On the numerical treatment of finite deformations in elastoviscoplasticity
This paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application. The formulation 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. 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 Gauß 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.
scientific article; zbMATH DE number 1079159