A phase-field modeling for brittle fracture and crack propagation based on the cell-based smoothed finite element method

Abstract

This work develops a phase field model in the framework of cell-based smoothed finite element method (CS-FEM) aiming to solve problems of brittle fracture in solids. The phase-field method is employed to model complex discontinuous behaviors including crack initiation, crack coalescence, crack branching without using any ad hoc models. The CS-FEM which has been proven softer than the standard FEM is used to solve the equations that govern the continuum mechanics of solids. The current CS-FEM phase field method offers advantages of both S-FEM and phase field method in accurately predicting the evolution process of complex fracture patterns in solids. This CS-FEM phase-field technique is implemented in the commercial software ABAQUS using its user-element (UEL) and user-material (UMAT) modules. The coupled non-linear system of equations is solved by the built-in solver by decoupling the phase and displacement field parameters. Several examples have been presented to demonstrate the feasibility and effectiveness of the present method.