现代织物类膜材料力学性能研究进展

张营营; 张其林; 徐俊豪; 生凌宇

doi:10.3724/j.gjgS23080101

现代织物类膜材料力学性能研究进展

doi: 10.3724/j.gjgS23080101

1. 中国矿业大学, 江苏省土木工程环境灾变与结构可靠性重点实验室, 江苏徐州 221116;
2. 中国矿业大学力学与土木工程学院, 江苏徐州 221116;
3. 同济大学土木工程学院, 上海 200092

基金项目:

国家自然科学基金(52308222，52278229)；中国博士后科学基金(2023M733775)；工程结构性能演化与控制教育部重点实验室开放基金(2019KF-3)。

详细信息

作者简介:
张营营，博士，教授，主要从事大跨空间结构研究。Email：yyzhang@cumt.edu.cn

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出版历程
- 收稿日期: 2023-08-01
- 网络出版日期: 2024-03-29
- 刊出日期: 2024-02-25

Advances in Research on Material Mechanical Properties of Modern Architectural Coated Fabrics

1. Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Engineering, China University of Mining and Technology, Xuzhou 221116, China;
2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China;
3. College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 织物膜材因其轻质、高强、耐候性及加工运输便捷等优势，广泛应用于公共建筑、应急救援、航空航天、工业及军事等领域。近年来，为精确分析织物膜结构并推动其在不同领域应用，织物膜材的力学性能成为研究焦点。为此采用CiteSpace对国内外20余年的相关文献进行深入分析，通过可视化知识图谱阐述了织物膜结构研究热点的演化进程，并系统分析了织物膜材测试方法、力学性能及宏-细观本构模型等方面的研究进展。梳理发现国内膜结构的早期研究主要集中在结构找形和静力分析，随着膜结构在我国不同领域的深入运用，相关研究逐渐扩展到材料的本构模型、强度准则、结构风致灾变等方面： 1)织物膜材的拉伸性能与其细观结构、基布编织工艺、涂层工艺及纤维类型等多种因素相关，呈现典型的各向异性，其抗拉强度随偏轴角度的增加呈现“U”型和“W”型两种变化特征。2)双轴剪切测试法可使得试件核心区域的剪应力呈均匀分布，目前被广泛应用于膜材剪切性能测试。3)膜材撕裂强度受测试方法的影响显著，现有研究多集中在材料撕裂性能上，初始缺陷对膜结构的静、动力学性能的影响机理需进一步明确。4)目前关于膜结构连接部位的研究多集中在膜片与膜片热合连接试件的面内拉伸性能上，忽略了面外荷载下连接部位易出现的剥离破坏。5)织物膜材本构模型分为细观机理模型与宏观唯象模型，现有的宏观模型基本实现了膜材非线性、非弹性、黏弹性等力学特征的描述，细观模型多注重拉伸刚度预测，缺乏对抗拉强度预测的相关研究。织物膜材的研究目前已取得长足发展，但一些方面仍需进一步研究： 1)现阶段织物膜材分类依据单调，未考虑预定用途和特性差异，有必要对其分类依据进一步细化和完善。2)撕裂破坏是膜结构的主要破坏模式，但现行设计规范中并没有得到充分的体现。3)面内拉伸试验难以反映膜材热合区域真实的应力状态、力学性能和失效模式，热合焊接工艺对拼接膜材性能的影响机理有待研究。4)目前关于织物膜材以及连接部位的疲劳性能研究极少，膜材的疲劳损伤机理尚未明确。
- 织物膜材 /
- 力学性能 /
- 本构模型 /
- CiteSpace
Abstract: Due to the advantages such as lightweight, high strength, weather resistance and convenient processing and transportation, coated fabrics are widely applicated in various domains, including public buildings, emergency rescue, aerospace, industry, and the military. In recent years, to precisely analyze coated fabrics and drive their applications across multiple fields, the mechanical properties have become a central focus. An in-depth analysis of relevant literature spanning over two decades from both domestic and international sources was conducted utilizing CiteSpace. It employs visual knowledge mapping to elucidate the evolution of research hotspots in membrane structure and systematically examines research advancements in testing methods, mechanical properties and macro-micro constitutive models. A review reveals that the early stages were primarily centered around structural form-finding and static analysis. However, with the wide application of membrane structure in different fields in China, the research has been expanded to various fields such as material non-linear constitutive behavior, strength criteria and structural risk assessment. 