Numerical convergence in simulations of multiaxial ratcheting with directional distortional hardening

In this work, we investigate the numerical convergence of a set of plasticity models with different kinematic and directional distortional hardening rules under cyclic plastic loading. In particular, we revisit the results presented in Feigenbaum et al. (2012) in order to more robustly check for convergence during the numerical integration procedure, and show that the results presented in the previous work do not converge. We investigate the role of the step-size and numerical scheme on the convergence of these models when predicting ratcheting. By reducing step-sizes and using a forward Euler scheme during numerical integration, converged solutions are obtained. The new converged results lead to new conclusions. Results still suggest that directional distortional hardening can improve ratcheting predictions, however the addition of directional distortional hardening yields less improvements compared to kinematic hardening alone than previously thought. This new conclusion, strongly suggests the need for additional modeling developments in order accurately predict ratcheting strains under a wide variety of cyclic plastic loadings.