A large deformation theory for rate-dependent elastic-plastic materials with combined isotropic and kinematic hardening

We have developed a large deformation viscoplasticity theory with combined isotropic and kinematic hardening based on the dual decompositions F = (FFp)-F-e [Kroner, E., 1960. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Archive for Rational Mechanics and Analysis 4, 273-334] and F-p = (FenFdisp)-F-p [Lion, A., 2000. Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models. International Journal of Plasticity 16, 469-494]. The elastic distortion F-e contributes to a standard elastic free-energy psi((e)), while F-en(p), the energetic part of F-p, contributes to a defect energy psi((p)) - these two additive contributions to the total free energy in turn lead to the standard Cauchy stress and a back-stress. Since F-e = FFp-1 and F-en(p) = (FFdisp-1)-F-p, the evolution of the Cauchy stress and the back-stress in a deformation-driven problem is governed by evolution equations for F-p and F-dis(p) - the two flow rules of the theory. We have also developed a simple, stable, semi-implicit time-integration procedure for the constitutive theory for implementation in displacement-based finite element programs. The procedure that we develop is simple in the sense that it only involves the solution of one non-linear equation, rather than a system of non-linear equations. We show that our time-integration procedure is stable for relatively large time steps, is first-order accurate, and is objective. (C) 2008 Elsevier Ltd. All rights reserved.