三维负泊松比织物结构的设计制造和变形机理研究
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摘要
天然材料通常表现为正泊松比,即拉伸时材料变窄,压缩时变宽。近几十年来发现了一些具有负泊松比性能的材料,并于1991年被Evans等人命名为拉胀材料(Auxetic material),其泊松比的绝对值越大,负泊松比效应越明显。研究发现,拉胀材料除具有负泊松比外,与传统材料相比,还具有其他独特性能,如剪切刚度、断裂韧性、抗压痕性、能量吸收能力(超声波、声、阻尼)等都有所提高。以上优良的力学性能使得拉胀材料可望应用于航空航天、环保、生物医学及其他国防领域,从而使拉胀材料的开发和研究具有重要意义。
本课题旨在设计开发一种具有负泊松比效应的三维织物结构,研究其产生负泊松比的压缩变形机理并讨论其结构参数对负泊松比的影响。该结构包括经纱、纬纱及捆绑纱,其结构特点是经纬纱多层排列,不进行交织,层间垂直交叉排列,层内纱线一隔一或完全平行排列,同时由织针在垂直于经纬纱交叉排列平面的方向编织经编编链结构形成捆绑纱。标记经纬纱其中一组纱线一隔一排列的结构为结构A,经纬纱同时一隔一排列的结构为结构B。定义该织物的结构松弛率为理想状态下即经纬纱都完全平直情况下织物的厚度与下机后织物的厚度差占理想状态下织物厚度的比例,则影响织物的相关结构参数有：经纬纱半径、不同层相邻经纱间的水平距离、不同层相邻纬纱间的水平距离、经纬纱弹性模量、结构松弛率。
本课题研究工作主要分为四部分：(1)设计一种具有负泊松比效应的三维织物结构,建立该结构的二维几何模型,考察该结构中各参数对其泊松比性能的影响。制造三维织机实现以上结构的织造。(2)通过手工和机械的方法编织出14种不同结构参数的试样,并对以上试样进行压缩实验测试,研究织物产生负泊松比的变形机理以及结构参数对负泊松比的影响。(3)根据经典弹性理论和接触理论建立该结构的二维力学模型,比较该模型所得结果与二维几何模型及压缩实验结果的差别。(4)利用有限元分析方法建立该结构的有限元模型,讨论其结果与二维力学模型及压缩实验结果的差别。
研究主要结论：
(1)三维织物结构在二维几何原理上能够展现负泊松比效应。二维几何模型表明,该结构的负泊松比随着压缩应变的增加而增加。该结构经纱半径增加,不同层相邻经纱间的水平距离减小,同时避免纬纱半径及其结构松弛率过大就可得到负泊松比更明显的织物。
(2)该类结构在一向具有负泊松比。结构在压缩过程中产生负泊松比性能的原因是弯曲刚度大的一组纱线一隔一排列。手工编织试样与三维织机织造试样压缩试验对比发现,两种编织方法得到的试样都能使三维织物结构的展现负泊松比性能。但由于编织方法的不同,相同编织参数织物的结构松弛率有所不同,其泊松比性能也有些微差异。经纱半径和不同层相邻经纱间的水平距离对织物泊松比的影响与二维几何模型具有相同变化趋势：随着以上参数的增加织物负泊松比性能增加。但纬纱半径对泊松比影响的变化趋势则刚好相反。
(3)三维织物结构的二维力学模型计算结果与实验结果显示相同的变化趋势,随着压缩应变的增加,结构的负泊松比效应愈加明显。但其二维力学模型所得负泊松比略大于、受力明显大于实验结果。二维力学模型研究发现经纱半径的增加、纬纱半径的减小,不同层相邻经纱间的水平距离的减小,经纱弹性模量的增加,纬纱弹性模量的减小都使该结构负泊松比效应增加。结构松弛率的增加虽能增加结构的负泊松比性能,却使结构的最大压缩应变降低。
(4)有限元分析表明,以该结构的最小单元作为有限元模型足以模拟该结构的泊松比、受力状况与压缩应变的关系。结构A和结构B在结构参数相同时,具有几乎相同的泊松比—压缩应变曲线及受力—压缩应变曲线。有限元模型中结构参数变化对结构泊松比—压缩应变关系的影响趋势与压缩实验结果和二维力学模型结果相同。
Natural materials usually exhibit positive Poisson's ratio; that is, such materials tend to contract or expand in the transverse direction if they are stretched or compressed, respectively, in the longitudinal direction. In recent decades, some materials with negative Poisson's ratio (NPR) have been found, and named as auxetic materials by Evans et al in1991. The greater the absolute values of Poisson's ratio of auxetic materials have, the higher the NPR effect. Compared with common materials, in addition to NPR, auxetic materials possess other unique properties, such as high shear stiffness, high fracture toughness, high resilience and energy, ultrasound, sound absorption capacity, etc. These excellent mechanical properties make auxetic materials good candidates for the applications in aerospace, environmental protection, biomedicine and other defense field. Hence, the development and study of auxetic materials are of great significance.
The study aims to design and develop an innovative kind of three dimensional fabrics with negative Poisson's ratio, and analyze their deformation mechanism under compression process and influences of structure parameters on the NPR effect. The fabric structrure is composed of three yarn systems, i.e., weft yarns, warp yarns and stitch yarns. The structure features include:1) the weft and warp yarns layers are not interlaced;2) the weft and warp layers are fully or partially arranged in each layer;3) the weft and warp yarns are bound by the stitch yarns through the fabric thickness direction. Two kinds of structures, structure A and structure B, were suggested and produced. In structure A, the weft yarns are fully arranged, and the warp yarns are partially arranged. In structure B, both of the weft and warp yarns are partially arranged. The relaxation rate of the two kinds of stuructures is defined to describe the initial state of the fabric at which the weft and warp yarns are crimped or completely straight. The structural parameters including radiuses of the weft and warp yarns, the spacing of two adjacent warp yarns in the same layer, the spacing of two adjacent weft yarns in the same layer, the Young's modulus of the weft and warp yarns and structure relaxation rate, are the factors affecting auxetic effect of the fabric structures.
The study includes four parts. An innovative three dimensional structure with NPR was first designed and developed. In the first part, a geometric model was established, and the effects of structural parameters on NPR of the fabrics were discussed based on the model established. Then, a machine to produce this kind of3D fabric structure was manufactured to produce. In the second part, fourteen fabric samples were manufactured manually and produced using the machine, respectively, and compressed using an Instron5566machine. The reasons for the fabric structure with axuetic effect under compression and the affecting trends of structural parameters on negative Poisson's ratio were experimentally analyzed. In the third part, a2D analytical model was established based on the classical theory of elasticity and contact theory, and compared with the experimental results and the above mentioned geometric model. In the last part, a finite element model was built, and the simulation results were compared with the results from the compression tests and the2D analytical model.
The main conclusions of the study are as follows:
(1) The results of the geometric model confirm that the innovative structure has a negative Poisson's ratio which increases with the compression strain. To obtain more obvious auxetic effect of the structure, the radius of the warp yarns and the spacing of two adjacent warp yarns should be increased,, and the radius of the weft yarns and structure relaxation rate should be not too high.
(2) The innovative three-dimensional structure can only have NPR in one direction for both the structure A and structure B. The axuetic effect under compression results from a group of yarns with higher bending stiffness and alternately arranged. Comparative experiments between the fabrics produced by hand and the fabrics manufactured by machine show that all the samples have NPR. The fabrics with the same structural parameters having different structural relaxation rates lead to different Poisson's ratios. The increase of radius of warp yarns and the spacing of two adjacent warp yarns in the same layer enhances the auxetic effect and this trend agrees well with the prediction of the2D geometric model.
(3) The results from the2D analytical model showed that the theoretical Poisson's ratio-compression strain curves had the same trends as the experiment results. Auxetic effect of the structure was more obvious with the increasing the compressive strain. But the NPR values obtained from this2D analytical model are slightly greater than the experiment results, and the force of unit cell is significantly greater than that from experiment. In addition, the results showed that increasing the radius and elastic modulus of the warp yarns, and decreasing the spacing of two adjacent warp yarns in the same layer and the radius and elastic modulus of the weft yarns have a significant and positive impact on the NPR ratio effect. Although the structural relaxation rate at the initial state had significantly improved the NPR performance of the fabric structure, it can affect the compressive strain rate of the fabric structure to a certain extent.