1) The tensile performance of coated fabrics is influenced by various factors, including microstructure, base fabric weaving process, coating technique and fiber type, resulting in distinct anisotropic characteristics. The tensile strength exhibits two distinct variations, resembling a "U" shape and a "W" shape, with increasing off-axis angles. 2) Biaxial shear testing methods have been widely adopted to ensure a uniform distribution of shear stress in the core region of specimens and are currently prevalent in assessing shear performance of coated fabrics. 3) The tear strength of coated fabrics is significantly influenced by the testing method, with current research predominantly focused on tear performance of coated fabrics. The impact mechanism of initial defects on the static and dynamic performance of membrane structures requires further clarification. 4) Presently, research on membrane structure connections primarily emphasizes in-plane tensile performance of bonded connections between membrane panels, overlooking the potential of delamination failures under out-of-plane loads. 5) Constitutive models for coated fabrics are categorized into micromechanical models and macroscopic phenomenological models. Existing macroscopic models have largely succeeded in describing the nonlinear, non-elastic and viscoelastic mechanical characteristics of coated fabrics, while micro-mechanical models tend to focus more on predicting tensile stiffness, with relatively limited research pertaining to predicting tensile strength. After years of effort, the research on coated fabrics has made substantial progress. However, several issues still require further investigation. 1) The current classification of coated fabrics is monotonous and fails to consider differences in intended use and characteristics. 2) Membrane structure damage primarily involves tearing, yet design specifications have not been adequately addressed. 3) In-plane tensile testing is difficult to accurately reflect the real stress states, mechanical properties and failure modes in the heat-sealed regions of coated fabrics. The impact mechanisms of heat-sealing welding processes on the performance of joint of coated fabrics require further investigation. 4) Currently, there is a paucity of research on the fatigue performance of coated fabrics and the connection points, and the fatigue damage mechanisms have yet to be clearly elucidated.
- coated fabrics /
- mechanical properties /
- constitutive model /
- CiteSpace

