Phase-field implicit material point method with the convected particle domain interpolation for brittle–ductile failure transition in geomaterials involving finite deformation

Abstract

A phase-field implicit material point method with the convected particle domain interpolation (PF-ICPDI) is proposed to model the brittle–ductile failure transition in pressure-sensitive geomaterials involving finite deformation. In this method, the phase-field fracture formulation relying on the microforce balance law and the second law of thermodynamics is adopted as a nonlocal damage function for the elastoplastic fracture analysis. A smooth two-yield-surface plasticity constitutive model is utilized to evaluate the brittle–ductile failure transition behavior of pressure-sensitive geomaterials. The coupling effect of phase-field fracture model and cap plasticity model is established by introducing an effective phase-field stress and splitting the total stored energy into elastic and plastic parts. The implicit material point method that can avoid severe mesh distortion and improve numerical stability is then developed to solve the quasi-static elastoplastic fracture finite deformation problem. Furthermore, the convected particle domain interpolation technique is adopted to eliminate numerical noises and improve computational accuracy while material points crossing cell boundaries in modeling the large deformation brittle–ductile failure transition process. The staggered incremental iterative scheme is carried out to solve the coupled discrete governing equations. The accuracy and capability of the proposed PF-ICPDI method are demonstrated through several representative numerical examples, as well as the effects of main material parameters on the phase-field brittle–ductile failure transition modeling of geomaterials are discussed.