On the numerical treatment of finite deformations in elastoviscoplasticity Original Research Article

This paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application. We owe the original formulation of the applied model to Perzyna and Chaboche; it includes nonlinear isotropic and kinematic hardening as well as a nonlinear rate dependence. The constitutive equations are integrated numerically in the context of a finite element formulation. From theoretical 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 reduced to the asymptotic limit in a most simple way, namely by setting the viscosity parameter equal to zero. Furthermore, it is shown that the numerical integration of the constitutive model involves the solution of only one nonlinear equation for one scalar unknown. This even applies to a sum of Armstrong-Frederick terms. The algorithm incorporates the inelastic incompressibility on the level of the Gauβ points. Numerical computations of examples taken from metal forming technology show the physical significance of the model and the reliability of the numerical algorithm. These calculations have been carried out by means of the finite element program PSU.