流场中高聚物复杂流体内部结构的唯象定律[J].高分子材料科学与工程.1999,15(5)：1-4.
[214]Fan X J. Molecular models and flow calculations. Ⅱ. Simulation of steady planar flow[J]. Acta Mechanic Sinica,1989,5(3):216-226.
[215]范西俊.定常流动中聚合物分子的取向[J].力学学报,1991.23：400-410.
[2]6]方建农.范西俊.聚合物分子模型的Brown动力学模拟[J].力学进展,1999.29(1)：112-120.
[217]王克俭,周持兴.考虑壁面滑移的Z-W流变模型及其应用[J].高分子通报.2003(1)：8-17.
[218]Ngamaramvaranggul V, Webster M F. Viscoelastic simulations of stick-slip and die-swell flows[J]. International Journal for Numerical Methods in Fluids,2001,36:539-595.
[219]Bishko G. McLeish T C B, Harlen O G. Theoretical Molecular Rheology of Branched Polymers in Simple and Complex Flows:The Pom-Pom Model[J]. Physical Review Letters,1997,79(12):2352-2355.
[220]Bishko G B, Harlen O G, McLeish T C B, et al. Numerical simulation of the transient flow of branched polymer melts through a planar contraction using the 'pom-pom' model [J]. Journal of Non-Newtonian Fluid Mechanics,1999,82(2-3):255-273.
[221]Ottinger H C. Thermodynamic admissibility of the pompon model for branched polymers[J]. Rheologica Acta,2001,40:317-321.
[222]Inkson N J, Phillips T N, van Os R G M. Numerical simulation of flow past a cylinder using models of XPP type[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156:7-20.
[223]Baltussen M G H M, Verbeeten W M H, Bogaerds A C B, et al. Anisotropy parameter restrictions for the eXtended Pom-Pom model[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156:7-20.
[224]Aguayo J P, Tamaddon-Jahromi H R, Webster M F. Extensional response of the pom-pom model through planar contraction flows for branched polymer melts[J]. Journal of Non-Newtonian Fluid Mechanics,2006,134:105-126.
[225]Han X H, Li X K. A mixed finite element scheme for modelling of XPP viscoelastic flows[J]. Acta Mechanica Sinica,2008,24(6):671-680.
[226]Li X K, Han X H. Numerical modeling of viscoelastic flows using equal low-order finite elements[J]. Computer Methods in Applied Mechanics and Engineering,2010,199:570-581.
[227]Pivokonsky R, Zatloukalb M, Filip P, et al. Rheological characterization and modeling of linear and branched metallocene polypropylenes prepared by reactive processing[J]. Journal of Non-Newtonian Fluid Mechanics,2009,156:1-6.
[228]Pivokonsky R, Zatloukal M, Filip P. On the predictive/fitting capabilities of the advanced differential constitutive equations for linear polyethylene melts[J]. Journal of Non-Newtonian Fluid Mechanics,2008,150:56-64.
[229]Piau J M, Agassant J F.Rheology for Polymer Melt Processing[M]. Amsterdam:Elsevier,1996.
[230]Baaijens F P T. An iterative solver for the DEVSS/DG method with application to smooth and non-smooth flows of the upper convected Maxwell fluid[J]. Journal of Non-Newtonian Fluid Mechanics. 1998(75):119-138.
[231]Chorin A J. Numerical solution of the Navier-Stokes equations[J]. Mathematics of Computation, 1968,22:742-762.
[232]Temam R. Sur l'approximation de la solution des equations de Navier-Stokes par la me thode des pas fractionnaries Ⅱ[J]. Archives for Rational Mechanics and Analysis,1969,33:377-385.
[233]Comini G, Guidice S D. Finite element solution of incompressible Navier-Stokes equations[J]. Numerical Heat Transfer, Part A,1972,5:463-478.
[234]Donea J, Giuliani S, Laval H, et al. Finite element solution of the unsteady Navier-Stokes equations by a fractional step method[J]. Computer Methods in Applied Mechanics and Engineering,1982,30: 53-73.
[235]Aguayo J P, Phillips P M, Phillips T N, et al. The numerical prediction of planar viscoelastic contraction flows using the pom-pom model and higher-order finite volume schemes[J]. Journal of Computational Physics,2007,220:586-611.
