A Phase Field Approach to Fracture Mechanics Problems

Abstract

Abstract Phase field modeling of fracture is a widely used numerical method for predicting fracture-related phenomena in solids. The phase field method is a continuous or diffused approach to fracture that approximates the original crack into a diffused zone of fracture. The diffused region is represented by an auxiliary variable called the phase field, which takes values between one and zero for broken and unbroken phases, respectively. The method is becoming increasingly popular since it conveniently solves the difficulty of explicitly tracing the cracks as displacement jumps and incorporating the same in the finite element mesh. The method gives accurate results for finite element meshes that are sufficiently refined. Exponential finite element shape functions offer a way of enhancing the computational efficiency of simulations. These special shape functions, due to their exponential nature, can capture sharp changes in solution variables with a lesser number of elements employed along the crack propagation path. However, exponential finite element shape functions need to be oriented with respect to the crack propagation path in order to provide a good approximation. This study presents an efficient implementation. An efficient implementation of the phase field fracture model is presented by employing automatically oriented exponential finite element shape functions. The orientation of these shape functions is informed by an approximate analysis using bilinear shape functions. The implementation is validated with previous simulations available in the literature. Computational costs and the accuracy of solutions are investigated for a few common fracture problems.