Contact problems of the theory of plasticity for complex loading (Q1071596)

The problem of the interaction between a stamp and an elastic-plastic body for a non-proportional change in the given loads and taking the contact area indeterminacy into account, is considered. It is assumed that the material properties are described by differential-linear or differential-nonlinear relationships between the stress rates and the strain rates encompassing a fairly broad group of the theory of plasticity. It is shown that the initial problem in a generalized formulation is equivalent to a certain quasivariational inequality in the displacement velocities. By using a formulation in the form of a quasivariational inequality, existence conditions are studied for the solution, and a numerical method of investigation is proposed and verified.