Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration

TL;DR

This paper presents a phenomenological viscoplasticity model incorporating nonlinear kinematic hardening, along with two implicit time integration methods that accurately satisfy plastic incompressibility, validated through numerical simulations.

Contribution

It introduces a novel multiplicative decomposition framework for nonlinear kinematic hardening and compares two implicit time-stepping methods for its numerical integration.

Findings

Both time integration methods produce similar results for finite inelastic increments.

The model accurately captures basic features of viscoplastic material response.

Numerical tests validate the effectiveness of the proposed methods.

Abstract

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of Armstrong-Frederick type. Two implicit time-stepping methods are adopted for numerical integration of evolution equations, such that the plastic incompressibility constraint is exactly satisfied. The first method is based on the tensor exponential. The second method is a modified Euler-Backward method. Special numerical tests show that both approaches yield similar results even for finite inelastic increments. The basic features of the material response, predicted by the material model, are illustrated with a series of numerical simulations.