The governing parameter method for implicit integration of viscoplastic constitutive relations for isotropic and orthotropic metals

A general algorithm of implicit stress integration in viscoplasticity, based on the governing parameter method (GPM) is briefly presented. It is assumed that the associative viscoplastic constitutive relations are governed by the Perzyna formulation with a generalization suggested by Simo and Hughes. The algorithm is first applied to isotropic metals obeying the von Mises yield condition with mixed hardening and then, to orthotropic metals with a generalized Hill's yield condition including a mixed hardening assumption. Derivation of consistent tangent moduli is presented for both viscoplastic material models. The proposed computational procedures are efficient, since they reduce the problem of stress integration to the solution of one nonlinear equation, can use large time steps and are applicable to 2-D, 3-D, shell and beam structures. The tangent elastic viscoplastic matrix provides high convergence rate in the overall equilibrium iterations. Numerical examples illustrate the main characteristics of the developed computational procedures.