Dissipative Nature of Plastic Deformations in Finite Anisotropic Elasto-Plasticity

Abstract

This paper deals with anisotropic elasto-plastic materials with relaxed configuration and internal variables, which undergo large deformations and obey the Il'yushin-type dissipation postulate. We emphasize new consequences of the dissipation postulate, when the definitions are built in the total strain space, and the irreversible behavior is described by the appropriate differential systems. The normality conditions prove that the appropriate stress release rates are collinear with the interior normal to the current yield surface and lead to the rate-type constitutive equations compatible with the dissipation postulate. The rate-type constitutive equations are derived in the initial and actual, as well as in the relaxed, configurations. For anisotropic Σ models, the rates of irreversible variables are linked through the flow rule in Σ space up to a term, generated by a gk -invariant, skew-symmetric tensor. Here Σ is Mandel's non-symmetric stress measure, and gk characterizes the pre-existing anisotropy. Due to the non-injectivity of Mandel's stress elastic function, we construct the strain elastic range involved in the dissipation postulate, as the pre-image of Σ stress range.