Objective Time-Integration Procedure for Isotropic Rate-Independent and Rate-Dependent Elastic-Plastic Constitutive Equations

摘要

In a large class of rate-independent and rate-dependent elastic-plastic constitutive equations the elasticity is modeled in hypo-elastic form, with the stress rate being taken as the Jaumann derivative, so as to make the constitutive model properly frame-indifferent or objective. The paper presents a fully-implicit, stable time-integration procedure for implementing such constitutive models in displacement-based finite element procedures. The numerical procedure preserves the very desirable feature of incremental objectivity. The overall procedure is a generalization of the well-known 'radial-return' algorithm of classical rate-independent plasticity and is, therefore, well suited for implementation in large-scale finite element codes. As an example, the time-integration procedure has been implemented in the finite element code ABAQUS. To check the incremental objectivity, accuracy, and stability of the algorithm, some representative problems are solved.