On strong solutions of viscoplasticity without safe-load conditions

Abstract

In this paper we discuss existence of pointwise solutions for dynamical models of viscoplasticity. Among other things, this work answers the question about necessity of safe-load conditions in case of viscoplasticity, which arise in the paper of K. Chełmiński (2001) [11]. We proved that solutions can be obtained without assuming any kind of safe-load conditions. Moreover, in the manuscript we consider much more general model than in the above mentioned paper. Namely, we consider the model with mixed boundary conditions and we allow a possible disturbance of the inelastic constitutive function by a globally Lipschitz function. Presented approach shows that via the same methods one can prove existence of pointwise solutions for: coercive models, self-controlling models, models with polynomial growth (not necessary of single valued) and monotone-gradient type models of viscoplasticity.