Processing math: 100%
EI、Scopus 收录
中文核心期刊
Han Lei, Wang Xintong, Li Luxian. Complete constitutive relation of hyperelastic materials for Treloar’s experimental data. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3444-3455. DOI: 10.6052/0459-1879-22-317
Citation: Han Lei, Wang Xintong, Li Luxian. Complete constitutive relation of hyperelastic materials for Treloar’s experimental data. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3444-3455. DOI: 10.6052/0459-1879-22-317

COMPLETE CONSTITUTIVE RELATION OF HYPERELASTIC MATERIALS FOR TRELOAR’S EXPERIMENTAL DATA

  • Received Date: July 09, 2022
  • Accepted Date: October 26, 2022
  • Available Online: October 27, 2022
  • Hyperelastic material is a typical one widely used in many fields such as aerospace engineering and civil industrials. However, due to the property of nonlinear large deformation, the constitutive behavior of hyperelastic materials is extremely complex and the models are quite different in form. Starting from the strain energy function, a complete constitutive relation of hyperelastic materials is studied within the theoretical framework of continuum mechanics in this paper. Firstly, the feature is analyzed for the experimental curves under three essential deformation modes like uniaxial tension, equibiaxial tension and pure shear, which are conducted by Treloar for a vulcanized rubber hyperelastic material. Next, the same stress conditions of the three deformation modes are summarized in detail, based on which the constitutive relationship is derived in a same manner in terms of the stress and the principal stretch ratio in the loading direction for the three modes according to the hyperelastic constitutive theory. The constitutive behaviors of two typical power-law strain energy functions, namely Im1 and Im2, are accordingly studied for the three essential modes. The experimental curves are divided into the initial regime and the remaining regime, and then the neo-Hookean model is adopted for the initial regime while the power-law functions with variable exponents are used for the remaining regime. The complete constitutive model is eventually established after the model parameters are identified by minimizing the overall error functional of the three modes. The responses are re-predicted for the three essential deformation modes, and the results agree better with the experimental than other models available in published literature. The present work indicates that a complete constitutive relation can be obtained for a hyperelastic material in light of the experimental curves with whole deformation range under multiple deformation modes, which is therefore instructive and meaningful to theoretical research and engineering application of complex practical problems such as fracture of hyperelastic materials.
  • [1]
    Nkenfack AN, Beda T, Feng ZQ, et al. HIA: A hybrid integral approach to model incompressible isotropic hyperelastic materials—Part 1: Theory. International Journal of Non-Linear Mechanics, 2016, 84: 1-11 doi: 10.1016/j.ijnonlinmec.2016.04.005
    [2]
    Lu Y, Gu ZX, Yin ZN, et al. New compressible hyper-elastic models for rubberlike materials. Acta Mechanica, 2015, 226(12): 4059-4072 doi: 10.1007/s00707-015-1475-3
    [3]
    郭辉, 胡文军, 陶俊林. 泡沫橡胶材料的超弹性本构模型. 计算力学, 2013, 30(4): 575-579 (Guo Hui, Hu Wenjun, Tao Junlin. The superelasticty constitutive model for foam rubber materials. Chinese Journal of Computational Mechanics, 2013, 30(4): 575-579 (in Chinese)
    [4]
    Boyce MC, Arruda EM. Constitutive models of rubber elasticity: A review. Rubber Chemistry and Technology, 2000, 73(3): 504-523 doi: 10.5254/1.3547602
    [5]
    Dal H, Acikgoz K, Badienia Y. On the performance of isotropic hyperelastic constitutive models for rubber-like materials: A state of the art review. Applied Mechanics Reviews, 2021, 73(2): 020802 doi: 10.1115/1.4050978
    [6]
    Steinmann P, Hossain M, Possart G. Hyperelastic materials behavior modeling using consistent strain energy density functions. Archive of Applied Mechanics, 2012, 82(9): 1183-1217 doi: 10.1007/s00419-012-0610-z
    [7]
    Bazkiaei AK, Shirazi KH, Shishesaz M. A framework for model base hyperelastic material simulation. Journal of Rubber Research, 2020, 23(4): 287-299 doi: 10.1007/s42464-020-00057-5
    [8]
    Beda T. Reconciling the fundamental phenomenological expression of the strain energy of rubber with established experimental facts. Journal of Polymer Science Part B: Polymer Physics, 2005, 43(2): 125-134 doi: 10.1002/polb.20308
    [9]
    Nunes LCS. Mechanical characterization of hyperelastic polydimethylsiloxane by simple shear test. Materials Science and Engineering A, 2011, 528(3): 1799-1804 doi: 10.1016/j.msea.2010.11.025
