The variational formulation of viscoplastic constitutive updates

Abstract

We present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations, non-Newtonian viscosity, rate-sensitivity and arbitrary flow and hardening rules. The distinguishing characteristic of the proposed constitutive updates is that, by construction, the corresponding incremental stress—strain relations derive from a pseudo-elastic strain-energy density. This, in turn, confers the incremental boundary value problem a variational structure. In particular, the incremental deformation mapping follows from a minimum principle. This minimum principle may conveniently be taken as a basis for error estimation and mesh adaption. The accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely-deforming Mises solid and ductile single crystals. The ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy.