A modified damage and fracture phase field model considering heterogeneity for rock-like materials

Damage and fracture are the most extensive failure modes of rock materials, which may easily induce disaster and instability of engineering structures. This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks. The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations. Meanwhile, the free energy was constructed by the elastic strain energy sphere-bias decomposition and the plastic strain energy. As for the numerical implementation, the three layers finite elements method structure was used in the frame of the finite element method. The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre-existing cracks under compression. This paper constructs a nonlocal damage fracture phase field model for rocks considering the plastic strain energy and nonhomogeneous characteristics of rocks, mainly including considering the difference of critical energy release rate and nonhomogeneous characteristics of rocks. image This paper developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks. The modified phase field model introduces the heterogeneity of fracture parameters and modifies the governing equations. The numerical implementation uses the three layers finite elements method structure.