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显式模拟类橡胶材料应力软化引起的不可恢复变形及其各向异性特征

王晓明 吴荣兴 蒋义 肖衡

王晓明, 吴荣兴, 蒋义, 肖衡. 显式模拟类橡胶材料应力软化引起的不可恢复变形及其各向异性特征. 力学学报, 2021, 53(7): 1929-1939 doi: 10.6052/0459-1879-21-060
引用本文: 王晓明, 吴荣兴, 蒋义, 肖衡. 显式模拟类橡胶材料应力软化引起的不可恢复变形及其各向异性特征. 力学学报, 2021, 53(7): 1929-1939 doi: 10.6052/0459-1879-21-060
Wang Xiaoming, Wu Rongxing, Jiang Yi, Xiao Heng. Explicitly modeling permanent set and anisotropy property induced by stress softening for rubber-like materials. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1929-1939 doi: 10.6052/0459-1879-21-060
Citation: Wang Xiaoming, Wu Rongxing, Jiang Yi, Xiao Heng. Explicitly modeling permanent set and anisotropy property induced by stress softening for rubber-like materials. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1929-1939 doi: 10.6052/0459-1879-21-060

显式模拟类橡胶材料应力软化引起的不可恢复变形及其各向异性特征

doi: 10.6052/0459-1879-21-060
基金项目: 2020访问工程师项目校企合作资助项目(FG2020038)
详细信息
    作者简介:

    王晓明, 讲师, 智能材料本构建模. Email: wangxiaoming.g@163.com

  • 中图分类号: O343; O345

EXPLICITLY MODELING PERMANENT SET AND ANISOTROPY PROPERTY INDUCED BY STRESS SOFTENING FOR RUBBER-LIKE MATERIALS

  • 摘要: 类橡胶材料在经过初次加载后会产生应力软化现象, 也就是Mullins效应. 实验证明应力软化现象会导致材料产生不可恢复变形, 同时引入各向异性特征. 本文基于对数应变构造一个多轴可压缩应变能函数, 先引入耗散来表征应力软化现象, 再引入依赖耗散大小的不可恢复变形量以及各向异性特征量, 使得新模型既可以表征Mullins效应, 又能模拟应力软化作用下产生的不可恢复变形和各向异性特征. 本文在各向同性形函数的基础上, 通过球坐标系的思想, 进一步发展并提出了一个任意方向适用的各向异性形函数. 新模型在材料尚未发生软化(耗散为0)的情况下, 表现出各向同性; 一旦发生应力软化(耗散大于0), 则变为各向异性. 随着加载−卸载循环的累积, 耗散逐渐变大, 不可恢复变形也随之变大直到达到一个稳定的值, 各向异性特性也逐渐变得明显. 新方法得到的结果可以精确匹配经典的实验数据, 并预测不同方向的应力软化现象以及由此产生的不可恢复变形和各向异性特征.

     

  • 图  1  Mullins效应产生不可恢复变形示意图

    Figure  1.  Schematic of Mullins effects with permanent set

    图  2  六面体橡胶块三维受力示意图

    Figure  2.  Schematic of hexahedral rubber block with three-dimensional force

    图  3  Diani等[26]证明引入各向异性的实验数据

    Figure  3.  An experimental evidence of induced anisotropy by Diani et al.[26]

    图  4  任意方向受力的球坐标示意图

    Figure  4.  Schematic of loading in arbitrary direction by Spherical coordinate system

    图  5  模型结果和实验结果[26]对比图. 横坐标表示对数应变, 纵坐标表示基尔霍夫应力

    Figure  5.  Comparison between model result and the experimental data[26]. “x” axis represents the Hencky strain, and “y” axis represents the Kirchhoff stress

    图  6  Diani等[26]的实验数据和模型结果对比

    Figure  6.  Comparison between experimental data of Diani et al.[26] and model result

