Finite element simulation of crack propagation based on phase field theory

The finite element approach is applied to predict crack patterns in a single or composite material under loadings. Crack patterns are represented as variations of a field variable. These variations are determined from the solution of a coupled system of equations consisting of an Allen-Cahn or Ginzburg-Landau type field equation and elasticity equations based on phase field theory. This representation does not require tracking crack tips as in the conventional finite element approach for the modeling of crack propagation problems. For a numerical solution for the system, a finite element algorithm is proposed and implemented into the finite element program “FEAP”. Several numerical simulations are performed and analyzed to predict the crack patterns in 2D single or composite materials under the loadings.