A method of successive approximations in a class of problems of the general theory of plasticity

We describe and elaborate a successive approximation method for solving a class of the value problems of the general plasticity, the boundary value problems in the theory of small-curvature elastoplastic processes. The core of the method is in solving a recursive series of elementary boundary problems yielding the discrete (in time) values of the unknown functions of a process. We give some modifications of the method. We prove the convergence theorem thus settling the existence of the solution to the boundary problem.