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参考文献(98)

[1]	中国工程建设标准化协会. 膜结构技术规程:CECS 158:2015[S]. 北京:中国计划出版社, 2015.
[2]	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.
[3]	Chen Z Q, Zhang Y Y, Xu J H, et al. Off-axis tearing properties of the biaxial warp-knitted fabrics[J/OL]. Composite Structures, 2022, 300[2022-08-29]. https://doi.org/10.1016/j.compstruct.2022.116168.
[4]	张营营, 徐俊豪, 曹原, 等. PTFE膜材料的偏轴拉伸性能及破坏机理[J]. 哈尔滨工业大学学报, 2016, 48(12):135-141 , 164.
[5]	王腾飞. 建筑织物膜材拉伸与撕裂性能研究[D]. 哈尔滨:哈尔滨工业大学, 2018.
[6]	徐俊豪. 涂层织物类建筑膜材料的本构关系模型研究[D]. 徐州:中国矿业大学, 2018.
[7]	杨彬, 霍震霆, 罗晓群, 等. 针织物与机织物膜材的力学特性对比[J]. 建筑材料学报, 2022, 25(8):860-868.
[8]	张营营, 黄源, 徐俊豪, 等. 不同拉伸速率下平织PVC膜材偏轴拉伸性能[J]. 建筑材料学报, 2016, 19(3):606-612.
[9]	Chen J W, Chen W J, Zhang D X. Experimental study on uniaxial and biaxial tensile properties of coated fabric for airship envelopes[J]. Journal of Reinforced Plastics and Composites, 2014, 33(7):630-647.
[10]	Ambroziak A. Mechanical properties of polyester coated fabric subjected to biaxial loading[J/OL]. Journal of Materials in Civil Engineering, 2015, 27(11)[2015-02-10]. https://doi.org/10.1061/(ASCE)MT.1943- 5533.0001265.
[11]	Ambroziak A, Kłosowski P. Influence of water-induced degradation of polytetrafluoroethylene (PTFE)-coated woven fabrics mechanical properties[J]. Materials, 2022, 15:1-19.
[12]	徐俊豪. 织物类建筑膜材料力学模型及多尺度计算方法研究[D]. 徐州:中国矿业大学, 2022.
[13]	易洪雷, 丁辛, 陈守辉. 建筑膜材料双轴向拉伸弹性常数的估算方法[J]. 工程力学, 2006, 23(10):180-183.
[14]	Chen W J, Gao C J, Zhang D X, et al. A new biaxial tensile shear test method to measure shear behaviour of coated fabrics for architectural use[J]. Composite Structures, 2018, 203:943-951.
[15]	The Membrane Structures Association of Japan. Test methods for membrane materials (coated fabrics)-qualities and performances[S]. Japan:The Membrane Structures Association of Japan, 2003.
[16]	上海市住房和城乡建设管理委员会. 膜结构检测标准:DG/T J08-2019-2019[S]. 上海:同济大学出版社, 2020.
[17]	Forster M M. European design guide for tensile surface structures[S]. Germany:Tensinet, 2004.
[18]	Société d'Edition du Bâtiment et des Travaux Publics (SEBTP). Recommandations pour la conception, la confection et la mise en oeuvre des ouvrages permanents de couverture textile[S]. Paris:SEBTP, 2009.
[19]	The American Society of Civil Engineers. Tensile membrane structures[S]. American:American Society of Civil Engineers, 2010.
[20]	European Committee for Standardisation (CEN). EN 17117-1 rubber or plastic-coated fabrics-mechanical test methods under biaxial stress states-part 1:tensile stiffness properties[S]. European:CEN, 2018.
[21]	Uhlemann J. Elastic constants of architectural fabrics for design purposes[D]. Duisburg:Universität Duisburg-Essen, 2016.
[22]	Uhlemann J, Stranghöner N, Schmidt H, et al. Effects on elastic constants of technical membranes applying the evaluation methods of MSAJ/M-02-1995[J]. Proceedings of the Structural Membranes, 2011, 5-7:648-659.
[23]	Bridgens B N, Gosling P D. Interpretation of results from the MSAJ testing method for elastic constants of mem brane materials[J/OL]. Neuroscience Letters, 2010[2020-01-13]. https://doi.org/10.1016/j.neulet.2015.12.011.
[24]	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.
[25]	Yang B, Shang Y, Yu Z, et al. Comprehensive study on mechanical properties of coated biaxial warp-knitted fabrics[J]. Journal of Reinforced Plastics and Composites, 2022, 41(1/2):3-19.
[26]	Uhlemann J, Stranghöner N, Motevalli M, et al. Architectural woven polyester fabrics:examination of possible classification of stiffness values in correlation with strength values[J]. Architectural Engineering and Design Management, 2021, 17(3/4):281-298.
