A natural vector/matrix notation applied in an efficient and robust return-mapping algorithm for advanced yield functions

A fast and robust stress-integration algorithm is the key to full exploitation of advanced anisotropic yield functions in computational mechanics. Poor global convergence of a direct application of the Newton-Raphson scheme has been rectified by applying line search strategies during the Newton iterations. In this work the line-search approach is further improved by a better first guess. The new algorithm is implemented into a user-defined material subroutine (UMAT) in a finite-element (FE) software and tested. The implementation is made easier and more efficient by a new advantageous vector/matrix notation for symmetric second- and fourth-order tensors, which is the second result of this work. Benefits of this notation are discussed with respect to formulation of continuum-plasticity models as well as their implementations. FE simulations were run to demonstrate the performance of the new implementation, which is available as open-source software via GitLab repository (see Appendix). The new return-mapping algorithm implementation runs equally fast and robust as the simple von Mises and Hill standard implementations in the Abaqus/Standard software. This enables full exploitation of advanced yield functions as the new standard in industrial FE applications.

Automated summary

A fast and robust stress-integration algorithm has been proposed in this study, addressing poor global convergence of the Newton-Raphson scheme by improving line search strategies and initial guess. The new notation for symmetric second- and fourth-order tensors simplifies implementation and improves the efficiency of continuum-plasticity models formulations and their implementations, showcasing better performance in FE simulations.