Optimized Method for Computing Phase-Field Model Using Decoupling Scheme

Fracture mechanisms in solids are governed by complex fracture phenomena such as crack initiation and multiple crack branching. Phase-field models are used to simulate crack propagation in materials subjected to mechanical loading. This approximation reduces the implementation complexity for fracture mechanics problems as it removes the need for numerical tracking of displacement discontinuities. This is accomplished by introducing a new damage variable representing the diffuse crack topology which is controlled by a numerical regularization parameter. Already, due to nonconvexity of the regularized energy functional, a robust staggered solution scheme based on the decoupling algorithm is used. An optimized computing method is presented. We propose quasi-static crack propagation where the damage variable is activated only if the maximum stress in the specimen reaches a critical value σ_c. This methodology reduces the time computing by 20%. A parametric study is done on the specimen geometry to study the ability of the algorithm to provide the crack path. We are interested in the determination of the influence of geometry of specimen on the evolution of energies and the crack path.