Framework and Numerical Algorithm for a Phase Field Fracture Model

. A phase field fracture model for quasi-brittle material in 2D is implemented in Abaqus software. The phase field damage variables 0 and 1 define undamaged and damaged regions of the material and simplify crack surface tracking. On the other hand, one has to use a fine spatial discretization for the smooth distribution of the phase field variable regularized by a small length scale parameter, which makes the method computationally expensive. At the fully damaged regions both the stiffness and stress reach zero. The displacements and damage are determined by a staggered approach, and a few standard benchmark fracture problems are used to demonstrate the work of the phase field fracture model under consideration.