On stability and efficiency of numerical integration of endochronic constitutive equations

Abstract

Two numerical integration procedures based on a nonlinear finite-difference formulation of the endochronic plasticity theory without a yield surface are discussed. One is for three-dimensional strain-controlled simulation, and the other is for strain-controlled simulation of tension-torsion loading. Unconditional stability of both procedures is proved for strain-hardening materials. The efficiency of the proposed numerical schemes is demonstrated by an extrordinary reduction in the number of tensiontorsion loading steps applied to OFHC copper specimens. The results suggest promising application of finite-difference formulation in finite element analysis using a tangential stiffness method. Since no yield surface is involved, the FE computation should be extremely straightforward.