Integral convexity argument for plasticity function and monotonicity of iteration process for elasto-plastic problems

The variational approach for boundary value problems related to non-linear materials is presented. The approach is based on the introduced integral convexity argument and monotone operator theory. This permits to obtain an existence and uniqueness of the solution within the range of Kachanov's theory, under natural and general conditions. The introduced argument allows to prove monotonicity of the sequence of potentials on the sequence of iterations. As a result monotonicity of the iteration process for elastoplastic problems is obtained. Theoretical results are illustrated by computational experiments.