The Variational Formulation of Viscoplastic Constitutive Updates

We present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as nite elastic and plastic deformations, non-Newtonian viscosity, rate-sensitivity and arbitrary ow 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 nitely-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.