Abstract
The isothermal version of a unified constitutive model for isotropic elasto-viscoplasticity proposed by Anand and co-workers (Anand [1,2], Brown, Kim, and Anand [3]) consists of a coupled set of differential evolution equations for the state variables (T, s), where T is the Cauchy stress tensor, and s is a scalar internal variable representing the isotropic resistance to plastic flow offered by the underlying microstructural state of the material. Constitutive equations of this type have long been known to be numerically very stiff. Here, we outline a fully-implicit, robustly stable time integration procedure, based on the Euler backward method, for implementing Anand’s single scalar internal variable model in displacement-based finite element procedures. The numerical procedure preserves the very desirable feature of 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.
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