Existence of solutions to a class of quasi-static problems in viscoplasticity theory

We prove existence of solutions for quasi-static initial-boundary value problems to a class of constitutive equations with internal variables. This class consists of constitutive equations of monotone type with positive definite free energy. They model the deformation behavior of metallic bodies. The existence theorem is proved by reduction of the initial-boundary value problem to an abstract evolution equation with a time dependent maximal monotone evolution operator, and by application of known existence results for such evolution equations. The proofs are sketched. At the end an example is given for a constitutive equation satisfying the hypotheses of the existence theorem.