Multisurface thermoplasticity for single crystals at large strains in terms of eulerian vector updates

Abstract

This paper presents a formulation of large-strain rate-independent multisurface thermoplasticity for single crystals and addresses aspects of its numerical implementation. The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A key feature of the present paper is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. This observation is intrinsically exploited on the numerical side by formulating a new fully implicit stress update algorithm and the associated consistent elastoplastic moduli in terms of these Eulerian vectors. The proposed return mapping algorithm treats the possibly redundant constraints of large-strain multisurface plasticity for single crystals by means of an active set search. Furthermore, it satisfies in an algorithmically exact way the plastic incompressibility condition in situations of multislip. The performance of the proposed formulation is demonstrated for two representative numerical simulations of thermoplastic deformation processes in single crystals with isotropic Taylor-type hardening.