Improving Convergence and Robustness of the Phase-Field Method for Fracture Mechanics using a Gradient-based Line Search Strategy for the L-BFGS Algorithm

Resumo

Phase-field models are widely recognized for their capability to simulate intricate crack propagation processes. Despite their advantages, the nonlinear and non-convex nature of their variational formulation poses significant challenges for numerical solvers, particularly in scenarios involving rapid crack growth. Traditional Newton-based solvers often struggle with convergence, while the commonly used alternating minimization approach, though robust, leads to high computational costs due to its iterative nature. In this presentation, we introduce a novel improvement to the L-BFGS algorithm by incorporating a gradient-based line search strategy. This modification aims to improve both the efficiency and robustness of phase-field fracture simulations. We will showcase numerical experiments involving brittle and quasi-brittle fracture cases, highlighting the method's ability to reduce computational costs while maintaining accuracy. A stand-alone implementation of the proposed method will be provided, allowing for easy integration into existing phase-field frameworks.