(4) The finite element analysis showed that using the smallest unit cell of the structure to simulate Poisson ratio and stress in compression process was reasonable. Additionally, structure A and structure B with the same structural parameters have the same trends in the Poisson's ratio-compressive strain and stress-compressive strain relationships. The influences of structural parameters on Poisson's ratio in the finite element model had the same trend as the results of compression test and2D analytical model.
本课题旨在设计开发一种具有负泊松比效应的三维织物结构,研究其产生负泊松比的压缩变形机理并讨论其结构参数对负泊松比的影响。该结构包括经纱、纬纱及捆绑纱,其结构特点是经纬纱多层排列,不进行交织,层间垂直交叉排列,层内纱线一隔一或完全平行排列,同时由织针在垂直于经纬纱交叉排列平面的方向编织经编编链结构形成捆绑纱。标记经纬纱其中一组纱线一隔一排列的结构为结构A,经纬纱同时一隔一排列的结构为结构B。定义该织物的结构松弛率为理想状态下即经纬纱都完全平直情况下织物的厚度与下机后织物的厚度差占理想状态下织物厚度的比例,则影响织物的相关结构参数有：经纬纱半径、不同层相邻经纱间的水平距离、不同层相邻纬纱间的水平距离、经纬纱弹性模量、结构松弛率。
本课题研究工作主要分为四部分：(1)设计一种具有负泊松比效应的三维织物结构,建立该结构的二维几何模型,考察该结构中各参数对其泊松比性能的影响。制造三维织机实现以上结构的织造。(2)通过手工和机械的方法编织出14种不同结构参数的试样,并对以上试样进行压缩实验测试,研究织物产生负泊松比的变形机理以及结构参数对负泊松比的影响。(3)根据经典弹性理论和接触理论建立该结构的二维力学模型,比较该模型所得结果与二维几何模型及压缩实验结果的差别。(4)利用有限元分析方法建立该结构的有限元模型,讨论其结果与二维力学模型及压缩实验结果的差别。
研究主要结论：
(1)三维织物结构在二维几何原理上能够展现负泊松比效应。二维几何模型表明,该结构的负泊松比随着压缩应变的增加而增加。该结构经纱半径增加,不同层相邻经纱间的水平距离减小,同时避免纬纱半径及其结构松弛率过大就可得到负泊松比更明显的织物。
(2)该类结构在一向具有负泊松比。结构在压缩过程中产生负泊松比性能的原因是弯曲刚度大的一组纱线一隔一排列。手工编织试样与三维织机织造试样压缩试验对比发现,两种编织方法得到的试样都能使三维织物结构的展现负泊松比性能。但由于编织方法的不同,相同编织参数织物的结构松弛率有所不同,其泊松比性能也有些微差异。经纱半径和不同层相邻经纱间的水平距离对织物泊松比的影响与二维几何模型具有相同变化趋势：随着以上参数的增加织物负泊松比性能增加。但纬纱半径对泊松比影响的变化趋势则刚好相反。
(3)三维织物结构的二维力学模型计算结果与实验结果显示相同的变化趋势,随着压缩应变的增加,结构的负泊松比效应愈加明显。但其二维力学模型所得负泊松比略大于、受力明显大于实验结果。二维力学模型研究发现经纱半径的增加、纬纱半径的减小,不同层相邻经纱间的水平距离的减小,经纱弹性模量的增加,纬纱弹性模量的减小都使该结构负泊松比效应增加。结构松弛率的增加虽能增加结构的负泊松比性能,却使结构的最大压缩应变降低。
(4)有限元分析表明,以该结构的最小单元作为有限元模型足以模拟该结构的泊松比、受力状况与压缩应变的关系。结构A和结构B在结构参数相同时,具有几乎相同的泊松比—压缩应变曲线及受力—压缩应变曲线。有限元模型中结构参数变化对结构泊松比—压缩应变关系的影响趋势与压缩实验结果和二维力学模型结果相同。
Natural materials usually exhibit positive Poisson's ratio; that is, such materials tend to contract or expand in the transverse direction if they are stretched or compressed, respectively, in the longitudinal direction. In recent decades, some materials with negative Poisson's ratio (NPR) have been found, and named as auxetic materials by Evans et al in1991. The greater the absolute values of Poisson's ratio of auxetic materials have, the higher the NPR effect. Compared with common materials, in addition to NPR, auxetic materials possess other unique properties, such as high shear stiffness, high fracture toughness, high resilience and energy, ultrasound, sound absorption capacity, etc. These excellent mechanical properties make auxetic materials good candidates for the applications in aerospace, environmental protection, biomedicine and other defense field. Hence, the development and study of auxetic materials are of great significance.
The study aims to design and develop an innovative kind of three dimensional fabrics with negative Poisson's ratio, and analyze their deformation mechanism under compression process and influences of structure parameters on the NPR effect. The fabric structrure is composed of three yarn systems, i.e., weft yarns, warp yarns and stitch yarns. The structure features include:1) the weft and warp yarns layers are not interlaced;2) the weft and warp layers are fully or partially arranged in each layer;3) the weft and warp yarns are bound by the stitch yarns through the fabric thickness direction. Two kinds of structures, structure A and structure B, were suggested and produced. In structure A, the weft yarns are fully arranged, and the warp yarns are partially arranged. In structure B, both of the weft and warp yarns are partially arranged. The relaxation rate of the two kinds of stuructures is defined to describe the initial state of the fabric at which the weft and warp yarns are crimped or completely straight. The structural parameters including radiuses of the weft and warp yarns, the spacing of two adjacent warp yarns in the same layer, the spacing of two adjacent weft yarns in the same layer, the Young's modulus of the weft and warp yarns and structure relaxation rate, are the factors affecting auxetic effect of the fabric structures.
The study includes four parts. An innovative three dimensional structure with NPR was first designed and developed. In the first part, a geometric model was established, and the effects of structural parameters on NPR of the fabrics were discussed based on the model established. Then, a machine to produce this kind of3D fabric structure was manufactured to produce. In the second part, fourteen fabric samples were manufactured manually and produced using the machine, respectively, and compressed using an Instron5566machine. The reasons for the fabric structure with axuetic effect under compression and the affecting trends of structural parameters on negative Poisson's ratio were experimentally analyzed. In the third part, a2D analytical model was established based on the classical theory of elasticity and contact theory, and compared with the experimental results and the above mentioned geometric model. In the last part, a finite element model was built, and the simulation results were compared with the results from the compression tests and the2D analytical model.
The main conclusions of the study are as follows:
(1) The results of the geometric model confirm that the innovative structure has a negative Poisson's ratio which increases with the compression strain. To obtain more obvious auxetic effect of the structure, the radius of the warp yarns and the spacing of two adjacent warp yarns should be increased,, and the radius of the weft yarns and structure relaxation rate should be not too high.
(2) The innovative three-dimensional structure can only have NPR in one direction for both the structure A and structure B. The axuetic effect under compression results from a group of yarns with higher bending stiffness and alternately arranged. Comparative experiments between the fabrics produced by hand and the fabrics manufactured by machine show that all the samples have NPR. The fabrics with the same structural parameters having different structural relaxation rates lead to different Poisson's ratios. The increase of radius of warp yarns and the spacing of two adjacent warp yarns in the same layer enhances the auxetic effect and this trend agrees well with the prediction of the2D geometric model.
(3) The results from the2D analytical model showed that the theoretical Poisson's ratio-compression strain curves had the same trends as the experiment results. Auxetic effect of the structure was more obvious with the increasing the compressive strain. But the NPR values obtained from this2D analytical model are slightly greater than the experiment results, and the force of unit cell is significantly greater than that from experiment. In addition, the results showed that increasing the radius and elastic modulus of the warp yarns, and decreasing the spacing of two adjacent warp yarns in the same layer and the radius and elastic modulus of the weft yarns have a significant and positive impact on the NPR ratio effect. Although the structural relaxation rate at the initial state had significantly improved the NPR performance of the fabric structure, it can affect the compressive strain rate of the fabric structure to a certain extent.