[27]	Van Craenenbroeck M, Mollaert M, De Laet L. Analysis and statistical interpretation of biaxial material constants derived according to EN 17117-1:2018[J/OL]. Composite Structures, 2021, 259[2021-01-13]. https://doi.org/10.1016/j.compstruct.2020.113235.
[28]	陈务军, 高成军, 石泰百, 等. 一种双轴拉伸强度试验十字型试件及其制作方法:CN107271275B[P]. 2020-11-10.
[29]	Shi T B, Hu J H, Chen W J, et al. Biaxial tensile behavior and strength of architectural fabric membranes[J/OL]. Polymer Testing, 2020, 82[2020-02-01]. https://api.semanticscholar.org/CorpusID:210238908.
[30]	Gao C J, Chen W J, Hu J H, et al. A new constitutive model on biaxial tensile behavior of architectural fabrics[J/OL]. Polymer Testing, 2020, 87[2020-04-14]. https://doi.org/10.1016/j.polymertesting.2020.106519.
[31]	Chen S H, Ding X, Yi H L. On the anisotropic tensile behaviors of flexible polyvinyl chloride-coated fabrics[J]. Textile Research Journal, 2007, 77(6):369-374.
[32]	Qiu Z Y, Chen W J, Gao C J, et al. Experimental and numerical study on nonlinear mechanical properties of laminated woven fabrics[J]. Construction and Building Materials, 2018, 164:672-681.
[33]	Kawabata S, Niwa M. Objective measurement of fabric mechanical property and quality[J]. International Journal of Clothing Science and Technology, 1991, 3(1):7-18.
[34]	Vysochina K, Gabor A, Bigaud D, et al. Identification of shear stiffness of soft orthotropic textile composites:part I-development of a mixed method for shear elastic constant identification[J]. Journal of Industrial Textiles, 2005, 35(2):137-155.
[35]	Xu J H, Zhang Y Y, Wu M E, et al. A phenomenological material model for PTFE coated fabrics[J/OL]. Construction and Building Materials, 2020, 237[2020-03-20]. https://doi.org/10.1016/j.conbuildmat.2019. 117667.
[36]	高成军, 陈务军, 邱振宇, 等. 建筑织物膜材双轴剪切试验与分析[J]. 实验力学, 2016, 31(1):25-30.
[37]	汪泽幸, 吴波, 朱文佳, 等. 应力回复对PVC膜材应力松弛行为的影响[J]. 东华大学学报(自然科学版), 2020, 46(5):712-718.
[38]	Meng L, Wu M E. Study on stress relaxation of membrane structures in the prestress state by considering viscoelastic properties of coated fabrics[J]. Thin-Walled Structures, 2016, 106:18-27.
[39]	Zhang Y Y, Xu S S, Zhang Q L, et al. Experimental and theoretical research on the stress-relaxation behaviors of PTFE coated fabrics under different temperatures[J]. Advances in Materials Science and Engineering, 2015, 2015:1-12.
[40]	汪泽幸, 李帅, 谭冬宜, 等. 循环加载对PVC膜材应力松弛行为的影响[J]. 空间结构, 2023, 29(1):83-88.
[41]	杨彬, 吴梦琳, 吕冰, 等. PVDF膜材在自然老化和人工加速老化下力学性能变化的相关性研究[J]. 建筑结构, 2021, 51(23):48-53 , 60.
[42]	郭珊珊, 郝恩全, 李宏杰, 等. 聚氯乙烯膜结构复合材料的光氧老化行为及评价[J]. 纺织学报, 2022, 43(6):1-8.
[43]	Krimi I, Ducoulombier L, Dakhli Z, et al. Durability of textile facing materials for construction:operating accelerated ageing protocol results in basic medium for lifetime estimation in conditions of use[J].Journal of Industrial Textiles, 2016, 46(3):929-949.
[44]	Zhang Y Y, Wu M, Xu J H, et al. Dynamic mechanical properties of architectural coated fabrics under different temperature and excitation frequency[J]. Polymer Composites, 2020, 41(12):5156-5166.
[45]	Zhang Y Y, Zhang Q L, Zhou C Z, et al. Effect of temperature and water mmersion on the mechanical properties of coated fabrics[J]. Advanced Materials Research, 2010, 129-131:230-234.
[46]	Chen Z R, Kuai B L, Zhang Q L. Experimental research on mechanical properties of PVC membrane after artificial accelerated aging[J]. Structural Engineers, 2013, 5:1-5.