    图  7  不同方向上模型结果对比

    Figure  7.  Comparison of model results in different directions

  • [1] Mullins L. Softening of rubber by deformation. Rubber Chemistry and Technology, 1969, 42(1): 339-362 doi: 10.5254/1.3539210
    [2] Mullins L. Effect of stretching on the properties of rubber. Rubber Chemistry and Technology, 1948, 21(2): 281-300 doi: 10.5254/1.3546914
    [3] Mullins L. Permanent set in vulcanized rubber. Rubber Chemistry and Technology, 1949, 22(4): 1036-1044 doi: 10.5254/1.3543010
    [4] Bueche F. Molecular basis of the Mullins effect. Journal of Appli-ed Polymer Science, 1960, 4: 107-114 doi: 10.1002/app.1960.070041017
    [5] Bueche F. Mullins effect and rubber-filler interaction. Journal of Applied Polymer Science, 1961, 5: 271-281 doi: 10.1002/app.1961.070051504
    [6] Lee M, William M. Application of a new structural theory to pol-ymers. A. Uniaxial stress in crosslinked rubbers. Journal of the Mechanics and Physics of Solids, 1985, 45: 1805-1834
    [7] Harwood JAC, Mullins L, Payne AR. Stress softening in natural rubber vulcanizates. Part II. Stress softening effects in pure gum and filler load rubbers. Journal of Applied Polymer Science, 1965, 9: 3011-3021.
    [8] Govindjee S, Simo JC. A mirco-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullin-s’ effect. Journal of the Mechanics and Physics of Solids, 1991, 39(1): 87-112 doi: 10.1016/0022-5096(91)90032-J
    [9] Marckmann G, Verron E, Gornet L, et al. A theory of network alteration for the Mullins effect. Journal of the Mechanics and Physics of Solids, 2002, 50: 2011-2028 doi: 10.1016/S0022-5096(01)00136-3
    [10] Göktepe S, Miehee C. A micro-macro approach to rubber-like mat-erials. Part III: The micro-sphere model of anisotropic Mullins-typedamage. Journal of the Mechanics and Physics of Solids, 2005, 53: 2259-2283 doi: 10.1016/j.jmps.2005.04.010
    [11] Blanchard AF, Parkinson D. Breakage of carbon-rubber networks by applied stress. Rubber Chemistry and Technology, 1952, 44(4): 799-812
    [12] Arrude EM, Boyce MC. A three-dimensional constitutive model forthe large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids, 1993, 41(2): 389-412 doi: 10.1016/0022-5096(93)90013-6
    [13] Mullins L, Tobin, NR. Theoretical model for the elastic behavior of filler reinforced vulcanized rubbers. Rubber Chemistry and Technology, 1957, 30(2): 555-571 doi: 10.5254/1.3542705
    [14] Mullins L, Tobin NR. Stress softening rubber vulcanizates Part I. Use of a strain amplification factor to describe the elastic behavior of filler-reinforced vulcanized rubber. Journal of Applied polymer Science, 1965, 9: 2993-3009 doi: 10.1002/app.1965.070090906
    [15] Klüppel M, Schramm J. An advanced micro-mechanical model of hyper-elasticity and stress softening of reinforced rubbers // Dorf-mann, Eds. Constitutive Models for Rubber. 1999, 211-218
    [16] Govindjee S. An evaluation of strain amplification concepts via Monte Carlo simulations of an ideal composite. Rubber Chemistry and Technology, 1997, 70: 25-37 doi: 10.5254/1.3538416
    [17] Bergström JS, Boyce MC. Mechanical behavior of particle filled elastomers. Rubber Chemistry and Technology, 1999, 72: 633-656 doi: 10.5254/1.3538823
    [18] Simo JC. On a fully three-dimensional finite-strain viscoelastic da-mage model: Formulation and computational aspects. Computer Methods in Applied Mechanics & Engineering, 1987, 60: 153-173
    [19] Miehe C. Discontinuous and continuous damage evolution in Ogde-n-type large-strain elastic materials. European Journal of Mechanics A/Solids, 1995, 14: 697-720
    [20] Miehe C, Keck J. Superimposed finite elastic-viscoelastic-plastoelas-tic stress response with damage in filled rubbery polymers. Experi-ments, modeling and algorithmic implementation. Journal of Mech-anics and Physicals of Solids, 2000, 48(2): 323-365 doi: 10.1016/S0022-5096(99)00017-4
    [21] Kaliske M, Nasdala L, Rothert H. On damage modeling for elasticand viscoelastic materials at large strain. Computer & Structures, 2001, 79: 2133-2141
    [22] Lin RC, Schomburg U. A finite elastic-viscoelastic-elastoplastic material low with damage: theoretical and numerical aspects. Com-puter Methods in Applied Mechanics & Engineering, 2003, 192: 1591-1627
    [23] Ogden RW, Roxburgh DG. A pseudo-elastic model for the Mullins effect in filled rubber. Proceedings of the Royal Society, 1999, 455: 2861-2878 doi: 10.1098/rspa.1999.0431
