Nonlinear Numerical Integration Scheme in Strain Space Plasticity

Strains are applied to the integration procedure in nonlinear increments to decrease the errors arising from the linearization of plastic equations. Two deformation vectors are used to achieve this. The first vector is based on the deformations obtained by the first iteration of the equilibrium step, and the second is acquired from the sum of the succeeding iterations. By applying these vectors and using sub-increments, the total strainincrement can vary nonlinearly during the integration of the flow rule. Four individualvariation schemes are presented for this purpose. In this paper, the strain space formulation is investigated. Numerical examples are analyzed using the traditional linear method and the suggested schemes. The examples are solved using the von Mises yield criterion and Prager's linear hardening rule. Results indicate that all nonlinear techniques increase the convergence rate of plastic analysis. In addition, such integration methods are shown to increase the stability of incremental-iterative analyses.