A length insensitive modified phase field model for quasi-brittle failure and brittle fracture.

In response to the problem that the standard AT2 phase field model cannot effectively model quasi-brittle failure and the existence of length dependence, a new modified phase field model is presented in this paper. By introducing an additional energy, the competing relationship between elastic strain energy and dissipation energy during fracture is changed. A new crack dissipation functional is established using the energy equivalent approach. By introducing a novel rational degradation function, not only can the strength of material failure be effectively utilized, but the model can also reproduce the cohesive softening relationship. A multi-field finite element method is used to discretize the model governing equations, and the equations are solved by an efficient BFGS monolithic algorithm. Finally, some representative numerical examples are used to analyze the effects of parameters in degradation function, length scale and mesh size on the results. The presented numerical simulation results demonstrate length scale and mesh scale independence, and are in good agreement with the experimental results and previous numerical results. At the same time, the numerical results also exhibit cohesive softening properties similar to the current phase field cohesive zone model. These results verify the robustness and effectiveness of the modified phase field model presented in this paper for simulating quasi-brittle failure and brittle fracture. [ABSTRACT FROM AUTHOR]