[47]	Laure D, Zakaria D, Zoubeir L. Durability of textile facing materials for construction:implementation of an accelerated aging test by hydrolysis[J]. Journal of Industrial Textiles, 2014, 45(6):1288-1307.
[48]	Imane K, Laure D, Zakaria D, et al. Durability of textile facing materials for construction:operating accelerated ageing protocol results in basic medium for lifetime estimation in conditions of use[J]. Journal of Industrial Textiles, 2015, 46(3):929-949.
[49]	Luis S J, Raquel C, Raul F. A study on the durability properties of textile membranes for architectural purposes[J]. Procedia Engineering, 2016, 155:230-237.
[50]	Zhang Y Y, Zhang M Y. Aging properties of polyvinylidenefluoridecoated polyesters used in tensioned membrane structure:effect of loading protocol and environment[J]. Advances in Materials Science and Engineering, 2017, 24:1-10.
[51]	Pawel K, Krzysztof Z, Krzysztof W. Influence of artificial thermal ageing on polyester-reinforced and polyvinyl chloride coated AF9032 technical fabric[J]. Textile Research Journal, 2019, 89(21/22):4632-4646.
[52]	包晗, 张旭波, 吴明儿. PVC涂层聚酯纤维膜材撕裂性能试验研究[J]. 建筑材料学报, 2020, 23(3):631-641.
[53]	何日劲. 建筑织物膜材撕裂强度理论与破坏机理研究[D]. 哈尔滨:哈尔滨工业大学, 2021.
[54]	陈建稳, 关晓宇, 张若男, 等. 拉剪耦合应力对经编织物类膜材双轴撕裂破坏影响机制[J]. 华南理工大学学报(自然科学版), 2021, 49(10):78-86.
[55]	丁凯, 陈永霖, 陈亚飞, 等. 平流层飞艇蒙皮材料撕裂性能影响因素研究[J]. 空间结构, 2021, 27(3):61-67.
[56]	陈亚飞, 陈永霖, 王凤欣, 等. 平流层飞艇蒙皮膜材的撕裂性能研究[J]. 空间结构, 2018, 34(3):66-74 , 82.
[57]	陈建稳, 马俊杰, 赵兵, 等. 双轴经编织物膜梯形撕裂扩展机理及其拉剪耦合行为[J]. 复合材料学报, 2023, 40(12):6922-6933.
[58]	张旭波, 吴明儿, 包晗. 涂层织物类膜材的偏轴梯形撕裂行为[J]. 建筑材料学报, 2021, 24(1):121-130.
[59]	Bao H, Wu M E, Zhang X B. Influencing factors and evaluation methods of tearing resistance of coated fabric membranes[J/OL]. Journal of Industrial Textiles, 2022[2022-10-26].https://doi.org/10.1177/15280837221136308.
[60]	全国纺织品标准化技术委员会. 纺织品织物撕破性能:GB/T 3917.3-2009[S]. 北京:中国标准出版社, 2009.
[61]	Bao H, Wu M E, Zhang X B. Tearing analysis of PVC coated fabric under uniaxial and biaxial central tearing tests[J]. Journal of Industrial Textiles, 2022, 51(6):900-925.
[62]	Bao H, Wu M E, Zhang X B. Study on tearing tests and the determination of fracture toughness of PVC-coated fabric[J]. Journal of Industrial Textiles, 2022, 51(6):977-1006.
[63]	Sun X Y, He R J, Wu Y, et al. Uniaxial tearing properties and the tearing residual strength models of PTFE coated fabric[J]. Structures, 2021, 33:1354-1364.
[64]	Dobilaitė V, Jucienė M, Bliūdžius R, et al. Investigation of some weathering impacts on tearing properties of PVC-coated fabrics used for architectural purposes[J]. Journal of Industrial Textiles, 2022, 51(3):5328-5346.
[65]	He R J, Sun X Y, Wu Y. Central crack tearing test and fracture parameter determination of PTFE coated fabric[J]. Construction and Building Materials, 2019, 208:472-481.
[66]	Zhang Y Y, Xu J H, Zhou Y, et al. Central tearing behaviors of PVC coated fabrics with initial notch[J]. Composite Structures, 2019, 208:618-633.
[67]	生凌宇, 张兰兰, 张营营, 等. 裂纹-孔洞缺陷下PVC涂层织物类膜材的撕裂行为[J/OL]. 哈尔滨工业大学学报, 2023[2023-07-14]. http://kns.cnki.net/kcms/detail/23. 1235.T.20230331.1711.020.html.
[68]	Xu J H, Zhang Y Y, Wang Y H, et al. Quasi-static puncture resistance behaviors of architectural coated fabric[J/OL]. Composite Structures, 2021, 273[2021-07-12]. https://doi.org/10.1016/j.compstruct.2021. 114307.
[69]	徐英, 胡红. 经编双轴向柔性复合材料的顶破性能[J]. 东华大学学报(自然科学版), 2007(4):475-477.
[70]	侯利民, 王盛楠. 柔性复合材料及其增强体顶破形态和机理的研究[J]. 纤维复合材料, 2012, 33(1):33-36.
[71]	侯利民. 柔性复合材料顶破机理和破坏形态的分析模型[D]. 上海:东华大学, 2013.