(4) The finite element analysis showed that using the smallest unit cell of the structure to simulate Poisson ratio and stress in compression process was reasonable. Additionally, structure A and structure B with the same structural parameters have the same trends in the Poisson's ratio-compressive strain and stress-compressive strain relationships. The influences of structural parameters on Poisson's ratio in the finite element model had the same trend as the results of compression test and2D analytical model.
引文
[1]Wan H, Ohtaki H, Kotosaka S, et al. A study of negative Poisson's ratios in auxetic honeycombs based on a large deflection model[J]. European Journal of Mechanics-A/Solids,2004,23(1):95-106.
[2]Alderson K L, Alderson A, Evans K E. The interpretation of the strain-dependent Poisson's ratio in auxetic polyethylene[J]. The Journal of Strain Analysis for Engineering Design,1997,32(3):201-212.
[3]Lakes R S. Foam structures with a negative Poisson's ratio[J]. Science,1987,235:1038-1040.
[4]Huang X, Blackburn S. Developing a new processing route to manufacture honeycomb ceramics with negative Poisson's ratio[J]. Key Engineering Materials,2001,206:201-204.
[5]Choi J B, Lakes R S. Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis [J]. International Journal of Fracture,1996,80(1):73-83.
[6]Lakes R S, Elms K. Indentability of conventional and negative Poisson's ratio foams[J]. Journal of composite materials,1993,27(12):1193-1202.
[7]Scarpa F, Ciffo L G, Yates J R. Dynamic properties of high structural integrity auxetic open cell foam[J]. Smart materials and structures,2004,13(1):49.
[8]Scarpa F, Bullough W A, Lumley P. Trends in acoustic properties of iron particle seeded auxetic polyurethane foam[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2004,218(2):241-244.
[9]Scarpa F, Smith F C. Passive and MR fluid-coated auxetic PU foam-mechanical, acoustic, and electromagnetic properties[J]. Journal of intelligent material systems and structures,2004,15(12): 973-979.
[10]易洪雷.三维机织复合材料的结构设计与力学性能研究[D].上海：东华大学,2000.
[11]戎琦.三维机织复合材料的织造技术[J].纤维复合材料,2007,24(1)：31-33.
[12]A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity[M]. New York:Dover Publications,1920.
[13]Gunton D J, Saunders G A. The Young's modulus and Poisson's ratio of arsenic, antimony and bismuth[J]. Journal of Materials Science,1972,7(9):1061-1068.
[14]Li Y. The anisotropic behavior of Poisson's ratio, Young's modulus, and shear modulus in hexagonal materials[J]. physica status solidi (a),1976,38(1):171-175.
[15]Nur A, Simmons G. The effect of saturation on velocity in low porosity rocks[J]. Earth and Planetary Science Letters,1969,7(2):183-193.
[16]Williams J L, Lewis J L. Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis[J]. Journal of biomechanical engineering,1982,104(1):50-56.
[17]Evans K E, Nkansah M A, Hutchinson I J, et al. Molecular network design[J]. Nature,1991, 353(6340):124-124.
[18]Tretiakov K V. Negative Poisson's ratio of two-dimensional hard cyclic tetramers[J]. Journal of Non-Crystalline Solids,2009,355(24):1435-1438.
[19]Gibson L J, Ashby M F, Schajer G S, et al. The mechanics of two-dimensional cellular materials[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences,1982, 382(1782):25-42.
[20]杨智春,邓庆田.负泊松比材料与结构的力学性能研究及应用[J].力学进展,2011,41(3)：335-350.
[21]Alderson A, Alderson K. L. Auxetic materials[J]. Proceedings of the Institution of Mechanical Engineers, Part G:Journal of Aerospace Engineering,2007,221(4):565-575.
[22]Larsen U D, Sigmund O, Bouwstra S. Larsen U D, Sigmund O. Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio[J]. Journal of microelectromechanical systems,1997,6(2):99-106.
[23]Theocaris P S, Stavroulakis G E, Panagiotopoulos P D. Negative Poisson's ratios in composites with star-shaped inclusions:a numerical homogenization approach[J]. Archive of Applied Mechanics, 1997,67(4):274-286.
[24]Lakes R. Deformation mechanisms in negative Poisson's ratio materials:structural aspects[J]. Journal of materials science,1991,26(9):2287-2292.
[25]Smith C W, Grima J N, Evans K E. A novel mechanism for generating auxetic behaviour in reticulated foams:missing rib foam model[J]. Acta materialia,2000,48(17):4349-4356.
[26]Gaspar N, Ren X J, Smith C W, et al. Novel honeycombs with auxetic behaviour[J]. Acta Materialia, 2005,53(8):2439-2445.
[27]Dolla W J S, Fricke B A, Becker B R. Structural and drug diffusion models of conventional and auxetic drug-eluting stents[J]. Journal of Medical Devices,2007,1:47.
[28]Evans K E, Nkansah M A, Hutchinson I J. Auxetic foams:modelling negative Poisson's ratios[J]. Acta metallurgica et materialia,1994,42(4):1289-1294.
[29]Choi J B, Lakes R S. Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson's ratio[J]. International journal of mechanical sciences,1995,37(1): 51-59.
[30]Liu Y, Hu H, Lam J K C, et al. Negative poisson's ratio weft-knitted fabrics[J]. Textile Research Journal,2010,80(9):856-863.
[31]Glazzard M, Breedon P. Weft-knitted auxetic textile design[J]. physica status solidi (b),2013.
[32]卢子兴,刘强,杨振宇.拉胀泡沫材料力学性能[J].宇航材料工艺,2011,41(1)：7-13.
[33]Tretiakov K V, Wojciechowski K W. Poisson's ratio of simple planar'isotropic'solids in two dimensions[J]. physica status solidi (b),2007,244(3):1038-1046.
[34]Wojciechowski K W. Solid phases of two-dimensional hard dumb-bells in the free volume approximation:Crystal-aperiodic-solid phase transition[J]. Physics Letters A,1987,122(6):377-380.
[35]Wojciechowski K W. Two-dimensional isotropic system with a negative Poisson ratio[J]. Physics Letters A,1989,137(1):60-64.
[36]Prall D, Lakes R S. Properties of a chiral honeycomb with a poisson's ratio of-1 [J]. International Journal of Mechanical Sciences,1997,39(3):305-314.
[37]Alderson A, Alderson K L, Attard D, et al. Elastic constants of 3-,4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading[J]. Composites Science and Technology, 2010,70(7):1042-1048.
[38]Grima J N, Farrugia P S, Gatt R, et al. On the auxetic properties of rotating rhombi and parallelograms: A preliminary investigation[J]. physica status solidi (b),2008,245(3):521-529.
[39]Gatt R, Attard D, Farrugia P S, et al. A realistic generic model for anti-tetrachiral systems[J]. physica status solidi (b),2013.
[40]Caddock B D, Evans K E. Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties[J]. Journal of Physics D:Applied Physics,1989,22(12):1877.
[41]Lakes R. Advances in negative Poisson's ratio materials[J]. Advanced Materials,1993,5(4):293-296.
[42]Pickles A P, Alderson K L, Evans K E. The effects of powder morphology on the processing of auxetic polypropylene (PP of negative Poisson's ratio)[J]. Polymer Engineering & Science,1996, 36(5):636-642.
[43]Alderson K L, Alderson A, Webber R S, et al. Evidence for uniaxial drawing in the fibrillated microstructure of auxetic microporous polymers[J]. Journal of materials science letters,1998,17(16): 1415-1419.
[44]Ravirala N, Alderson K L, Davies P J, et al. Negative Poisson's ratio polyester fibers[J]. Textile research journal,2006,76(7):540-546.
[45]Alderson K L, Fitzgerald A, Evans K E. The strain dependent indentation resilience of auxetic microporous polyethylene[J]. Journal of materials science,2000,35(16):4039-4047.
[46]Liu Y, Hu H. A review on auxetic structures and polymeric materials[J]. Sci. Res. Essays,2010,5(10): 1052-1063.
[47]He C, Liu P, Griffin A C. Toward negative Poisson ratio polymers through molecular design[J]. Macromolecules,1998,31(9):3145-3147.
[48]Liu P, He C, Griffin A C. Liquid crystalline polymers as potential auxetic materials[C]//Abstracts of papers of the american chemical society. New York:Division of Polymer Chemistry, American Chemical Society,1997,214:85.