    [10]
    彭向峰, 李录贤. 超弹性材料本构关系的最新研究进展. 力学学报, 2020, 52(5): 1221-1234 (Peng Xiangfeng, Li Luxian. State of the art of constitutive relations of hyperelastic materials. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1221-1234 (in Chinese) doi: 10.6052/0459-1879-20-189
    [11]
    Khodadadi A, Liaghat G, Ahmadi H, et al. Numerical and experimental study of impact on hyperelastic rubber panels. Iranian Polymer Journal, 2019, 28(2): 113-122 doi: 10.1007/s13726-018-0682-x
    [12]
    Shahzad M, Kamran A, Siddiqui MZ, et al. Mechanical characterization and FE modelling of a hyperelastic material. Materials Research, 2015, 18(5): 918-924 doi: 10.1590/1516-1439.320414
    [13]
    Destrade M, Saccomandi G, Sgura I. Methodical fitting for mathematical models of rubber-like materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017, 473(2198): 20160811 doi: 10.1098/rspa.2016.0811
    [14]
    Han L, Peng XF, Li LX. Entire-region constitutive relation for Treloar’s data. Rubber Chemistry and Technology, 2022, 95(1): 119-127 doi: 10.5254/rct.21.78993
    [15]
    魏志刚, 陈海波. 一种新的橡胶材料弹性本构模型. 力学学报, 2019, 51(2): 473-483 (Wei Zhigang, Chen Haibo. A new elastic model for rubber-like materials. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 473-483 (in Chinese) doi: 10.6052/0459-1879-18-303
    [16]
    Hossain M, Steinmann P. More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study. Journal of the Mechanical Behavior of Materials, 2013, 22(1-2): 27-50 doi: 10.1515/jmbm-2012-0007
    [17]
    Arruda EM, Boyce MC. A three-dimensional constitutive model for the 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
    [18]
    Marckmann G, Verron E. Comparison of hyperelastic models for rubber-like materials. Rubber Chemistry and Technology, 2006, 79(5): 835-858 doi: 10.5254/1.3547969
    [19]
    Bien-Aimé LKM, Blaise BB, Beda T. Characterization of hyperelastic deformation behavior of rubber-like materials. SN Applied Sciences, 2020, 2(4): 1-10
    [20]
    Blaise BB, Bien-Aimé LKM, Betchewe G, et al. A phenomenological expression of strain energy in large elastic deformations of isotropic materials. Iranian Polymer Journal, 2020, 29(6): 525-533 doi: 10.1007/s13726-020-00816-6
    [21]
    Darijani H, Naghdabadi R. Hyperelastic materials behavior modeling using consistent strain energy density functions. Acta Mechanica, 2010, 213(3): 235-254
    [22]
    Mansouri MR, Darijani H. Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach. International Journal of Solids and Structures, 2014, 51(25-26): 4316-4326 doi: 10.1016/j.ijsolstr.2014.08.018
    [23]
    Doğan Kİ. A hyperelastic constitutive model for rubber-like materials. Archive of Applied Mechanics, 2020, 90(3): 615-622 doi: 10.1007/s00419-019-01629-7
    [24]
    Bahreman M, Darijani H, Fooladi M. Constitutive modeling of isotropic hyperelastic materials using proposed phenomenological models in terms of strain invariants. Polymer Engineering and Science, 2016, 56(3): 299-308 doi: 10.1002/pen.24255
    [25]
    李雪冰, 危银涛. 一种改进的Yeoh超弹性材料本构模型. 工程力学, 2016, 33(12): 38-43 (Li Xuebing, Wei Yintao. An improved Yeoh constitutive model for hyperelastic material. Engineering Mechanics, 2016, 33(12): 38-43 (in Chinese) doi: 10.6052/j.issn.1000-4750.2015.05.0388
    [26]
    Carroll MM. A strain energy function for vulcanized rubbers. Journal of Elasticity, 2011, 103(2): 173-187 doi: 10.1007/s10659-010-9279-0
    [27]
    徐中明, 袁泉, 张志飞等. 基于超静定方程的橡胶材料本构模型参数识别. 重庆大学学报, 2017, 40(2): 1-9 (Xu Zhongming, Yuan Quan, Zhang Zhifei, et al. Parameter identification of constitutive models of rubber material based on hyperstatic equations. Journal of Chongqing University, 2017, 40(2): 1-9 (in Chinese) doi: 10.11835/j.issn.1000-582X.2017.02.001
    [28]
    肖锐, 向玉海, 钟旦明等. 考虑缠结效应的超弹性本构模型. 力学学报, 2021, 53(4): 1028-1037 (Xiao Rui, Xiang Yuhai, Zhong Danming, et al. Hyperelastic model with entanglement effect. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1028-1037 (in Chinese) doi: 10.6052/0459-1879-21-008
    [29]
    Rivlin RS. Large elastic deformations of isotropic materials IV. Further developments of the general theory. Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, 1948, 241(835): 379-397
    [30]
    Treloar LRG. Stress-strain data for vulcanised rubber under various types of deformation. Transactions of the Faraday Society, 1944, 40: 59-70 doi: 10.1039/tf9444000059
    [31]
    Jones DF, Treloar LRG. The properties of rubber in pure homogeneous strain. Journal of Physics D: Applied Physics, 1975, 8(11): 1285-1304 doi: 10.1088/0022-3727/8/11/007
  • Related Articles

