An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic-plastic constitutive equations

In a large class of rate-independent and rate-dependent elastic-plastic constitutive equations the elasticity is modeled in hypoelastic form, with the stress rate being taken as the Jaumann derivative, so as to make the constitutive model properly frame-indifferent or objective. Here, we present 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 it is therefore well suited for implementation in large-scale finite element codes. As an example, we have implemented the time-integration procedure in the finite element code ABAQUS. To check the incremental objectivity, accuracy, and stability of the algorithm some representative problems are solved.