Plasticity Models and Nonlinear SemigroupsU

The evolution of an elastic-plastic material is modeled as an initial boundary value problem consisting of the dynamic momentum equation coupled with a constitutive law for which the hysteretic dependence between stress and strain is described by a system of variational inequalities. This system is posed as an evolution equation in Hilbert space for which is proved the existence and uniqueness of three classes of solutions which are distinguished by their regularity. Weak solutions are obtained in a very general situation, strong solutions arise in the presence of kinematic work-hardening or viscosity, and the solution is even more regular under a stability assumption connecting the constraint set with the divergence operator.