Chinese Journal of Theoretical and Applied Mechanics ›› 2019, Vol. 51 ›› Issue (1): 182-191.DOI: 10.6052/0459-1879-18-138

• Solid Mechanics • Previous Articles     Next Articles

A LARGE DEFORMATION ELASTOPLASTIC MODEL BASED ON THE INTERMEDIATE CONFIGURATION

Meng Chunyu, Tang Zhengjun, Chen Mingxiang1)()   

  1. School of Civil Engineering, Wuhan University, Wuhan 430072, China
  • Online:2019-01-18 Published:2019-03-01

Abstract:

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.

Key words: large deformation elastoplastic model|deformation gradient multiplicative decomposition|tensor function representation theorem|constitutive relation|in the intermediate configuration

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