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Meng Chunyu, Tang Zhengjun, Chen Mingxiang. A LARGE DEFORMATION ELASTOPLASTIC MODEL BASED ON THE INTERMEDIATE CONFIGURATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 182-191. DOI: 10.6052/0459-1879-18-138
Citation: Meng Chunyu, Tang Zhengjun, Chen Mingxiang. A LARGE DEFORMATION ELASTOPLASTIC MODEL BASED ON THE INTERMEDIATE CONFIGURATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 182-191. DOI: 10.6052/0459-1879-18-138

A LARGE DEFORMATION ELASTOPLASTIC MODEL BASED ON THE INTERMEDIATE CONFIGURATION

  • In the large deformation elastoplastic constitutive theory, a basic problem is the decomposition of elastic deformation and plastic deformation. In the usual case, two decomposition methods are adopted. One method is to decompose deformation rate (or strain rate) into elastic and plastic parts. Among them, the elastic deformation rate and the objective rate of Kirchhoff stress are linked by elastic tensors, and by using this way, a sub-elastic model can be established. In the mean time,the plastic deformation rate is related to Kirchhoff stress by using flow law. Another method is to decompose the deformation gradient tensor based in the intermediate configuration. It is supposed that by considering the virtual unloading process, an unstressed intermediate configuration can be obtained and the so-called hyperelastic-plastic model can be established. In this paper, a large number of properties of a large deformation elastoplastic model which is based on the deformation gradient multiplicative decomposition are studied, and the model is built in the intermediate configuration. These properties include: in different configurations, the existence of the plastic spin rate; the symmetry of back stress; the orthogonality of plastic deformation rate and yield surface; and the relationships between plastic spin rate, back stress, plastic deformation rate and yield surface. First of all, by using the tensor function representation theorem which is in the appendix, some special properties of the isotropic function are obtained and some formula relationships are established, and some simple relationships of tensor value function between the intermediate configuration and the current configuration are derived. Secondly, based on these properties and relationships, and in combination with the laws of thermodynamics, the mathematical expression of the model in different configurations is established, which consists of objective rate representation and continuous tangential stiffness. Thus, some properties of the large deformation elastoplastic model based on the intermediate configuration are obtained. Finally, the model is compared and analyzed with the four models.
  • [1] 谢多夫. 连续介质力学. 李植译. 北京: 高等教育出版社, 2007
    [1] (Aleksandr Aleksandroviq Andronov.Continuum Mechanics, fransl. Li Zhi. Beijing: Higher Education Press, 2007 (in Chinese))
    [2] 黄克智, 程莉. 大变形弹塑性本构理论的几个基本问题. 力学学报, 1989, 21(s1): 7-17
    [2] (Huang Kezhi, Cheng Li.Some fundamental problems in elastic-plastic constitutive theory of finite deformation. Chin J Theor Appl Mech, 1989, 21(s1): 7-17 (in Chinese))
    [3] Bertram A.Elasticity and Plasticity of Large Deformations. Berlin,Heidelberg: Springer 2005
    [4] Lee EH.Elasto-plastic deformation at finite strain. Journal of Applied Mechanics, 1969, 36: 1-23
    [5] Lee EH, Mcmeeking RM.Concerning elastic and plastic components of deformation. International Journal of Solids & Structures, 1980, 16(8): 715-721
    [6] Brannon RM.Caveats concerning conjugate stress and strain measures for frame indifferent anisotropic elasticity. Acta Mechanica, 1998, 129(1-2): 107-116
    [7] Nemat-Nasser S.Decomposition of strain measures and their rates in finite deformation elastoplasticity. International Journal of Solids & Structures 1979, 15(2): 155-166
    [8] Nemat-Nasser S.On finite deformation elasto-plasticity. International Journal of Solids & Structures, 1982, 18(10): 857-872
