Finite deformation plasticity and viscoplasticity laws exhibiting nonlinear hardening rules Part I: Constitutive theory and numerical integration

This paper deals with plasticity and viscoplasticity laws exhibiting nonlin ear kinematic hardening as well as nonlinear isotropic hardening rules. In Tsakmakis (1996a, b) a constitutive theory has been formulated within the f ramework of finite deformations, which is based on the concept of so-called dual variables and associated time derivatives. Within two families of dua l variables, two different formulations have been proposed for kinematic ha rdening, referred to as Models 1 and 2. In particular, rigid plastic deform ations without isotropic hardening have been considered. In the present pap er, the constitutive theory of Tsakmakis (1996a, b) is appropriately extend ed to take into account isotropic hardening as well as elastic deformations . Care is taken that the evolution equations governing the hardening respon se fulfill the intrinsic dissipation inequality in every admissible process . For the case of small elastic strains combined with a simplification conc erning kinematic hardening, to be explained in the paper, an efficient, imp licit time-integration algorithm is presented. The algorithm is developed w ith a view to implementation in the ABAQUS Finite Element code. Also, expli cit formulas for the consistent tangent modulus are derived.