近场动力学方法研究复合材料失效的进展
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摘要
复合材料与单一材料相比具有更高的比刚度和比模量,是重要的工程结构材料,但复合材料失效产生和扩展的机理非常复杂。基于传统连续介质力学理论的方法(如有限元法)求解复合材料的静态和准静态问题时,其理论解和标准试验结果一致。但在求解动态问题时,则需要对连续介质理论进行修改,而且需要额外的失效判断标准和附加函数。尽管如此,传统方法仍无法准确模拟三维裂纹和群裂纹等复杂裂纹的扩展。近场动力学理论(简称PD理论)将传统连续介质力学本构方程中的微分项用积分项代替,避免了由裂纹造成的导数求解奇异性。PD理论应用于失效扩展的模拟具有三大优势:(1)不需要额外的失效判断标准,自发模拟裂纹的产生和扩展;(2)更改本构力函数能对不同尺度的问题进行建模;(3)同一计算体系框架下,能够同时处理多条裂纹的产生和扩展,并考虑它们之间的相互作用。复合材料的不均匀性及其力学性能的各向异性,使得PD模型中的点对力函数无法全面地描述复合材料的各向异性行为,构建理想的数学模型较为困难。PD理论的实质是将模型离散为一系列点,计算在一个点近场范围内所有其他点对该点作用力的合力,这导致PD方法的计算量非常大。因此,近几年PD方法应用于复合材料失效的研究主要集中于理论模型和计算体系的不断发展完善,并取得一系列成果。目前,已发展出多种复合材料的PD模型,开发出新的算法和求解策略,能够较好地模拟复合材料的多种失效模式,并提高计算效率。成功模拟复合材料多种失效模式的PD模型包括:基于纤维键和基体键的模型与基于法向键和剪切键的模型。基于纤维键和基体键的模型是最早建立的复合材料PD模型,通过在材料点对的本构力函数中增加适当的修改项来描述材料的本构信息。基于法向键和剪切键构建的模型,本构力函数中变形量的求解形式类似于传统连续介质力学中应变的表达,能直接在失效结果图中显示力学参量的变化。动态自适应松弛技术、并行算法等已经应用于PD方法并成功提高了计算效率,此外,针对PD方法的计算体系开发了快速算法和转化方程;求解策略上,成功将PD模型和有限元模型进行耦合,将PD模型布置在核心(失效扩展)区域,有限元模型布置在其他区域,在保证求解精度和正确性的基础上提高计算效率。本文归纳了PD方法研究复合材料失效的进展,分别对PD方法的理论框架、复合材料的PD模型、新的求解算法和求解策略以及PD方法在复合材料失效方面的应用等进行介绍,分析了PD方法在研究复合材料失效中存在的问题并展望其前景,以期为PD方法在复合材料失效机理研究中的进一步应用提供参考。
It is universally known that composite materials possess higher specific stiffness and specific modulus than conventional single materials. There-fore,composite materials have become important structural materials in engineering practice. Nevertheless,the mechanism of failure generation and propagation for composite materials is quite complicated. Although,accordant results of the theoretical solution and standard tests concerning the static and quasi-static problems of composite materials can be achieved by traditional continuum mechanics theory( like the finite element method),modification of the continuum theory,as well as additional the criterion of failure and functions are needed when it comes to dynamic problems. However,the traditional method still cannot accurately simulate the propagation of complex cracks,like 3 D cracks and group cracks. Fortunately,the peridynamics theory( referred to as PD theory) replaces the differential term in the traditional constitutive equations of continuum mechanics with the integral term,avoiding the singularity of derivative solution caused by the crack. The application of PD theory to failure-propagation simulation presents the following three major advantages. Ⅰ. It can spontaneously simulate the crack generation and propagation without additional failure criterion. Ⅱ. It is capable of modeling issues in different scales by varying the constitutive force function. Ⅲ. It can simultaneously handle the propagation of multiple cracks while considering their interactions under the framework of the same computing system.Unfortunately,the heterogeneity of composite materials and their anisotropy of mechanical properties make it difficult to construct an ideal mathematical model because the point-to-point force function in the PD model cannot fully describe the anisotropic behavior of the composites. In addition,the essence of PD theory is to discrete the model into a series of points,and calculate the resultant force of all the other points in the nearfield range of one point,which leads to a huge amount of computation of the PD method. Therefore,in recent years,the application of PD theory in the study of composite material failure mainly focus on building a reasonable theoretical model of composite materials and continuous development of the computational efficiency,and a series of results have been achieved. At present,a variety of composite materials PD models have been developed,which can effectively simulate the multiple failure of fiber fracture,matrix crack and delamination. The new algorithm and the solution strategy can greatly speed up the calculation of solution while ensure the accuracy.The PD models that successfully simulated the failure modes of composites include models based on fiber bonds and matrix bonds,and models based on normal bonds and shear bonds. The model based on fiber bonds and matrix bonds is the earliest established PD model of composite materials,which describe the constitutive information of materials by adding appropriate modification items to the constitutive force functions of two material point pairs. For the model based the normal bond and shear bond,the solution of deformation in the constitutive force function is similar to the expression of the strain in the traditional continuum mechanics,and the change of the mechanical parameters can be directly displayed in the final failure result graph. For the sake of improving computational efficiency,dynamic adaptive relaxation techniques and parallel algorithms have been successfully applied to the PD method. In addition,fast algorithms and transformation equations have been developed for the PD model. Moreover,the PD model and the finite element model also have been successfully coupled to solve the problem. The PD model is arranged in the core( failure expansion) area,and the finite element model is arranged in other areas,so as to reduce the calculation amount and improve the calculation efficiency,as well as ensure the accuracy and correctness of the solution.In this article,the progress of PD method in the study of composite failure is summarized. The theoretical framework of the PD method,the PD model of the composite material,the new solution algorithm and solution strategy,and the application of the PD method in the failure of composite materials are introduced respectively. The problems and prospects in the study of composite materials failure are proposed,so as to provide a reference for the further application of PD method in the study of failure mechanism of composite materials.