[72]	徐文建, 赵俐. 玻璃纤维经编柔性复合材料顶破性能的研究[J]. 国际纺织导报, 2007, 35(1):70-73.
[73]	季阳. 气囊式充气膜结构抗顶破性能研究[D]. 徐州:中国矿业大学, 2021.
[74]	Zhao Z Y, Li B, Ma P B. Advances in mechanical properties of flexible textile composites[J/OL]. Composite Structures, 2023, 303[2023-01-01]. https://doi.org/10.1016/j.compstruct.2022.116350.
[75]	Li D, Zheng Z L, Yang R, et al. Analytical solutions for stochastic vibration of orthotropic membrane under random impact load[J]. Materials, 2018, 11(7):1231-1259.
[76]	Li D, Zheng Z L, Liu C Y, et al. Dynamic response of rectangular prestressed membrane subjected to uniform impact load[J]. Archives of Civil and Mechanical Engineering, 2017, 17(3):586-598.
[77]	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.
[78]	张其林, 张营营, 陈鲁, 等. 上海世博会世博轴膜结构边界连接件性能检测[J]. 施工技术, 2009, 38(8):38-40.
[79]	陈政, 赵海涛, 黄继平等.焊接带对飞艇蒙皮强度的影响[J]. 机械强度, 2021, 43(4):814-820.
[80]	赵飞龙, 陈务军, 何艳丽, 等. PVDF涂层织物膜材和节点高温力学性能试验研究[J]. 空间结构, 2014, 20(3):42-47.
[81]	殷志祥, 李秀晨, 焦东, 等. 膜结构螺栓夹板与U形夹具连接节点的破坏试验研究[J]. 铁道科学与工程学报, 2019, 16(3):788-795.
[82]	Yang B, Yu Z L, Zhang Q L, et al. The nonlinear orthotropic material model describing biaxial tensile behavior of PVC coated fabrics[J/OL].Composite Structures, 2020, 236[2020-03-15]. https://doi.org/10.1016/j.compstruct.2019.111850.
[83]	Liu Y, Zhang D X, Hu J H, et al. Design and structural analysis of an inflatable coated fabric manipulation arm[J]. Thin-Walled Structures, 2019, 139:310-320.
[84]	Chen J W, Luo F, Fan J, et al. Detailed deformation behaviors and tensile parameters for coated warp-knitted fabrics in 2D stressspace[J/OL]. Journal of materials in Civil Engineering, 2021, 33(12)[2020-09-16]. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003961.
[85]	Pargana J B, Leitão 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.
[86]	Dinh T D, Rezaei A, De Laet L, et al. A new elasto-plastic material model for coated fabric[J]. Engineering Structures, 2014, 71:222-233.
[87]	徐俊豪, 张营营, 赵玉帅, 等. 聚氯乙烯膜材各向异性超弹性本构模型[J]. 建筑结构学报, 2019, 40(2):198-205.
[88]	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:Engineering, 2013, 52:275-281.
[89]	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.
[90]	Peirce F T. The geometry of cloth structure[J]. Journal of the Textile Institute Transactions, 1937, 28(3):45-96.
[91]	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.
[92]	Pargana J B, Lloyd-Smith D, Izzuddin B A. Advanced material model for coated fabrics used in tensioned fabric structures[J]. Engineering Structures, 2007, 29(7):1323-1336.
[93]	Gade J, Kemmler R, Drass M, et al. Enhancement of a meso-scale material model for nonlinear elastic finite element computations of plain-woven fabric membrane structures[J]. Engineering Structures, 2018, 177:668-681.
[94]	Reese S. Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large elastoplastic deformation[J]. International Journal of Solids and Structures, 2003, 40(4):951-980.
[95]	Yang Y, Zeng P, Pindera M. Capturing the multiscale effects in the response of coated woven fabrics[J]. Composite Structures, 2016, 136:566-581.
[96]	Dinh T D, Rezaei A, Daelemans L, et al. A hybrid micro-meso-scale unit cell model for homogenization of the nonlinear orthotropic material behavior of coated fabrics used in tensioned membrane structures[J]. Composite Structures, 2017, 162:271-279.
[97]	Freeston W D, Platt M M, Schoppee M M. Mechanics of elastic performance of textile materials[J]. Textile Research Journal, 1937, 37(11):948-975.
[98]	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.