Convergence of Newton-type methods in incremental return mapping analysis of elasto-plastic problems

The incremental finite element algorithm with return mapping stress computation is considered for the solution of problems of elasto-plasticity. This algorithm, performed in load steps, leads to the necessity of solving large scale nonlinear systems. The properties of these systems are investigated in the presented paper together with two iterative techniques for their solution. The main results of the paper are rigorous proofs of the convergence of the inexact initial stiffness method and the local quadratic convergence of the inexact Newton method with the consistent tangent operator.