[49]刘应良.负泊松比材料的合成及阻燃抗静电PVC新配方设计[D].郑州：郑州大学,2002.
[50]Li C, Xie X, Cao S. Synthesis and characterization of liquid crystalline copolyesters containing horizontal and lateral rods in main chain[J]. Polymers for Advanced Technologies,2002,13(3-4): 178-187.
[51]Grima J N, Jackson R, Alderson A, et al. Do zeolites have negative Poisson's ratios?[J]. Advanced Materials,2000,12(24):1912-1918.
[52]Grima J N, Evans K E. Auxetic behavior from rotating squares[J]. Journal of materials science letters, 2000,19(17):1563-1565.
[53]Grima J N, Evans K E. Auxetic behavior from rotating triangles[J]. Journal of materials science,2006, 41(10):3193-3196.
[54]Grima J N, Alderson A, Evans K E. Auxetic behaviour from rotating rigid units[J]. physica status solidi (b),2005,242(3):561-575.
[55]Alderson A. A triumph of lateral thought[J]. Chem. Ind,1999,10:384.
[56]Miki M, Murotsu Y. The peculiar behavior of the Poisson's ratio of laminated fibrous composites[J]. JSME international journal. Ser.1, Solid mechanics, strength of materials,1989,32(1):67-72.
[57]Milton G W. Composite materials with Poisson's ratios close to-1[J]. Journal of the Mechanics and Physics of Solids,1992,40(5):1105-1137.
[58]史炜,杨伟,李忠明,等.负泊松比材料研究进展[J].高分子通报,2003,6.
[59]Clarke J F, Duckett R A, Hine P J, et al. Negative Poisson's ratios in angle-ply laminates:theory and experiment[J]. Composites,1994,25(9):863-868.
[60]Hine P J, Duckett R A, Ward I M. Negative Poisson's ratios in angle-ply laminates[J]. Journal of materials science letters,1997,16(7):541-544.
[61]Alderson K L, Simkins V R, Coenen V L, et al. How to make auxetic fibre reinforced composites[J]. physica status solidi (b),2005,242(3):509-518.
[62]Evans K E, Donoghue J P, Alderson K L. The design, matching and manufacture of auxetic carbon fibre laminates[J]. Journal of composite materials,2004,38(2):95-106.
[63]Hadi Harkati E, Bezazi A, Scarpa F, et al. Modelling the influence of the orientation and fibre reinforcement on the Negative Poisson's ratio in composite laminates[J]. physica status solidi (b), 2007,244(3):883-892.
[64]Miller W, Hook P B, Smith C W, et al. The manufacture and characterisation of a novel, low modulus, negative Poisson's ratio composite[J]. Composites Science and Technology,2009,69(5):651-655.
[65]Hook P B, Evans K E, Hannington J P, et al. Composite materials and structures[P]. U.S. Patent: 10551316,2004-3-26.
[66]Bertoldi K, Reis P M, Willshaw S, et al. Negative Poisson's ratio behavior induced by an elastic instability[J]. Advanced materials,2010,22(3):361-366.
[67]Shim J, Perdigou C, Chen E R, et al. Buckling-induced encapsulation of structured elastic shells under pressure[J]. Proceedings of the National Academy of Sciences,2012,109(16):5978-5983.
[68]Choi J B, Lakes R S. Non-linear properties of polymer cellular materials with a negative Poisson's ratio[J]. Journal of Materials Science,1992,27(17):4678-4684.
[69]Bianchi M, Scarpa F, Smith C W. Shape memory behaviour in auxetic foams:Mechanical properties[J]. Acta Materialia,2010,58(3):858-865.
[70]Alderson A, Rasburn J, Evans K E, et al. Auxetic polymeric filters display enhanced de-fouling and pressure compensation properties [J]. Membrane Technology,2001,2001(137):6-8.
[71]Alderson A, Davies P J, Williams M R, et al. Modelling of the mechanical and mass transport properties of auxetic molecular sieves:an idealised organic (polymeric honeycomb) host-guest system[J]. Molecular Simulation,2005,31(13):897-905.
[72]Smith W A. Optimizing electromechanical coupling in piezocomposites using polymers with negative Poisson's ratio[C]//New York:Ultrasonics Symposium,1991. IEEE,1991:661-666.
[73]Gibiansky L V, Torquato S. On the use of homogenization theory to design optimal piezocomposites for hydrophone applications[J]. Journal of the Mechanics and Physics of Solids,1997,45(5): 689-708.
[74]Evans K E, Alderson A. Auxetic materials:Functional materials and structures from lateral thinking![J]. Advanced materials,2000,12(9):617-628.
[75]Ugbolue S C, Kim Y K, Warner S B, et al. The formation and performance of auxetic textiles. Part I: theoretical and technical considerations[J]. The Journal of The Textile Institute,2010,101(7): 660-667.
[76]Lim T C. Semi-auxetic yarns[J]. physica status solidi (b),2013.
[77]Hu H, Wang Z, Liu S. Development of auxetic fabrics using flat knitting technology[J]. Textile Research Journal,2011,81(14):1493-1502.
[78]李刚,郭兴峰,刘兰芳.三维机织物的设计与织造方法探讨[J].河北纺织,2008(1)：17-22.
[79]王荣荣.三维弹性机织物的研制与性能分析[D].天津：天津工业大学,2006.
[80]余育.三维正交机织复合材料力学性能研究[D].合肥：中国科学技术大学,2008.
[81]周凤飞.三维纺织技术发展现状[J].产业用纺织品,1996,14(3)：8-11.
[82]左惟炜.三维编织复合材料力学性能与工程应用研究[D].武汉：华中科技大学,2006.
[83]刘辉,阎良敏,甘应进,等.三维织物的编织技术[J].天津纺织科技,2001,39(3)：18-20.
[84]季丹.变截面三维编织计算机模拟[D].天津：天津工业大学,2011.
[85]吴华利.三维正交机织复合材料结构与力学性能研究[D].武汉：武汉理工大学,2007.
[86]刘淑萍,刘让同.三维织物结构设计[J].纺织科技进展,2006,6：42-48.
[87]郭兴峰.三维正交机织物结构的研究[D].天津：天津工业大学,2003.
[88]聂建斌.角联锁织物的开发及性能研究[D].上海：东华大学,2007.
[89]Mohamed M H, Bilisik A K. Multi-layer three-dimensional fabric and method for producing[P]. U.S. Patent:5465760,1995-11-14.
[90]Greenwood K. Marshall dann[P]. U.S. Patent:3818951,1974-6-2.
[91]Fukuta K, Nagatsuka Y, Tsuburaya S, et al. Three-dimensional fabric, and method and loom construction for the production thereof[P]. U.S. Patent:3834424,1974-9-10.
[92]King R W. Three dimensional fabric material[P]. U.S. Patent:4038440,1977-7-26.
[93]Mohamed M H, Zhang Z H. Method of forming variable cross-sectional shaped three-dimensional fabrics[P]. U.S. Patent:5085252,1992-2-4.
[94]马崇.一种三维机织物的织造设备及织造方法[P].中国专利：CN1730751B,2010-06-09.
[95]RUZAND J M, GUENOT G. Multiaxial three-dimensional fabric and process for its manufacture[P]. WIPO Patent:1994020658,1994-9-16.
[96]Farley G L. Method and apparatus for weaving a woven angle ply fabric[P]. U.S. Patent:5224519, 1993-7-6.
[97]Khokar N. Network-like woven 3D fabric material[P]. U.S. Patent:6431222,2002-8-13.
[98]崔俊芳.三维机织物织造方法的研究[D].天津：天津工业大学,2002.
[99]Anahara M, Yasui Y, Omori H. Three dimensional fabric and method for producing the same[P]. U.S. Patent:5137058,1992-8-11.
[100]Uchida H, Yamamoto T, Takashima H, et al. Three-dimensional weaving machine[P]. U.S. Patent: 6003563,1999-12-21.
[101]Bilisik A K. Multiaxial three-dimensional (3-D) circular woven fabric[P]. U.S. Patent:6129122, 2000-10-10.
[102]Lempriere B M. Poisson's ratio in orthotropic materials[J]. AIAA Journal,1968,6(11):2226-2227.
