Numerical Implementation of A Model With Directional Distortional Hardening

Abstract

The presented work outlines and tests a finite-element (FE) implementation of a simple directional distortional hardening model. The evolution equations of internal variables are based on the Armstrong–Frederick evanescent memory-type hardening rule, and the associative flow rule is adopted. The directional distortion of the yield function is governed by the contraction of the backstress tensor with the so-called unit radial tensor, and incorporates a fixed scalar distortional parameter. Therefore, the variety of possible shapes of predicted subsequent yield surfaces is limited. The tangent stiffness–radial corrector method with fine subincrementation is used. This implementation is verified by comparing numerical results with analytical solutions pertinent to proportional load cases and semianalytical solutions for nonproportional loadings. The template of the whole implementation is included in the Appendix.