A local-domain based phase field method for crack propagation

Abstract

The phase field method transfers the crack surface area into a domain integral through a smeared damage parameter. As a result, the fracture energy release rate can be directly incorporated into the energy form without tracking of crack surface, and a minimization approach to optimize the crack shape becomes possible. This nonlocal damage approach requires a fine mesh discretization to capture the damage gradient in the smeared crack zone, which produces a significant degree of freedom problem to optimize over the entire domain. In this research, a local-domain based phase field method is proposed. This method considers only elements in critical regions for energy minimization, whose internal energy are dominant, thus significantly reducing the degree of freedom to be solved. A numerical verification is carried out to demonstrate the feasibility of this approach, and simulations are presented to verify the accuracy of the new method.