Quasistatic problems in viscoplasticity theory II: Models with nonlinear hardening

The existence theory to an internal variable model for viscoelastic or viscoplastic solids at small strain is studied. The model consists of an initial-boundary value problem to a system of linear partial differential equations coupled with nonlinear ordinary differential equations. It belongs to the subclass of monotone type models, which typically describe solids with rate dependent behavior exhibiting nonlinear hardening. The monotone type class includes all generalized standard materials. Solutions are found in L-p and H-p, the proof is based on monotonicity properties.