It is universally known that composite materials possess higher specific stiffness and specific modulus than conventional single materials. There-fore,composite materials have become important structural materials in engineering practice. Nevertheless,the mechanism of failure generation and propagation for composite materials is quite complicated. Although,accordant results of the theoretical solution and standard tests concerning the static and quasi-static problems of composite materials can be achieved by traditional continuum mechanics theory( like the finite element method),modification of the continuum theory,as well as additional the criterion of failure and functions are needed when it comes to dynamic problems. However,the traditional method still cannot accurately simulate the propagation of complex cracks,like 3 D cracks and group cracks. Fortunately,the peridynamics theory( referred to as PD theory) replaces the differential term in the traditional constitutive equations of continuum mechanics with the integral term,avoiding the singularity of derivative solution caused by the crack. The application of PD theory to failure-propagation simulation presents the following three major advantages. Ⅰ. It can spontaneously simulate the crack generation and propagation without additional failure criterion. Ⅱ. It is capable of modeling issues in different scales by varying the constitutive force function. Ⅲ. It can simultaneously handle the propagation of multiple cracks while considering their interactions under the framework of the same computing system.Unfortunately,the heterogeneity of composite materials and their anisotropy of mechanical properties make it difficult to construct an ideal mathematical model because the point-to-point force function in the PD model cannot fully describe the anisotropic behavior of the composites. In addition,the essence of PD theory is to discrete the model into a series of points,and calculate the resultant force of all the other points in the nearfield range of one point,which leads to a huge amount of computation of the PD method. Therefore,in recent years,the application of PD theory in the study of composite material failure mainly focus on building a reasonable theoretical model of composite materials and continuous development of the computational efficiency,and a series of results have been achieved. At present,a variety of composite materials PD models have been developed,which can effectively simulate the multiple failure of fiber fracture,matrix crack and delamination. The new algorithm and the solution strategy can greatly speed up the calculation of solution while ensure the accuracy.The PD models that successfully simulated the failure modes of composites include models based on fiber bonds and matrix bonds,and models based on normal bonds and shear bonds. The model based on fiber bonds and matrix bonds is the earliest established PD model of composite materials,which describe the constitutive information of materials by adding appropriate modification items to the constitutive force functions of two material point pairs. For the model based the normal bond and shear bond,the solution of deformation in the constitutive force function is similar to the expression of the strain in the traditional continuum mechanics,and the change of the mechanical parameters can be directly displayed in the final failure result graph. For the sake of improving computational efficiency,dynamic adaptive relaxation techniques and parallel algorithms have been successfully applied to the PD method. In addition,fast algorithms and transformation equations have been developed for the PD model. Moreover,the PD model and the finite element model also have been successfully coupled to solve the problem. The PD model is arranged in the core( failure expansion) area,and the finite element model is arranged in other areas,so as to reduce the calculation amount and improve the calculation efficiency,as well as ensure the accuracy and correctness of the solution.In this article,the progress of PD method in the study of composite failure is summarized. The theoretical framework of the PD method,the PD model of the composite material,the new solution algorithm and solution strategy,and the application of the PD method in the failure of composite materials are introduced respectively. The problems and prospects in the study of composite materials failure are proposed,so as to provide a reference for the further application of PD method in the study of failure mechanism of composite materials.