[103]郭兴峰,王瑞,黄故,等.接结经纱对三维正交机织物结构的影响[J].纺织学报,2005,26(1)：56-58.
[104]Byun J H, Chou T W. Three-dimensional textile composites. A review[C]//112th ASME Winter Annual Meeting, Symposium on Composites in Transportaion Vehicles, Atlanta, Georgia.1991.
[105]Whitney T J, Chou T W. Modeling of 3-D angle-interlock textile structural composites[J]. Journal of Composite Materials,1989,23(9):890-911.
[106]Peirce F T. The geometry of cloth structure[J]. The journal of the Textile Institute. Transactions, 1937,28:45-96.
[107]蔡雨,郑天勇,景书娟,等Peirce平纹机织物结构模型的计算精确度[J].纺织学报,2012,33(1)：48-53.
[108]贺显伟,汪军.织物组织几何模型及其在织物外观模拟上的应用[J].纺织导报,2003,6：114-116.
[109]Peirce F T. Geometrical principles applicable to the design of functional fabrics[J]. Textile Research Journal,1947,17(3):123-147.
[110]Kemp A, An extension of Peirce's cloth geometry to the treatment of nonlinear threads[J]. Journal of the Textile Institute,1958,49:44-48.
[111]Hearle J W S, Shanahan W J. An energy method for calculations in fabric mechanics part I: principles of the method[J]. Journal of the Textile Institute,1978,69(4):81-91.
[112]Hearle J W S, Potluri P, Thammandra V S. Modelling fabric mechanics[J]. Journal of the Textile Institute,2001,92(3):53-69.
[113]Weissenberg K. The use of a trellis model in the mechanics of homogeneous materials[J]. Journal of the Textile Institute Transactions,1949,40(2):89-110.
[114]Kilby W F. Planar stress-strain relationships in woven fabrics[J]. Journal of the Textile Institute Transactions,1963,54(1):9-27.
[115]Olofsson B. A general model of a fabric as a geometric-mechanical structure[J]. Journal of the Textile Institute Transactions,1964,55(11):541-557. [116] Kawabata S, Niwa M, Nanashima Y, et al. The Theoretical Investigation on the Biaxial Tensile Properties of Plain Knitted Fabrics, Part 1: Theory[J]. Sen'i Kikai Gakkaishi,1970,23:95-108.
[117]Hearle J W S, Grosberg P, Backer S. Structural Mechanics of Fibers, Yarns, and Fabrics[M]. New York:Wiley-Interscience,1969.
[118]Shanahan W J, Postle R. A theoretical analysis of the tensile properties of plain-knitted fabrics. Part I: the load-extension curve for fabric extension parallel to the courses[J]. Journal of the Textile Institute,1974,65(4):200-212.
[119]Leaf G A V, Kandil K H. The initial load-extension behaviour of plain-woven fabrics[J]. Journal of the textile institute,1980,71(1):1-7.
[120]Warren W E. The elastic properties of woven polymeric fabric[J]. Polymer Engineering & Science, 1990,30(20):1309-1313.
[121]Hu H, De Araujo M D, Fangueiro R, et al. Theoretical analysis of load-extension properties of plain weft knits made from high performance yarns for composite reinforcement[J]. Textile research journal,2002,72(11):991-996.
[122]Timosenko S P. History of strength of materials:with a brief account of the history of theory of elasticity and theory of structures[M]. New York:Dover publications,1953.
[123]Han S M, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories[J]. Journal of Sound and Vibration,1999,225(5):935-988.
[124]Hertz H. On the contact of elastic solids[J]. J. reine angew. Math,1881,92:156-171.
[125]Hamrock B J, Dowson D. Ball Bearing Lubrication:The Elastohydrodynamics of Elliptical Contacts[M]. New York:Wiley,1981.
[126]Prescott J. Applied elasticity[M]. London:Longmans, Green and Co.,1924.
[127]Puttock M J, Thwaite E G. Elastic compression of spheres and cylinders at point and line contact[M]. Melbourne, Australia:Commonwealth Scientific and Industrial Research Organization,1969.
[128]孔祥安,固体接触力学[M].北京：中国铁道出版社,1999.
[129]Sadykova F K. The Poisson ratio of textile fibres and yarns[J]. Fibre Chemistry,1972,3(2):180-183.
[130]Kellog O D, Foundations of Potential Theory[M]. New York:Dover,1929.
[131]王勖成.有限单元法[M].北京：清华大学出版社,2003.
[132]Clough R W. The finite element method in plane stress analysis[M] New York:American Society of Civil Engineers,1960.
[133]Turner M J. Stiffness and deflection analysis of complex structures[J]. J. Aeronautical Science,1956, 23(9):805-823.
[134]顾伯洪.机织物拉伸的有限元模拟及应用[J].中国纺织大学学报,1998,3：12-13.
[135]Lloyd D W. The analysis of complex fabric deformations[J]. Mechanics of flexible fibre assemblies, 1980:311-342.
[136]Collier B J. Measurement of fabric drape and its relation to fabric mechanical properties and subjective evaluation[J]. Clothing and Textiles Research Journal,1991,10(1):46-52.
[137]Kim J H. Fabric mechanics analysis using large deformation orthotropic shell theory[D]. Raleigh: North Carolina State University,1991.
[138]Simo J C, Fox D D. On a stress resultant geometrically exact shell model. Part Ⅰ:Formulation and optimal parametrization[J]. Computer Methods in Applied Mechanics and Engineering,1989,72(3): 267-304.
[139]Simo J C, Fox D D, Rifai M S. On a stress resultant geometrically exact shell model. Part Ⅲ: Computational aspects of the nonlinear theory [J]. Computer Methods in Applied Mechanics and Engineering,1990,79(1):21-70.
[140]Simo J C, Fox D D, Rifai M S. On a stress resultant geometrically exact shell model. Part Ⅱ:The linear theory; computational aspects[J]. Computer Methods in Applied Mechanics and Engineering, 1989,73(1):53-92.
[141]Deng S. Nonlinear fabric mechanics including material nonlinearity, contact, and an adaptive global solution algorithm[D]. Raleigh:North Carolina State University,1994.
[142]Eischen J W, Deng S, Clapp T G. Finite-element modeling and control of flexible fabric parts[J]. Computer Graphics and Applications, IEEE,1996,16(5):71-80.
[143]Kang T J, Yu W R. Drape simulation of woven fabric by using the finite-element method[J]. Journal of the Textile Institute,1995,86(4):635-648.
[144]Ascough J, Bez H E, Bricis A M. A simple beam element, large displacement model for the finite element simulation of cloth drape[J]. Journal of the Textile Institute,1996,87(1):152-165.
[145]Tarfaoui M, Akesbi S. A finite element model of mechanical properties of plain weave[J]. Colloids and Surfaces A:Physicochemical and Engineering Aspects,2001,187:439-448.
[146]Boisse P, Buet K, Gasser A, et al. Meso/macro-mechanical behaviour of textile reinforcements for thin composites[J]. Composites Science and Technology,2001,61(3):395-401.
[147]Gu B, Xu J. Finite element calculation of 4-step 3-dimensional braided composite under ballistic perforation[J]. Composites Part B:Engineering,2004,35(4):291-297.
[148]Littell J D, Binienda W K, Arnold W A, et al. Effect of microscopic damage events on static and ballistic impact strength of triaxial braid composites[J]. Composites Part A:Applied Science and Manufacturing,2009,40(12):1846-1862.
[149]Lin H, Sherburn M, Crookston J, et al. Finite element modelling of fabric compression[J]. Modelling and Simulation in Materials Science and Engineering,2008,16(3):035010.
[150]McBride T M. The large deformation behavior of woven fabric and microstructural evolution in formed textile composites[M]. Boston:Boston University 1998.
[151]Boisse P, Gasser A, Hivet G. Analyses of fabric tensile behaviour:determination of the biaxial tension-strain surfaces and their use in forming simulations[J]. Composites Part A:Applied Science and Manufacturing,2001,32(10):1395-1414.
[152]袁国勇ANSYS网格划分方法的分析[J].现代机械,2009,6：59-60.
[153]仇亚萍,黄俐军,冯立飞.基于ANSYS的有限元网格划分方法[J].机械管理开发,2007,6(99)：76-77.
