Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model

The phase-field model for fractures regularizes crack diffusion using a length-scale parameter. The displacement fields and the phase-field in a coupled system can be solved as either fully coupled “monolithic” or sequentially coupled “staggered” fields. In this paper, we employ the commercial finite-element software Abaqus to solve the monolithic and staggered phase-field models using a user-defined element (UEL) and user-defined material (UMAT/VUMAT) subroutines in two- and three-dimensions for quasi-static and dynamic fractures. We present the implementation procedures for both strategies, and make a detailed comparison using different applications. By comparing the phase-field model as a diffusive crack model and the extended finite-element method (XFEM) as a discrete crack model, we obtain good agreement. We investigate the influence of the model-regularization parameter based on experimental results. We adopt the thread-parallel execution and mutexes of Abaqus solvers.