    [1]Gong Chencheng, Chen Yan, Dai Lanhong. REVIEW ON MECHANICAL BEHAVIOR AND CONSTITUTIVE RELATION OF POLYUREA ELASTOMER[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 1-23. DOI: 10.6052/0459-1879-22-455
    [2]Qu Tongming, Feng Yuntian, Wang Mengqi, Zhao Tingting, Di Shaocheng. CONSTITUTIVE RELATIONS OF GRANULAR MATERIALS BY INTEGRATING MICROMECHANICAL KNOWLEDGE WITH DEEP LEARNING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2404-2415. DOI: 10.6052/0459-1879-21-221
    [3]Peng Xiangfeng, Li Luxian. STATE OF THE ART OF CONSTITUTIVE RELATIONS OF HYPERELASTIC MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1221-1234. DOI: 10.6052/0459-1879-20-189
    [4]The elasto-plastic damage constitutive relations of orthotropic materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(1): 67-75. DOI: 10.6052/0459-1879-2009-1-2006-585
    [5]Jinyang Liu, Jiazhen Hong. Nonlinear formulation for flexible multibody system with large deformation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(1): 111-119. DOI: 10.6052/0459-1879-2007-1-2006-113
    [6]THE CONSTITUTIVE RELATION OF SUPERPLASTICITY OF METAL WITH UNIFORM EQUIAXED FINE GRAIN[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(5): 560-568. DOI: 10.6052/0459-1879-1993-5-1995-678
    [7]基于变形动力学模型的黏弹性材料本构关系[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(3): 375-379. DOI: 10.6052/0459-1879-1993-3-1995-655
    [8]A CONSTITUTIVE RELATION OF ELASTO-BRITTLE MATERIAL WITH DAMAGE AND ITS APPLICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1991, 23(3): 374-378. DOI: 10.6052/0459-1879-1991-3-1995-852
    [9]ON HYPERELASTIC CONDITION OF RATE-FORM ELASTICPLASTIC CONSTITUTIVE LAW AT FINITE DEFORMATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1991, 23(2): 248-251. DOI: 10.6052/0459-1879-1991-2-1995-834
    [10]一种描述形状记忆合金拟弹性变形行为的本构关系[J]. Chinese Journal of Theoretical and Applied Mechanics, 1991, 23(2): 201-210. DOI: 10.6052/0459-1879-1991-2-1995-827
  • Cited by

    Periodical cited type(1)

    1. 李锋,彭天波. 包含Mullins效应的HDR热-超-黏弹性本构模型. 力学学报. 2024(12): 3498-3506 . 本站查看

    Other cited types(2)

Catalog

    Article Metrics

    Article views (860) PDF downloads (137) Cited by(3)
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return