Constitutive modeling and computational implementation for finite strain plasticity

Abstract

This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-type constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the “back-stress,” in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling a finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.