[1541覃小雄.有限元接触分析及其在飞机投放挂架中的应用[D].西安：西安电子科技大学,2007.
[155]王建江,胡仁喜,刘英林ANSYS 11.0结构与热力学有限元分析实例指导教程[M].北京：机械工业出版社,2008.
[2]Alderson K L, Alderson A, Evans K E. The interpretation of the strain-dependent Poisson's ratio in auxetic polyethylene[J]. The Journal of Strain Analysis for Engineering Design,1997,32(3):201-212.
[3]Lakes R S. Foam structures with a negative Poisson's ratio[J]. Science,1987,235:1038-1040.
[4]Huang X, Blackburn S. Developing a new processing route to manufacture honeycomb ceramics with negative Poisson's ratio[J]. Key Engineering Materials,2001,206:201-204.
[5]Choi J B, Lakes R S. Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis [J]. International Journal of Fracture,1996,80(1):73-83.
[6]Lakes R S, Elms K. Indentability of conventional and negative Poisson's ratio foams[J]. Journal of composite materials,1993,27(12):1193-1202.
[7]Scarpa F, Ciffo L G, Yates J R. Dynamic properties of high structural integrity auxetic open cell foam[J]. Smart materials and structures,2004,13(1):49.
[8]Scarpa F, Bullough W A, Lumley P. Trends in acoustic properties of iron particle seeded auxetic polyurethane foam[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2004,218(2):241-244.
[9]Scarpa F, Smith F C. Passive and MR fluid-coated auxetic PU foam-mechanical, acoustic, and electromagnetic properties[J]. Journal of intelligent material systems and structures,2004,15(12): 973-979.
[10]易洪雷.三维机织复合材料的结构设计与力学性能研究[D].上海：东华大学,2000.
[11]戎琦.三维机织复合材料的织造技术[J].纤维复合材料,2007,24(1)：31-33.
[12]A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity[M]. New York:Dover Publications,1920.
[13]Gunton D J, Saunders G A. The Young's modulus and Poisson's ratio of arsenic, antimony and bismuth[J]. Journal of Materials Science,1972,7(9):1061-1068.
[14]Li Y. The anisotropic behavior of Poisson's ratio, Young's modulus, and shear modulus in hexagonal materials[J]. physica status solidi (a),1976,38(1):171-175.
[15]Nur A, Simmons G. The effect of saturation on velocity in low porosity rocks[J]. Earth and Planetary Science Letters,1969,7(2):183-193.
[16]Williams J L, Lewis J L. Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis[J]. Journal of biomechanical engineering,1982,104(1):50-56.
[17]Evans K E, Nkansah M A, Hutchinson I J, et al. Molecular network design[J]. Nature,1991, 353(6340):124-124.
[18]Tretiakov K V. Negative Poisson's ratio of two-dimensional hard cyclic tetramers[J]. Journal of Non-Crystalline Solids,2009,355(24):1435-1438.
[19]Gibson L J, Ashby M F, Schajer G S, et al. The mechanics of two-dimensional cellular materials[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences,1982, 382(1782):25-42.
[20]杨智春,邓庆田.负泊松比材料与结构的力学性能研究及应用[J].力学进展,2011,41(3)：335-350.
[21]Alderson A, Alderson K. L. Auxetic materials[J]. Proceedings of the Institution of Mechanical Engineers, Part G:Journal of Aerospace Engineering,2007,221(4):565-575.
[22]Larsen U D, Sigmund O, Bouwstra S. Larsen U D, Sigmund O. Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio[J]. Journal of microelectromechanical systems,1997,6(2):99-106.
[23]Theocaris P S, Stavroulakis G E, Panagiotopoulos P D. Negative Poisson's ratios in composites with star-shaped inclusions:a numerical homogenization approach[J]. Archive of Applied Mechanics, 1997,67(4):274-286.
[24]Lakes R. Deformation mechanisms in negative Poisson's ratio materials:structural aspects[J]. Journal of materials science,1991,26(9):2287-2292.
[25]Smith C W, Grima J N, Evans K E. A novel mechanism for generating auxetic behaviour in reticulated foams:missing rib foam model[J]. Acta materialia,2000,48(17):4349-4356.
[26]Gaspar N, Ren X J, Smith C W, et al. Novel honeycombs with auxetic behaviour[J]. Acta Materialia, 2005,53(8):2439-2445.
[27]Dolla W J S, Fricke B A, Becker B R. Structural and drug diffusion models of conventional and auxetic drug-eluting stents[J]. Journal of Medical Devices,2007,1:47.
[28]Evans K E, Nkansah M A, Hutchinson I J. Auxetic foams:modelling negative Poisson's ratios[J]. Acta metallurgica et materialia,1994,42(4):1289-1294.
[29]Choi J B, Lakes R S. Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson's ratio[J]. International journal of mechanical sciences,1995,37(1): 51-59.
[30]Liu Y, Hu H, Lam J K C, et al. Negative poisson's ratio weft-knitted fabrics[J]. Textile Research Journal,2010,80(9):856-863.
[31]Glazzard M, Breedon P. Weft-knitted auxetic textile design[J]. physica status solidi (b),2013.
[32]卢子兴,刘强,杨振宇.拉胀泡沫材料力学性能[J].宇航材料工艺,2011,41(1)：7-13.
[33]Tretiakov K V, Wojciechowski K W. Poisson's ratio of simple planar'isotropic'solids in two dimensions[J]. physica status solidi (b),2007,244(3):1038-1046.
[34]Wojciechowski K W. Solid phases of two-dimensional hard dumb-bells in the free volume approximation:Crystal-aperiodic-solid phase transition[J]. Physics Letters A,1987,122(6):377-380.
[35]Wojciechowski K W. Two-dimensional isotropic system with a negative Poisson ratio[J]. Physics Letters A,1989,137(1):60-64.
[36]Prall D, Lakes R S. Properties of a chiral honeycomb with a poisson's ratio of-1 [J]. International Journal of Mechanical Sciences,1997,39(3):305-314.
[37]Alderson A, Alderson K L, Attard D, et al. Elastic constants of 3-,4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading[J]. Composites Science and Technology, 2010,70(7):1042-1048.
[38]Grima J N, Farrugia P S, Gatt R, et al. On the auxetic properties of rotating rhombi and parallelograms: A preliminary investigation[J]. physica status solidi (b),2008,245(3):521-529.
[39]Gatt R, Attard D, Farrugia P S, et al. A realistic generic model for anti-tetrachiral systems[J]. physica status solidi (b),2013.
[40]Caddock B D, Evans K E. Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties[J]. Journal of Physics D:Applied Physics,1989,22(12):1877.
[41]Lakes R. Advances in negative Poisson's ratio materials[J]. Advanced Materials,1993,5(4):293-296.
[42]Pickles A P, Alderson K L, Evans K E. The effects of powder morphology on the processing of auxetic polypropylene (PP of negative Poisson's ratio)[J]. Polymer Engineering & Science,1996, 36(5):636-642.
[43]Alderson K L, Alderson A, Webber R S, et al. Evidence for uniaxial drawing in the fibrillated microstructure of auxetic microporous polymers[J]. Journal of materials science letters,1998,17(16): 1415-1419.
[44]Ravirala N, Alderson K L, Davies P J, et al. Negative Poisson's ratio polyester fibers[J]. Textile research journal,2006,76(7):540-546.
[45]Alderson K L, Fitzgerald A, Evans K E. The strain dependent indentation resilience of auxetic microporous polyethylene[J]. Journal of materials science,2000,35(16):4039-4047.
[46]Liu Y, Hu H. A review on auxetic structures and polymeric materials[J]. Sci. Res. Essays,2010,5(10): 1052-1063.
[47]He C, Liu P, Griffin A C. Toward negative Poisson ratio polymers through molecular design[J]. Macromolecules,1998,31(9):3145-3147.
[48]Liu P, He C, Griffin A C. Liquid crystalline polymers as potential auxetic materials[C]//Abstracts of papers of the american chemical society. New York:Division of Polymer Chemistry, American Chemical Society,1997,214:85.
[49]刘应良.负泊松比材料的合成及阻燃抗静电PVC新配方设计[D].郑州：郑州大学,2002.
