Adaptive Configurational Force-based crack propagation for brittle and fatigue analysis

Abstract

This paper presents a ℎ𝑝𝑟-adaptive crack propagation method for highly accurate 2D crack propagation paths which requires no a priori knowledge of the tip solution. The propagation method is designed to be simple to implement, only ℎ𝑟-adaptivity is required, with the propagation step size independent of the initial mesh allowing users to obtain high fidelity crack path predictions for domains containing multiple cracks propagating at different rates. The proposed method also includes a crack path derefinement scheme, where elements away from the crack tip are derefined whilst elements close to the crack tip are small so capture the fidelity of the crack path. The result is that the propagation of cracks over an increasingly larger distances has negligible increased computational effort and effect on the propagation path prediction. The linear elastic problem is solved using the hp discontinuous Galerkin symmetric interior penalty (SIPM) finite element method, which is post-processed to obtain the configurational force (CF) at each tip to a user defined accuracy. Several numerical examples are used to demonstrate the accuracy, efficiency, and capability of the method. Due to the method’s high accuracy crack path solutions of benchmark problems that are prolifically used in the literature are challenged.