Computation of brittle phase field fracture by the quadrature element method

The phase field method (PFM) provides a novel perspective for fracture computation. It is capable of simulating the whole process of crack propagation without introducing additional fracture criteria and complex crack path-tracking techniques. From the computational point of view, however, the PFM requires very fine meshes for the conventional numerical methods to accurately characterize the crack, which leads to huge computational costs. This paper employs the quadrature element method (QEM) to compute the phase field model for the brittle fracture. Through the computation of a benchmark example, the accuracy and low cost of the present method are verified. The QEM, in comparison with the existing methods, can accurately simulate the crack propagation process using a very coarse mesh and thus much fewer degrees of freedom.