Investigation of the formulation of the boundary value problem of the local theory of elastoplastic processes (Q1314162)

A formulation is given of the quasistatic global boundary value problem. It is proved that the operator of the global problem, an operator of the variational calculus, is positive definite, strictly monotonic in the main and possesses the \((S)_ i\)-property. It is shown that a generalized solution exists. It is proved that the global solution is unique and continuously dependent on the external loads. For the step method, using discretization of the process with respect to the load parameter, and iterative methods, convergence of the approximate solutions to the exact solution of the global problem is proved.