[50]Li C, Xie X, Cao S. Synthesis and characterization of liquid crystalline copolyesters containing horizontal and lateral rods in main chain[J]. Polymers for Advanced Technologies,2002,13(3-4): 178-187.
[51]Grima J N, Jackson R, Alderson A, et al. Do zeolites have negative Poisson's ratios?[J]. Advanced Materials,2000,12(24):1912-1918.
[52]Grima J N, Evans K E. Auxetic behavior from rotating squares[J]. Journal of materials science letters, 2000,19(17):1563-1565.
[53]Grima J N, Evans K E. Auxetic behavior from rotating triangles[J]. Journal of materials science,2006, 41(10):3193-3196.
[54]Grima J N, Alderson A, Evans K E. Auxetic behaviour from rotating rigid units[J]. physica status solidi (b),2005,242(3):561-575.
[55]Alderson A. A triumph of lateral thought[J]. Chem. Ind,1999,10:384.
[56]Miki M, Murotsu Y. The peculiar behavior of the Poisson's ratio of laminated fibrous composites[J]. JSME international journal. Ser.1, Solid mechanics, strength of materials,1989,32(1):67-72.
[57]Milton G W. Composite materials with Poisson's ratios close to-1[J]. Journal of the Mechanics and Physics of Solids,1992,40(5):1105-1137.
[58]史炜,杨伟,李忠明,等.负泊松比材料研究进展[J].高分子通报,2003,6.
[59]Clarke J F, Duckett R A, Hine P J, et al. Negative Poisson's ratios in angle-ply laminates:theory and experiment[J]. Composites,1994,25(9):863-868.
[60]Hine P J, Duckett R A, Ward I M. Negative Poisson's ratios in angle-ply laminates[J]. Journal of materials science letters,1997,16(7):541-544.
[61]Alderson K L, Simkins V R, Coenen V L, et al. How to make auxetic fibre reinforced composites[J]. physica status solidi (b),2005,242(3):509-518.
[62]Evans K E, Donoghue J P, Alderson K L. The design, matching and manufacture of auxetic carbon fibre laminates[J]. Journal of composite materials,2004,38(2):95-106.
[63]Hadi Harkati E, Bezazi A, Scarpa F, et al. Modelling the influence of the orientation and fibre reinforcement on the Negative Poisson's ratio in composite laminates[J]. physica status solidi (b), 2007,244(3):883-892.
[64]Miller W, Hook P B, Smith C W, et al. The manufacture and characterisation of a novel, low modulus, negative Poisson's ratio composite[J]. Composites Science and Technology,2009,69(5):651-655.
[65]Hook P B, Evans K E, Hannington J P, et al. Composite materials and structures[P]. U.S. Patent: 10551316,2004-3-26.
[66]Bertoldi K, Reis P M, Willshaw S, et al. Negative Poisson's ratio behavior induced by an elastic instability[J]. Advanced materials,2010,22(3):361-366.
[67]Shim J, Perdigou C, Chen E R, et al. Buckling-induced encapsulation of structured elastic shells under pressure[J]. Proceedings of the National Academy of Sciences,2012,109(16):5978-5983.
[68]Choi J B, Lakes R S. Non-linear properties of polymer cellular materials with a negative Poisson's ratio[J]. Journal of Materials Science,1992,27(17):4678-4684.
[69]Bianchi M, Scarpa F, Smith C W. Shape memory behaviour in auxetic foams:Mechanical properties[J]. Acta Materialia,2010,58(3):858-865.
[70]Alderson A, Rasburn J, Evans K E, et al. Auxetic polymeric filters display enhanced de-fouling and pressure compensation properties [J]. Membrane Technology,2001,2001(137):6-8.
[71]Alderson A, Davies P J, Williams M R, et al. Modelling of the mechanical and mass transport properties of auxetic molecular sieves:an idealised organic (polymeric honeycomb) host-guest system[J]. Molecular Simulation,2005,31(13):897-905.
[72]Smith W A. Optimizing electromechanical coupling in piezocomposites using polymers with negative Poisson's ratio[C]//New York:Ultrasonics Symposium,1991. IEEE,1991:661-666.
[73]Gibiansky L V, Torquato S. On the use of homogenization theory to design optimal piezocomposites for hydrophone applications[J]. Journal of the Mechanics and Physics of Solids,1997,45(5): 689-708.
[74]Evans K E, Alderson A. Auxetic materials:Functional materials and structures from lateral thinking![J]. Advanced materials,2000,12(9):617-628.
[75]Ugbolue S C, Kim Y K, Warner S B, et al. The formation and performance of auxetic textiles. Part I: theoretical and technical considerations[J]. The Journal of The Textile Institute,2010,101(7): 660-667.
[76]Lim T C. Semi-auxetic yarns[J]. physica status solidi (b),2013.
[77]Hu H, Wang Z, Liu S. Development of auxetic fabrics using flat knitting technology[J]. Textile Research Journal,2011,81(14):1493-1502.
[78]李刚,郭兴峰,刘兰芳.三维机织物的设计与织造方法探讨[J].河北纺织,2008(1)：17-22.
[79]王荣荣.三维弹性机织物的研制与性能分析[D].天津：天津工业大学,2006.
[80]余育.三维正交机织复合材料力学性能研究[D].合肥：中国科学技术大学,2008.
[81]周凤飞.三维纺织技术发展现状[J].产业用纺织品,1996,14(3)：8-11.
[82]左惟炜.三维编织复合材料力学性能与工程应用研究[D].武汉：华中科技大学,2006.
[83]刘辉,阎良敏,甘应进,等.三维织物的编织技术[J].天津纺织科技,2001,39(3)：18-20.
[84]季丹.变截面三维编织计算机模拟[D].天津：天津工业大学,2011.
[85]吴华利.三维正交机织复合材料结构与力学性能研究[D].武汉：武汉理工大学,2007.
[86]刘淑萍,刘让同.三维织物结构设计[J].纺织科技进展,2006,6：42-48.
[87]郭兴峰.三维正交机织物结构的研究[D].天津：天津工业大学,2003.
[88]聂建斌.角联锁织物的开发及性能研究[D].上海：东华大学,2007.
[89]Mohamed M H, Bilisik A K. Multi-layer three-dimensional fabric and method for producing[P]. U.S. Patent:5465760,1995-11-14.
[90]Greenwood K. Marshall dann[P]. U.S. Patent:3818951,1974-6-2.
[91]Fukuta K, Nagatsuka Y, Tsuburaya S, et al. Three-dimensional fabric, and method and loom construction for the production thereof[P]. U.S. Patent:3834424,1974-9-10.
[92]King R W. Three dimensional fabric material[P]. U.S. Patent:4038440,1977-7-26.
[93]Mohamed M H, Zhang Z H. Method of forming variable cross-sectional shaped three-dimensional fabrics[P]. U.S. Patent:5085252,1992-2-4.
[94]马崇.一种三维机织物的织造设备及织造方法[P].中国专利：CN1730751B,2010-06-09.
[95]RUZAND J M, GUENOT G. Multiaxial three-dimensional fabric and process for its manufacture[P]. WIPO Patent:1994020658,1994-9-16.
[96]Farley G L. Method and apparatus for weaving a woven angle ply fabric[P]. U.S. Patent:5224519, 1993-7-6.
[97]Khokar N. Network-like woven 3D fabric material[P]. U.S. Patent:6431222,2002-8-13.
[98]崔俊芳.三维机织物织造方法的研究[D].天津：天津工业大学,2002.
[99]Anahara M, Yasui Y, Omori H. Three dimensional fabric and method for producing the same[P]. U.S. Patent:5137058,1992-8-11.
[100]Uchida H, Yamamoto T, Takashima H, et al. Three-dimensional weaving machine[P]. U.S. Patent: 6003563,1999-12-21.
[101]Bilisik A K. Multiaxial three-dimensional (3-D) circular woven fabric[P]. U.S. Patent:6129122, 2000-10-10.
[102]Lempriere B M. Poisson's ratio in orthotropic materials[J]. AIAA Journal,1968,6(11):2226-2227.
[103]郭兴峰,王瑞,黄故,等.接结经纱对三维正交机织物结构的影响[J].纺织学报,2005,26(1)：56-58.
[104]Byun J H, Chou T W. Three-dimensional textile composites. A review[C]//112th ASME Winter Annual Meeting, Symposium on Composites in Transportaion Vehicles, Atlanta, Georgia.1991.