引文
1 Zhang P,Zhu Q,Qin H R,et al.Materials Review A:Review Papers,2014,28(6),27(in Chinese).张鹏,朱强,秦鹤勇,等.材料导报:综述篇,2014,28(6),27.
2 Hallett S R,Wisnom M R.Journal of Composite Materials,2006,40(2),119.
3 Green B G,Wisnom M R,Hallett S R.Composites Part A Applied Science&Manufacturing,2007,38(3),867.
4 Wu E M.Fracture mechanics of anisotropic plates,Tech-nomic Publishing Co.,USA,1968.
5 Moes N,Dolbow J,Belytschko T.International Journal for Numerical Methods in Engineering,1999,46(1),131.
6 Lucy L.Astronomical Journal,1997,82(2),1013.
7 Silling S A.Journal of the Mechanics and Physics of Solids,2000,48,175.
8 Huang D,Zhang Q,Qiao P Z,et al.Advances in Mechanics,2010,40(4),448(in Chinese).黄丹,章青,乔丕忠,等.力学进展,2010,40(4),448.
9 Qiao P Z,Zhang Y,Zhang H,et al.Chinese Quarterly of Mechanics,2017(1),1(in Chinese).乔丕忠,张勇,张恒,等.力学季刊,2017(1),1.
10 Kilic B.Peridynamics theory for progressive failure prediction in homogeneous and heterogeneous materials.Ph.D.Thesis.University of Arizona,USA,2008.
11 Silling S A,Askari E.Computers&Structures,2005,83,526.
12 Macek R W,Silling S A.Finite Elements in Analysis and Design,2007,43(15),1169.
13 Silling S A,Simon K.In:Conference on High Speed Computing.Gleneden Beach,Oregon,2004,pp.32.
14 Emmrich E,Weckner O.Mathematics&Mechanics of Solids,2007,4(4),363.
15 Lapidus L,Pinder G F.Numerical Solution of Partial Differential Equations in Science and Engineering.John Wiley&Sons,USA,2011.
16 Askari E,Xu J,Silling S A.In:44th AIAA Aerospace Sciences Meeting and Exhibit.Reno,Nevada,2006,pp.88.
17 Kilic B,Agwai A,Madenci E.Composite Structures,2009,90,141.
18 Hu W,Ha Y D,Bobaru F.Computer Methods in Applied Mechanics and Engineering,2012,217-220,247.
19 Whitney J M,Ashton J E.Structural analysis of laminated anisotropic plates∥Structural analysis of laminated anisotropic plates.Technomic Pub.Co.,USA,1987.
20 Ravi-Chandar K,Knauss W G.International Journal of Fracture,1984,26(3),189.
21 Hu Y L,Yu Y,Wang H.Composite Structures,2014,108,801.
22 Oterkus E,Madenci E.Journal of Mechanics of Materials and Structures,2012,7(1),45.
23 Hu Y,Madenci E,Phan N D.In:57th AIAA/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.California,2016,pp.1723.
24 Roy P,Deepu S P,Pathrikar A,et al.Composite Structures,2017,180,972.
25 Diehl P,Franzelin F,Pflüger D,et al.International Journal of Fracture,2016,201(2),1.
26 Yaghoobi A,Mi G C.Engineering Fracture Mechanics,2016,169,238.
27 Gerstle W,Sau N,Silling S.In:Proceedings of the 8th International Conference on Structural Mechanics in Reactor Technology(SMiRT 18).Beijing,China,2005,pp.54.
