聚氯乙烯膜材各向异性超弹性本构模型
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摘要
为反映聚氯乙烯(PVC)膜材在拉剪耦合应力作用下呈现的大变形、非线性和各向异性等力学特性,基于纤维增强复合材料连续介质力学理论,将应变能解耦为经、纬向纤维束的拉伸变形能和两向纤维束间角度变化产生的剪切变形能,建立了各向异性超弹性本构模型。推导了适用于PVC膜材偏轴拉伸的本构模型表达式,给出了获取模型参数的具体方法,并通过堆载试验进行了验证分析。结果表明:该模型能够很好地预测PVC膜材偏轴拉伸应力-应变曲线,且较CECS 158:2015中建议模型的计算精度更高。
Based on the fiber-reinforced continuum mechanics theory, a simple anisotropic hyperelastic constitutive model was proposed to describe the large deformation, highly nonlinear and strongly anisotropic mechanical properties of PVC coated fabrics under tensile-shear coupling stresses. The strain energy of the model was additively decomposed into two parts nominally representing the fiber stretches and fiber-fiber interaction, respectively. The general expression of PVC coated fabrics was derived, and the specific method of obtaining model parameters was presented. The proposed model was verified by vertical loading tests. Results show that the proposed model can predict off-axis stress-strain curves of PVC coated fabrics, and the calculation accuracy is higher than the model recommended by the CECS 158:2015.
Based on the fiber-reinforced continuum mechanics theory, a simple anisotropic hyperelastic constitutive model was proposed to describe the large deformation, highly nonlinear and strongly anisotropic mechanical properties of PVC coated fabrics under tensile-shear coupling stresses. The strain energy of the model was additively decomposed into two parts nominally representing the fiber stretches and fiber-fiber interaction, respectively. The general expression of PVC coated fabrics was derived, and the specific method of obtaining model parameters was presented. The proposed model was verified by vertical loading tests. Results show that the proposed model can predict off-axis stress-strain curves of PVC coated fabrics, and the calculation accuracy is higher than the model recommended by the CECS 158:2015.
引文
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[12] JEKEL C F, VENTER G, VENTER M P. Modeling PVC-coated polyester as a hypoelastic non-linear orthotropic material[J]. Composite Structures, 2017, 161: 51- 64.
[13] 张营营,许珊珊,徐俊豪,等. 聚四氟乙烯膜材黏弹性本构关系[J]. 建筑结构学报, 2016, 37(6): 245-252. (ZHANG Yingying, XU Shanshan, XU Junhao, et al. Viscoelastic constitutive relations of polytetrafluoroethylene coated fabrics[J]. Journal of Building Structures,2016,37(6):245-252.(in Chinese))
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[16] PENG X Q, GUO Z Y, DU T L, et al. A simple anisotropic hyperelastic constitutive model for textile fabrics with application to forming simulation[J]. Composites: Part B, 2013, 52: 275-281.
[17] GONG Y, YAN D, YAO Y, et al. An anisotropic hyperelastic constitutive model with tension-shear coupling for woven composite reinforcements[J]. International Journal of Applied Mechanics, 2017, 9(6): 1750083.
[18] SPENCER A J M. Continuum theory of the mechanics of fibre-reinforced composites[M].Vienna:Springer-Verlag, 1984: 33-71.
[19] 董金平,张志强. 基于横观各向同性超弹性理论的短纤维增强橡胶本构模型的建立与应用[J]. 计算力学学报, 2016, 33(2): 231-237. (DONG Jinping, ZHANG Zhiqiang. Establishment and application of short fiber reinforced rubber constitutive model based on transversely isotropic hyperelastic theory[J]. Chinese Journal of Computational Mechanics, 2016, 33(2): 231-237.(in Chinese))
[20] 膜结构检测技术规程: DG/TJ 08-2019—2007[S]. 上海: 上海市建筑建材业市场管理总站,2012.
[21] ZHANG Y Y, XU S S, XUE J G, et al. Anisotropic mechanical properties and constitutive relations of PTFE coated glass fibers[J]. Composite Structures, 2017, 179: 601- 616.