[105]Whitney T J, Chou T W. Modeling of 3-D angle-interlock textile structural composites[J]. Journal of Composite Materials,1989,23(9):890-911.
[106]Peirce F T. The geometry of cloth structure[J]. The journal of the Textile Institute. Transactions, 1937,28:45-96.
[107]蔡雨,郑天勇,景书娟,等Peirce平纹机织物结构模型的计算精确度[J].纺织学报,2012,33(1)：48-53.
[108]贺显伟,汪军.织物组织几何模型及其在织物外观模拟上的应用[J].纺织导报,2003,6：114-116.
[109]Peirce F T. Geometrical principles applicable to the design of functional fabrics[J]. Textile Research Journal,1947,17(3):123-147.
[110]Kemp A, An extension of Peirce's cloth geometry to the treatment of nonlinear threads[J]. Journal of the Textile Institute,1958,49:44-48.
[111]Hearle J W S, Shanahan W J. An energy method for calculations in fabric mechanics part I: principles of the method[J]. Journal of the Textile Institute,1978,69(4):81-91.
[112]Hearle J W S, Potluri P, Thammandra V S. Modelling fabric mechanics[J]. Journal of the Textile Institute,2001,92(3):53-69.
[113]Weissenberg K. The use of a trellis model in the mechanics of homogeneous materials[J]. Journal of the Textile Institute Transactions,1949,40(2):89-110.
[114]Kilby W F. Planar stress-strain relationships in woven fabrics[J]. Journal of the Textile Institute Transactions,1963,54(1):9-27.
[115]Olofsson B. A general model of a fabric as a geometric-mechanical structure[J]. Journal of the Textile Institute Transactions,1964,55(11):541-557. [116] Kawabata S, Niwa M, Nanashima Y, et al. The Theoretical Investigation on the Biaxial Tensile Properties of Plain Knitted Fabrics, Part 1: Theory[J]. Sen'i Kikai Gakkaishi,1970,23:95-108.
[117]Hearle J W S, Grosberg P, Backer S. Structural Mechanics of Fibers, Yarns, and Fabrics[M]. New York:Wiley-Interscience,1969.
[118]Shanahan W J, Postle R. A theoretical analysis of the tensile properties of plain-knitted fabrics. Part I: the load-extension curve for fabric extension parallel to the courses[J]. Journal of the Textile Institute,1974,65(4):200-212.
[119]Leaf G A V, Kandil K H. The initial load-extension behaviour of plain-woven fabrics[J]. Journal of the textile institute,1980,71(1):1-7.
[120]Warren W E. The elastic properties of woven polymeric fabric[J]. Polymer Engineering & Science, 1990,30(20):1309-1313.
[121]Hu H, De Araujo M D, Fangueiro R, et al. Theoretical analysis of load-extension properties of plain weft knits made from high performance yarns for composite reinforcement[J]. Textile research journal,2002,72(11):991-996.
[122]Timosenko S P. History of strength of materials:with a brief account of the history of theory of elasticity and theory of structures[M]. New York:Dover publications,1953.
[123]Han S M, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories[J]. Journal of Sound and Vibration,1999,225(5):935-988.
[124]Hertz H. On the contact of elastic solids[J]. J. reine angew. Math,1881,92:156-171.
[125]Hamrock B J, Dowson D. Ball Bearing Lubrication:The Elastohydrodynamics of Elliptical Contacts[M]. New York:Wiley,1981.
[126]Prescott J. Applied elasticity[M]. London:Longmans, Green and Co.,1924.
[127]Puttock M J, Thwaite E G. Elastic compression of spheres and cylinders at point and line contact[M]. Melbourne, Australia:Commonwealth Scientific and Industrial Research Organization,1969.
[128]孔祥安,固体接触力学[M].北京：中国铁道出版社,1999.
[129]Sadykova F K. The Poisson ratio of textile fibres and yarns[J]. Fibre Chemistry,1972,3(2):180-183.
[130]Kellog O D, Foundations of Potential Theory[M]. New York:Dover,1929.
[131]王勖成.有限单元法[M].北京：清华大学出版社,2003.
[132]Clough R W. The finite element method in plane stress analysis[M] New York:American Society of Civil Engineers,1960.
[133]Turner M J. Stiffness and deflection analysis of complex structures[J]. J. Aeronautical Science,1956, 23(9):805-823.
[134]顾伯洪.机织物拉伸的有限元模拟及应用[J].中国纺织大学学报,1998,3：12-13.
[135]Lloyd D W. The analysis of complex fabric deformations[J]. Mechanics of flexible fibre assemblies, 1980:311-342.
[136]Collier B J. Measurement of fabric drape and its relation to fabric mechanical properties and subjective evaluation[J]. Clothing and Textiles Research Journal,1991,10(1):46-52.
[137]Kim J H. Fabric mechanics analysis using large deformation orthotropic shell theory[D]. Raleigh: North Carolina State University,1991.
[138]Simo J C, Fox D D. On a stress resultant geometrically exact shell model. Part Ⅰ:Formulation and optimal parametrization[J]. Computer Methods in Applied Mechanics and Engineering,1989,72(3): 267-304.
[139]Simo J C, Fox D D, Rifai M S. On a stress resultant geometrically exact shell model. Part Ⅲ: Computational aspects of the nonlinear theory [J]. Computer Methods in Applied Mechanics and Engineering,1990,79(1):21-70.
[140]Simo J C, Fox D D, Rifai M S. On a stress resultant geometrically exact shell model. Part Ⅱ:The linear theory; computational aspects[J]. Computer Methods in Applied Mechanics and Engineering, 1989,73(1):53-92.
[141]Deng S. Nonlinear fabric mechanics including material nonlinearity, contact, and an adaptive global solution algorithm[D]. Raleigh:North Carolina State University,1994.
[142]Eischen J W, Deng S, Clapp T G. Finite-element modeling and control of flexible fabric parts[J]. Computer Graphics and Applications, IEEE,1996,16(5):71-80.
[143]Kang T J, Yu W R. Drape simulation of woven fabric by using the finite-element method[J]. Journal of the Textile Institute,1995,86(4):635-648.
[144]Ascough J, Bez H E, Bricis A M. A simple beam element, large displacement model for the finite element simulation of cloth drape[J]. Journal of the Textile Institute,1996,87(1):152-165.
[145]Tarfaoui M, Akesbi S. A finite element model of mechanical properties of plain weave[J]. Colloids and Surfaces A:Physicochemical and Engineering Aspects,2001,187:439-448.
[146]Boisse P, Buet K, Gasser A, et al. Meso/macro-mechanical behaviour of textile reinforcements for thin composites[J]. Composites Science and Technology,2001,61(3):395-401.
[147]Gu B, Xu J. Finite element calculation of 4-step 3-dimensional braided composite under ballistic perforation[J]. Composites Part B:Engineering,2004,35(4):291-297.
[148]Littell J D, Binienda W K, Arnold W A, et al. Effect of microscopic damage events on static and ballistic impact strength of triaxial braid composites[J]. Composites Part A:Applied Science and Manufacturing,2009,40(12):1846-1862.
[149]Lin H, Sherburn M, Crookston J, et al. Finite element modelling of fabric compression[J]. Modelling and Simulation in Materials Science and Engineering,2008,16(3):035010.
[150]McBride T M. The large deformation behavior of woven fabric and microstructural evolution in formed textile composites[M]. Boston:Boston University 1998.
[151]Boisse P, Gasser A, Hivet G. Analyses of fabric tensile behaviour:determination of the biaxial tension-strain surfaces and their use in forming simulations[J]. Composites Part A:Applied Science and Manufacturing,2001,32(10):1395-1414.
[152]袁国勇ANSYS网格划分方法的分析[J].现代机械,2009,6：59-60.
[153]仇亚萍,黄俐军,冯立飞.基于ANSYS的有限元网格划分方法[J].机械管理开发,2007,6(99)：76-77.
[1541覃小雄.有限元接触分析及其在飞机投放挂架中的应用[D].西安：西安电子科技大学,2007.
[155]王建江,胡仁喜,刘英林ANSYS 11.0结构与热力学有限元分析实例指导教程[M].北京：机械工业出版社,2008.