Some Remarks on Dissipation Postulate in Anisotropic Finite Elasto-Plasticity

Abstract

In the paper a new version of the dissipation postulate is properly formulated for anisotropic (isothermic) finite elasto-plastic materials, in the context of Mandel’s type multiplicative decomposition of the deformation gradient. Our postulate requires that the work done by internal forces (in the initial
configuration) is non-negative on small cycles of strains only. The definitions are built in terms of the yield function in the elastic strain space, via the solutions of the differential system (rate-independent), which governs the evolution of the irreversible variables. Some properties that are postulated or tacitly accepted in approaches used by different authors, are proved in this approach. I emphasize some important consequences of the formulated postulate: the existence of the smooth stress potential, certain dissipation inequalities, which hold only for accessible pairs in the appropriate elastic range, some modified flow rules compatible with the dissipation postulate. Some comparison with the existing results in the domain is also presented.