[22] 李阳. 建筑膜材料和膜结构的力学性能研究与应用[D]. 上海:同济大学, 2007: 58-88. (LI Yang. Study and applications on mechanical properties of membrane materials and structures[D].Shanghai: Tongji University, 2007: 58-88. (in Chinese))
[2] 陈务军. 膜结构工程设计[M]. 北京: 中国建筑工业出版社, 2005: 8-14. (CHEN Wujun. Design of membrane structure engineering[M]. Beijing: China Architecture & Building Press, 2005: 8-14.(in Chinese))
[3] 膜结构技术规程:CECS 158:2015[S]. 北京: 中国计划出版社, 2015.(Specification for design of membrane structure: CECS 158:2015[S]. Beijing: China Planning Press, 2015. (in Chinese))
[4] 钱基宏,宋涛,刘枫,等. 关于张拉膜结构设计与施工规定的建议[J]. 建筑结构学报, 2003, 24(3): 55- 60. (QIAN Jihong, SONG Tao, LIU Feng, et al. Some suggestions about the provisions of design and construction of membrane structures[J]. Journal of Building Structures,2003,24(3):55- 60.(in Chinese))
[5] 汪大绥,张伟育,方卫,等. 世博轴大跨度索膜结构设计与研究[J]. 建筑结构学报, 2010,31(5): 1-12. (WANG Dasui, ZHANG Weiyu, FANG Wei, et al. Design and study of an long span cable-membrane structure for the Expo Axis[J]. Journal of Building Structures, 2010, 31(5): 1-12.(in Chinese))
[6] PEIRCE F T. The geometry of cloth structure[J]. Journal of the Textile Institute Transactions, 1937, 28(3): 45-96.
[7] TESTA R B, SPILLERS W R, STUBBS N. Bilinear model for coated square fabrics[J]. Journal of the Engineering Mechanics Division, 1978, 104(5): 1027-1042.
[8] 罗国建,丁辛,陈守辉,等.涂层过程中织物拉伸对膜材料拉伸性能的影响[J].纺织学报,2007, 28(7):47-51. (LUO Guojian, DING Xin, CHEN Shouhui, et al. Effects of fabric extension during coating on the tensile performance of membrane material[J]. Journal of Textile Research, 2007, 28(7): 47-51.(in Chinese))
[9] KATO S, YOSHINO T, MINAMI H. Formulation of constitutive equations for fabric membranes based on the concept of fabric lattice model[J]. Engineering Structures, 1999, 21(8): 691-708.
[10] PARGANA J B, LEIT?O V M A. A simplified stress-strain model for coated plain weave fabrics used in tensioned fabric structures[J]. Engineering Structures, 2015, 84: 439- 450.
[11] GALLIOT C, LUCHSINGER R H. A simple model describing the non-linear biaxial tensile behaviour of PVC-coated polyester fabrics for use in finite element analysis[J]. Composite Structures, 2009, 90(4): 438- 447.
[12] JEKEL C F, VENTER G, VENTER M P. Modeling PVC-coated polyester as a hypoelastic non-linear orthotropic material[J]. Composite Structures, 2017, 161: 51- 64.
[13] 张营营,许珊珊,徐俊豪,等. 聚四氟乙烯膜材黏弹性本构关系[J]. 建筑结构学报, 2016, 37(6): 245-252. (ZHANG Yingying, XU Shanshan, XU Junhao, et al. Viscoelastic constitutive relations of polytetrafluoroethylene coated fabrics[J]. Journal of Building Structures,2016,37(6):245-252.(in Chinese))
[14] DINH T D, REZAEI A, LAET L D, et al. A new elasto-plastic material model for coated fabric[J]. Engineering Structures, 2014, 71: 222-233.
[15] 张义同. 织物力学研究的新进展[J]. 力学进展, 2003, 33(2): 217-226. (ZHANG Yitong. The recent advances in fabric mechanics[J]. Advance in Mechanics, 2003, 33(2): 217-226.(in Chinese))
[16] PENG X Q, GUO Z Y, DU T L, et al. A simple anisotropic hyperelastic constitutive model for textile fabrics with application to forming simulation[J]. Composites: Part B, 2013, 52: 275-281.
[17] GONG Y, YAN D, YAO Y, et al. An anisotropic hyperelastic constitutive model with tension-shear coupling for woven composite reinforcements[J]. International Journal of Applied Mechanics, 2017, 9(6): 1750083.
[18] SPENCER A J M. Continuum theory of the mechanics of fibre-reinforced composites[M].Vienna:Springer-Verlag, 1984: 33-71.
[19] 董金平,张志强. 基于横观各向同性超弹性理论的短纤维增强橡胶本构模型的建立与应用[J]. 计算力学学报, 2016, 33(2): 231-237. (DONG Jinping, ZHANG Zhiqiang. Establishment and application of short fiber reinforced rubber constitutive model based on transversely isotropic hyperelastic theory[J]. Chinese Journal of Computational Mechanics, 2016, 33(2): 231-237.(in Chinese))
[20] 膜结构检测技术规程: DG/TJ 08-2019—2007[S]. 上海: 上海市建筑建材业市场管理总站,2012.
[21] ZHANG Y Y, XU S S, XUE J G, et al. Anisotropic mechanical properties and constitutive relations of PTFE coated glass fibers[J]. Composite Structures, 2017, 179: 601- 616.
[22] 李阳. 建筑膜材料和膜结构的力学性能研究与应用[D]. 上海:同济大学, 2007: 58-88. (LI Yang. Study and applications on mechanical properties of membrane materials and structures[D].Shanghai: Tongji University, 2007: 58-88. (in Chinese))