ON THE NUMERICAL TREATMENT OF FINITE DEFORMATIONS IN ELASTOVISCOPLASTICITY

This paper deals with the generalization of a geometric linear viscopl astic model to finite strains and its numerical application. We owe th e original formulation of the applied model to Perzyna and Chaboche; i t includes nonlinear isotropic and kinematic hardening as well as a no nlinear rate dependence. The constitutive equations are integrated num erically in the context of a finite element formulation. From theoreti cal considerations it is known that in the case of vanishing viscosity or slow processes rate-independent plasticity arises as an asymptotic limit. Accordingly, the numerical formulation includes this property. In fact, the stress algorithm corresponding to viscoplasticity is red uced to the asymptotic limit in a most simple way, namely by setting t he viscosity parameter equal to zero. Furthermore, it is shown that th e numerical integration of the constitutive model involves the solutio n of only one nonlinear equation for one scalar unknown. This even app lies to a sum of Armstrong-Frederick terms. The algorithm incorporates the inelastic incompressibility on the level of the Gauss points. Num erical computations of examples taken from metal Forming technology sh ow the physical significance of the model and the reliability of the n umerical algorithm. These calculations have been carried out by means of the finite element program PSU.