    [9] Nemat-Nasser S.Certain basic issues in finite-deformation continuum plasticity. Meccanica, 1990, 24: 223-229
    [10] Schieck B, Stumpf H.Deformation analysis for finite elastic-plastic strains in a lagrangean-type description. International Journal of Solids & Structures, 1993, 30(19): 2639-2660
    [11] Ghavam K, Naghdabadi R.Hardening materials modeling in finite elastic--plastic deformations based on the stretch tensor decomposition. Materials & Design, 2008, 29(1): 161-172
    [12] Heidari M, Vafai A, Desai C.An Eulerian multiplicative constitutive model of finite elastoplasticity. European Journal of Mechanics-A Solids, 2009, 28(6): 1088-1097
    [13] Moran B, Ortiz M, Shih CF.Formulation of implicit finite element methods for multiplicative finite deformation plasticity. International Journal for Numerical Methods in Engineering, 2010, 29(3): 483-514
    [14] 王自强. 理性力学基础. 北京: 科学出版社, 2000
    [14] (Wang Ziqiang.Foundation of Rational Mechanics. Beijing: Science Press, 2000 (in Chinese))
    [15] Mandel J.Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques. International Journal of Solids & Structures, 1973, 9(6): 725-740
    [16] Asaro RJ.Micromechanics of crystals and polycrystals. Advances in Appl Mech, 1983, 23(8): 1-115
    [17] Mandel J.Plasticité Elassique et Viscoplasticité. Vienna-New York: Springer-Verlag, 1972
    [18] Coleman BD, Noll W.The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity. The Foundations of Mechanics and Thermodynamics. Berlin, Heidelberg: Springer 1974: 167-178
    [19] Coleman BD, Gurtin ME.Thermodynamics with internal state variables. Journal of Chemical Physics, 2004, 47(2): 597-613
    [20] Lubliner J.Normality rules in large-deformation plasticity. Mechanics of Materials, 1986, 5(1): 29-34
    [21] Xiao H, Bruhns QT, Meyers A.A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradient. International Journal of Plasticity, 2000, 16(2): 143-177
    [22] Xiao H, Bruhns QT, Meyers A.The integrability criterion in finite elastoplasticity and its constitutive implications. Acta Mechanica, 2007, 188(3-4): 227-244
    [23] Eidel B, Gruttmann F, Elastoplastic orthotropy at finite strains: Multiplicative formulation and numerical implementation. Computational Materials Science, 2003, 28: 732-742
    [24] Xiao H, Bruhns OT, Meyers A,Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mechanica. 1997, 124: 89-105
    [25] Xiao H, Bruhns OT, Meyers A.Hypoelasticity model based upon the logarithmic stress rate. Journal of Elasticity, 1997, 47: 51-68
    [26] Xiao H, Bruhns OT, Meyers A.Elastoplasticity beyond small deformations. Acta Mechanica, 2006, 182: 31-111
    [27] Xiao H, Chen LS.Hencky's logarithmic strain and dual stress--strain and strain--stress relations in isotropic finite hyperelasticity. International Journal of Solids & Structures, 2003, 40(6): 1455-1463
    [28] Charlton DJ, Yang J, Teh KK.A review of methods to characterize rubber elastic behavior for use in finite element analysis. Rubber Chemistry & Technology, 67.3(1994): 481-503
    [29] Frederick CO, Armstrong PJ.A mathematical representation of the multiaxial Bauschinger effect. High Temperature Technology, 2007, 24(1): 1-26
    [30] Dettmer W, Reese S.On the theoretical and numerical modelling of Armstrong--Frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics & Engineering, 2004, 193(1): 87-116
    [31] Zheng QS.Theory of representations for tensor functions-A unified invariant approach to constitutive equations. Agronomy Journal, 1994, 47(11): 545
    [32] 兑关锁, 王正道, 金明. 各向同性张量函数的导数. 中国科学:物理学力学天文学, 2006, 36(1): 89-102
    [32] (Dui Guansuo, Wang Zhengdao, Jin Ming. The derivative of an isotropic tensor. Scientia Sinica Physica,Mechanica & Astronomica, 2006, 36(1): 89-102(in Chinese))
    [33] 王足. 连续介质力学中某些物理量的近似和大变形弹塑性定义的比较. [博士论文]. 北京:北京交通大学, 2010
    [33] (Wang Zu.The approximation of some variables and the comparison of elasto-plastic large deformation definitions in continuum mechanics. [PhD Thesis]. Beijing: Beijing Jiaotong University, 2010 (in Chinese))

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