Quasistatic viscoplasticity with a nonlinear force term of gradient type

The aim of this paper is to study the existence of solutions to the quasistatic model of viscoplasticity in which inelastic constitutive law is in form of differential inclusion and equation of motion has additional nonlinear force term. Both nonlinearities are assumed to be of gradient type. In presented work we analyse problem for three classes of models with mixed boundary conditions and without safe-load conditions. Presented approach allows us not only to consider models with L2 self-controlling property, but also models with polynomial growth and models with strictly convex quadratic potential of nonlinear force term. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data