Phase field fracture in elasto-plastic solids: Abaqus implementation and case studies

Phase field modelling for fracture has been extended from elastic solids to elasto-plastic solids. In this study, we present the implementation procedures of a staggered scheme for phase field fracture of elasto-plastic solids in commercial finite element software Abaqus using subroutines UEL and UMAT. The UMAT is written for the constitutive behaviour of elasto-plastic solids, while the UEL is written for the phase field fracture. The phase field and displacement field are solved separately using the Newton-Raphson iteration method. In each iteration, one field is computed by freezing the other field at the last loading increment. A number of benchmark examples are tested from one single element up to 3D problems. The correctness of the staggered scheme is verified analytically in terms of the stress-strain curve and the evolution of the phase field in the one single element example. In the 2D and 3D problems, the fracture behaviour of elasto-plastic solids can be reproduced in terms of reaction force curve and crack propagation, which exhibit good agreement with the experimental observations and numerical results in literature. Not only can the proposed implementation help attract more academic researchers, but also engineering practitioners to take the advantages of phase field modelling for fracture in elasto-plastic solids. The Abaqus subroutine codes can be downloaded online from Mendeley data repository linked to this work (The link is provided in Supplementary material).