Comprehensive implementations of phase-field damage models in Abaqus

Abstract

Despite the versatility in modeling complex crack configurations, phase-field damage models for fracture usually count only on in-house codes, greatly restricting their potential applications. It is thus of vital importance to implement them in those commonly used commercial software packages like Abaqus. However, so far only the less robust Newton’s monolithic algorithm or the inefficient staggered solver has been considered. In this work, taking the unified phase-field damage theory (Wu, 2017) as the particular example, we present three distinct strategies of implementing phase-field damage models into Abaqus: (i) UMAT-Newton-M: a thermo-mechanically coupled user-defined material (UMAT) implementation of the modified Newton monolithic solver; (ii) UEL-Staggered: a novel user-defined element (UEL) implementation of the iterative staggered (alternate minimization) algorithm with dummy dofs; (iii) UEL-BFGS: a UEL implementation of the recently advocated BFGS quasi-Newton monolithic algorithm. The aforesaid implementation strategies are then validated against several representative benchmark problems of brittle fracture and quasi-brittle failure. It is found that, the UMAT-Newton-M implementation is the simplest but not robust enough, while the UEL-Staggered implementation is robust but extremely inefficient. Comparatively, in all cases the UEL-BFGS scheme is of the best numerical performance with lest iterations and sufficient robustness. For the sake of reproducibility of the presented numerical results and the promotion of phase-field damage models, the source codes (programmed in the free format syntax of FORTRAN90) are also provided and interested users can download them at https://github.com/jianyingwu/pfczm-abaqus.