[236]Li X K, Han X H, Pastor M. An iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics[J]. Computer Methods in Applied Mechanics and Engineering,2003, 192:3845-3859.
[237]段庆林.成型充填过程中非等温非牛顿粘性流动的ALE有限元与无网格自适应耦合模拟[D]：[博士学位].大连：大连理工大学,2007.
[238]Alves M A, Oliveira P J. Pinho F T. Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions[J]. Journal of Non-Newtonian Fluid Mechanics,2003,110:45-75.
[239]Tanner R I. A theory of die-swell[J]. Journal of Polymer Science Part A,1970,8:2067-2078.
[240]Crochet M J, Keunings R. Die swell of a Maxwell fluid numerical prediction[J]. Journal of Non-Newtonian Fluid Mechanics,1980,7:199-212.
[241]Crochet M J, Keunings R. Finite element analysis of die swell of a highly elastic fluid[J]. Journal of Non-Newtonian Fluid Mechanics,1982,10:339-356.
[242]杨广军.申长雨,陈静波.聚合物挤出胀大的CAE分析[J].郑州工学院学报.1995.16(4)：38-44.
[243]涂志刚,柳和生,包忠诩.粘弹性聚合物熔体挤出胀大的三维计算机模拟[J].塑料科技.2003.153：15-19.
[244]张敏,孙胜,贾玉玺,等.聚合物共挤出过程的挤出胀大有限元分析[J].高分子材料科学与工程.2006,22(5)：36-40.
[245]Rutgers R P G, Mackley M R. The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE[J]. Journal of Non-Newtonian Fluid Mechanics, 2001,98:185-199.
[246]Beraudo C, Fortin A, Coupez T, et al. A finite element method for computing the flow of multi-mode viscoelastic fluids:comparison with experiments[J]. Journal of Non-Newtonian Fluid Mechanics,1998,75:1-23.
[247]Kalika D S, Denn M M. Wall slip and extrudate distortion in linear low density polyethylene[J]. Journal of Rheology,1987,31:815-834.
[248]Tanner R I. A theory of die-swell revisited[J]. Journal of Non-Newtonian Fluid Mechanics,2005, 129:85-87.
[249]Venet C, Vergnes B. Stress distribution around capillary die exit:an interpretation of the onset of sharkskin defect[J]. Journal of Non-Newtonian Fluid Mechanics,2000,93:117-132.
[250]Zhou H M, Li D Q. A numerical simulation of the filling stage in injection molding based on a surface model[J]. Advances in Polymer Technology,2001,20(2):125-131.
[251]申长雨。陈静波,刘春太,等.注射模充模过程CAE技术Ⅰ理论与算法[J].模具工业,2001(2)：51-56.
[252]耿铁,李德群,周华民,等.注塑充模过程中温度场的全三维数值模拟[J].化工学报,2005,56(9)：1612-1617.
[253]中长雨,王利霞,陈静波,等.注塑成型充填／后充填过程统一的可压缩流动分析[J].计算力学学报,2007,24(2)：159-165.
[254]Zhou H, Li D. Integrated simulation of the injection molding process with stereolithography molds[J]. The International Journal of Advanced Manufacturing Technology,2006,28:53-60.
[255]崔鹍,欧阳洁,郑素佩,等.三维熔体前沿界而的Level Set追踪[J].化工学报,2008,59(12)：3020-3026.
[256]Belytschko T, Liu W K, Moran B. Nonlinear finite elements for continua and structures[M]. New York:John Wiley & Sons,2000.
[257]Huynh B P. A numerical investigation of non-isothermal extrusion through annular dies[J]. International Journal of Engineering Science,1998,36(2):171-188.
[258]Pichelin E, Coupez T. A Taylor discontinuous Galerkin method for the thermal solution in 3D mold filling[J]. Computer Methods in Applied Mechanics and Engineering,1999,178:153-169.
[259]Zdanski P S B, Vaz Jr. M. Non-isothermal polymer melt flow in sudden expansions[J]. Journal of Non-Newtonian Fluid Mechanics,2009,161:42-47.