A phase field approach to the fracture simulation of quasi-brittle structures with initial state

To solve the simulation problem of crack propagation in solid structures with initial stress, this paper proposes a phase field approach that considers the initial state of the quasi-brittle structure. By using the initial equilibrium iteration method, the estimated initial state of the structure, including initial stress, is transformed into internal stress loads of the structure. Thus, the problem of non-convergence caused by inaccurate initial state estimation of the structure in engineering calculations was solved, and an improved subproblem staggered iteration method was adopted to simulate crack propagation of the structure under external loads. The universality and computational accuracy of this method for different phase field models were verified by using pre made notched thin plates for the expansion of mode I and II cracks in different initial states. Among them, the calculation error using the PF_CZM model is within 1%, and the calculation error of the AT2 model increases with the initial stress, but is less than 7%. At the same time, the crack growth problem of cracked structures under different uniform initial stresses is accurately simulated, which reflects the applicability of this method to actual engineering. In addition, the study also verified the universal applicability of the adaptive refinement strategy proposed based on the AT2 model for other phase field models.