    [24] Li on, A. A constitutive model for carbon black filled rubber: Exp-erimental investigations and mathematical representation. Continuum Mechanics and Thermodynamics, 1996, 8(3): 153-169 doi: 10.1007/BF01181853
    [25] Li on, A. On the large deformation behaviour of reinforced rubber at different temperatures. Journal of the Mechanics and Physics of Solids, 1997, 45(11-12): 1805-1834 doi: 10.1016/S0022-5096(97)00028-8
    [26] Diani J, Brieu M, Vacherand JM. A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy. European Journal of Mechanics A/Solids, 2006, 25: 483-496 doi: 10.1016/j.euromechsol.2005.09.011
    [27] Dorfmann A, Ogden RW. A constitutive model for the Mullins eff-ect with permanent set in particle-reinforced rubber. International Journal of Solids and Structures, 2004, 41: 1855-1878 doi: 10.1016/j.ijsolstr.2003.11.014
    [28] Pawelski H. Softening behavior of elastomeric media after loading in changing directions//Besdo D, Schuster RH, Ilheman J, Eds. Proceedings of the Second European Conference of the Constitutive Models for Rubber. Balkema, 1999, 27-34.
    [29] 谈炳东, 许进升, 孙朝翔, 等. 短纤维增强三元乙丙橡胶横观各向同性黏—超弹性本构模型. 力学学报, 2017, 49(3): 677-684 (Tan Bingdong, Xu Jinsheng, Sun Chaoxiang, et al. A transversely isotropic visco-hyperelastic constitutive model for short fiber reinforced EPDM. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 677-684 (in Chinese) doi: 10.6052/0459-1879-16-380
    [30] 谈炳东, 许进升, 贾云飞, 等. 短纤维增强 EPDM 包覆薄膜超弹性本构模型. 力学学报, 2017, 49(2): 317-323 (Tan Bingdong, Xu Jin-sheng, Jia Yunfei, et al. Hyperelastic constitutive model for short fiber reinforced EPDM inhibitor film. Chinese Journal of Theoreti-cal and Applied Mechanics, 2017, 49(2): 317-323 (in Chinese) doi: 10.6052/0459-1879-16-324
    [31] Mitsuteru A, Yoshiyuki K, Yoshimi S, et al. Constitutive modeling for texture reinforced rubber by using an anisotropic viscohypere-lastic model. Doboku Gakkai Ronbunshuu A, 2010, 66(2): 194-205 doi: 10.2208/jsceja.66.194
    [32] Rebouah M, Chagnon G. Permanent set and stress softening consti-tutive equation applied to rubber like materials and soft tissues. Acta Mechanica, 2013, 225(6): 1685-1698
    [33] Nasdala, L, Kempe A, Rolfes, R. An elastic molecular model for rubber inelasticity. Computational Materials Science, 2015, 106: 83-99 doi: 10.1016/j.commatsci.2015.04.036
    [34] Külcü ID, Tanrverdi HB. A constitutive model for hysteresis: the continuum damage approach for filled rubber-like materials. Archive of Applied Mechanics, 2020, 90: 1771-1781 doi: 10.1007/s00419-020-01695-2
    [35] Xiao H. An explicit, direct approach to obtaining multi-axial elasti-cpotentials which exactly match data of four benchmark tests for incompressible rubberlike materials-Part 1: incompressible deformat-ions. Acta Mechanica, 2012, 223(9): 2309-2063
    [36] Xiao H, Ding XF, Cao J, et al. New multi-axial constitutive mod-dels for large elastic deformation behaviors of soft solids up to breaking. International Journal of Solids and Structures, 2017, 109: 123-130 doi: 10.1016/j.ijsolstr.2017.01.013
    [37] Wang XM, Li H, Yin ZN, et al. Multiaxial strain energy functions of rubberlike materials: An explicit approach based on polynomial interpolation. Rubber Chemistry and Technology, 2014, 87(1): 168-183 doi: 10.5254/rct.13.86960
    [38] 王晓明, 吴荣兴, 肖衡. 显式模拟类橡胶材料Mullins效应滞回圈. 力学学报, 2019, 51(2): 484-493 (Wang Xiaoming, Wu Rongxing, Xiao Heng. Explicit modeling the hysteresis loops of the mullins effect for rubber-like materials. Chinses Journal of Theoretical and Applied Mechanics, 2019, 51(2): 484-493 (in Chinese) doi: 10.6052/0459-1879-18-334
    [39] 王晓明, 郑东, 吴荣兴等. 类橡胶材料变形直到破坏的显式本构模型. 力学季刊, 2019, 40(2): 252-264 (Wang Xiaoming, Zheng Dong, Wu Rongxing, et al. Explicit constitutive model of rubber-like materials up to failure. Chinese Quarterly of Mechanics, 2019, 40(2): 252-264 (in Chinese)
    [40] 王晓明, 肖衡. 显式方法精确模拟形状记忆聚合物热力学行为. 固体力学学报, 2020, 41(4): 366-378 (Wang Xiaoming, Xiao Heng. Accurately modeling thermomechancial behavior of shape memory polymer with explicit Method. Chinese Journal of Solid Mechani-cs, 2020, 41(4): 366-378 (in Chinese)
    [41] Xiao H, Chen LS. Hencky’s logarithmic strain and dual stress-stra-in and strain-stress relations isotropic finite hyperelasticity. Internat-ional Journal of Solids and Structures, 2003, 40(6): 1455-146 doi: 10.1016/S0020-7683(02)00653-4
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  • 收稿日期:  2021-02-03
  • 录用日期:  2021-06-08
  • 网络出版日期:  2021-06-08

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