28 Hu Y L,Carvalho N V D,Madenci E.Composite Structures,2015,132,610.
29 Hu Y L,Madenci E.In:57th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.San Diego,2016,pp.1722.
30 Hu Y L,Madenci E.Composite Structures,2016,153,139.
31 Hu Y,Madenci E,Phan N.Fatigue&Fracture of Engineering Materials&Structures,2017,40(8),1214.
32 Hu Y,Madenci E.In:58th AIAA/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Alabama,2017,pp.1140.
33 Hu Y L,Madenci E.Composite Structures,2017,160,169.
34 Littlewood D J.SAND Report,Sandia National Laboratories,USA,2015.
35 Kilic B,Madenci E.Theoretical and Applied Fracture Mechanics,2010,53(3),194.
36 Huang D,Lu G,Wang C,et al.Engineering Fracture Mechanics,2015,141(5),196.
37 Wang H,Tian H.Journal of Computational Physics,2012,231(23),7730.
38 Le Q,Chan W,Schwartz J.International Journal for Numerical Methods in Engineering,2011,98(8),1885.
39 Wang H,Du N.Journal of Computational&Applied Mathematics,2014,255(285),376.
40 Wang H,Du N.Journal of Computational Physics,2014,258(1),305.
41 Paola M D,Failla G,Zingales M.International Journal of Solids&Structures,2010,47(18-19),2347.
42 Lubineau G,Yan A,Han F,et al.Journal of the Mechanics&Physics of Solids,2012,60(6),1088.
43 Han F,Lubineau G,Yan A,et al.Computer Methods in Applied Mechanics&Engineering,2016,301,336.
44 Yan A,Han F,Lubineau G.International Journal of Solids&Structures,2013,50(9),1332.
45 Yan A,Han F,Lubineau G.Computational Mechanics,2014,54(3),711.
46 Lee J,Oh S E,Hong J W.International Journal of Fracture,2016,203(1-2),1.
47 Bobaru F,Ha Y D.International Journal for Multiscale Computational Engineering,2011,9(6),635.
48 Dipasquale D,Zaccariotto M,Galvanetto U.International Journal of Fracture,2014,190(1-2),1.
49 Ren H,Zhuang X,Cai Y,et al.International Journal for Numerical Methods in Engineering,2016,108(12),1451.
50 Ba6ant Z P,Luo W,Chau V T,et al.Journal of Applied Mechanics,2016,83(11),111004.
51 Silling S,Epton M,Weckner O,et al.Journal of Elasticity,2007,88(2),151.
52 Yang-Tian Y,Zhang Q,Xin G U.Engineering Mechanics,2016,33(12),80.
53 Gu X,Zhang Q,Huang D,et al.Engineering Fracture Mechanics,2016,160(160),124.
2 Hallett S R,Wisnom M R.Journal of Composite Materials,2006,40(2),119.
3 Green B G,Wisnom M R,Hallett S R.Composites Part A Applied Science&Manufacturing,2007,38(3),867.
4 Wu E M.Fracture mechanics of anisotropic plates,Tech-nomic Publishing Co.,USA,1968.
5 Moes N,Dolbow J,Belytschko T.International Journal for Numerical Methods in Engineering,1999,46(1),131.
6 Lucy L.Astronomical Journal,1997,82(2),1013.
7 Silling S A.Journal of the Mechanics and Physics of Solids,2000,48,175.
8 Huang D,Zhang Q,Qiao P Z,et al.Advances in Mechanics,2010,40(4),448(in Chinese).黄丹,章青,乔丕忠,等.力学进展,2010,40(4),448.
9 Qiao P Z,Zhang Y,Zhang H,et al.Chinese Quarterly of Mechanics,2017(1),1(in Chinese).乔丕忠,张勇,张恒,等.力学季刊,2017(1),1.
10 Kilic B.Peridynamics theory for progressive failure prediction in homogeneous and heterogeneous materials.Ph.D.Thesis.University of Arizona,USA,2008.
11 Silling S A,Askari E.Computers&Structures,2005,83,526.
12 Macek R W,Silling S A.Finite Elements in Analysis and Design,2007,43(15),1169.
13 Silling S A,Simon K.In:Conference on High Speed Computing.Gleneden Beach,Oregon,2004,pp.32.
14 Emmrich E,Weckner O.Mathematics&Mechanics of Solids,2007,4(4),363.
15 Lapidus L,Pinder G F.Numerical Solution of Partial Differential Equations in Science and Engineering.John Wiley&Sons,USA,2011.
