Nonlinear Numerical Integration Scheme in Strain Space Plasticity

Abstract

Strains are applied to the integration procedure in nonlinear increments todecrease the errors arising from the linearization of plastic equations. Two deformationvectors are used to achieve this. The first vector is based on the deformations obtained bythe first iteration of the equilibrium step, and the second is acquired from the sum of thesucceeding 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 formulationis investigated. Numerical examples are analyzed using the traditional linear method andthe suggested schemes. The examples are solved using the von Mises yield criterion andPrager's linear hardening rule. Results indicate that all nonlinear techniques increase theconvergence rate of plastic analysis. In addition, such integration methods are shown toincrease the stability of incremental-iterative analyses.