16 Askari E,Xu J,Silling S A.In:44th AIAA Aerospace Sciences Meeting and Exhibit.Reno,Nevada,2006,pp.88.
17 Kilic B,Agwai A,Madenci E.Composite Structures,2009,90,141.
18 Hu W,Ha Y D,Bobaru F.Computer Methods in Applied Mechanics and Engineering,2012,217-220,247.
19 Whitney J M,Ashton J E.Structural analysis of laminated anisotropic plates∥Structural analysis of laminated anisotropic plates.Technomic Pub.Co.,USA,1987.
20 Ravi-Chandar K,Knauss W G.International Journal of Fracture,1984,26(3),189.
21 Hu Y L,Yu Y,Wang H.Composite Structures,2014,108,801.
22 Oterkus E,Madenci E.Journal of Mechanics of Materials and Structures,2012,7(1),45.
23 Hu Y,Madenci E,Phan N D.In:57th AIAA/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.California,2016,pp.1723.
24 Roy P,Deepu S P,Pathrikar A,et al.Composite Structures,2017,180,972.
25 Diehl P,Franzelin F,Pflüger D,et al.International Journal of Fracture,2016,201(2),1.
26 Yaghoobi A,Mi G C.Engineering Fracture Mechanics,2016,169,238.
27 Gerstle W,Sau N,Silling S.In:Proceedings of the 8th International Conference on Structural Mechanics in Reactor Technology(SMiRT 18).Beijing,China,2005,pp.54.
28 Hu Y L,Carvalho N V D,Madenci E.Composite Structures,2015,132,610.
29 Hu Y L,Madenci E.In:57th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.San Diego,2016,pp.1722.
30 Hu Y L,Madenci E.Composite Structures,2016,153,139.
31 Hu Y,Madenci E,Phan N.Fatigue&Fracture of Engineering Materials&Structures,2017,40(8),1214.
32 Hu Y,Madenci E.In:58th AIAA/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Alabama,2017,pp.1140.
33 Hu Y L,Madenci E.Composite Structures,2017,160,169.
34 Littlewood D J.SAND Report,Sandia National Laboratories,USA,2015.
35 Kilic B,Madenci E.Theoretical and Applied Fracture Mechanics,2010,53(3),194.
36 Huang D,Lu G,Wang C,et al.Engineering Fracture Mechanics,2015,141(5),196.
37 Wang H,Tian H.Journal of Computational Physics,2012,231(23),7730.
38 Le Q,Chan W,Schwartz J.International Journal for Numerical Methods in Engineering,2011,98(8),1885.
39 Wang H,Du N.Journal of Computational&Applied Mathematics,2014,255(285),376.
40 Wang H,Du N.Journal of Computational Physics,2014,258(1),305.
41 Paola M D,Failla G,Zingales M.International Journal of Solids&Structures,2010,47(18-19),2347.
42 Lubineau G,Yan A,Han F,et al.Journal of the Mechanics&Physics of Solids,2012,60(6),1088.
43 Han F,Lubineau G,Yan A,et al.Computer Methods in Applied Mechanics&Engineering,2016,301,336.
44 Yan A,Han F,Lubineau G.International Journal of Solids&Structures,2013,50(9),1332.
45 Yan A,Han F,Lubineau G.Computational Mechanics,2014,54(3),711.
46 Lee J,Oh S E,Hong J W.International Journal of Fracture,2016,203(1-2),1.
47 Bobaru F,Ha Y D.International Journal for Multiscale Computational Engineering,2011,9(6),635.
48 Dipasquale D,Zaccariotto M,Galvanetto U.International Journal of Fracture,2014,190(1-2),1.
49 Ren H,Zhuang X,Cai Y,et al.International Journal for Numerical Methods in Engineering,2016,108(12),1451.
50 Ba6ant Z P,Luo W,Chau V T,et al.Journal of Applied Mechanics,2016,83(11),111004.
51 Silling S,Epton M,Weckner O,et al.Journal of Elasticity,2007,88(2),151.
52 Yang-Tian Y,Zhang Q,Xin G U.Engineering Mechanics,2016,33(12),80.
53 Gu X,Zhang Q,Huang D,et al.Engineering Fracture Mechanics,2016,160(160),124.