Dynamic analysis of bi-material interfacial cracks by the high-order GFDM with an enhanced Krylov deferred correction technique

This work introduces a high-order numerical methodology for simulating interfacial cracks in bi-material media under dynamic loadings. For discretizing the elastodynamic system, the proposed numerical framework utilizes an enhanced Krylov deferred correction (KDC) method for temporal discretization, integrated with the high-order generalized finite difference method (GFDM) for spatial discretization. The enhanced KDC technique incorporates a precise numerical implementation strategy to accurately match the boundary conditions. In the GFDM, the fourth-order Taylor series expansions are utilized near the crack tips, whereas second-order expansions are employed in the far-field. A node refinement technique is applied in vicinity of the crack-tips to improve the numerical accuracy. This integration of the enhanced KDC and the high-order GFDM allows for highly accurate simulations of dynamic interface cracks with large time steps. Extensive numerical experiments validate the effectiveness of this method in addressing bi-material dynamic interface crack problems under impact loadings. Furthermore, the dynamic stress intensity factors (DSIFs) generated through the proposed approach are compared with those obtained from the finite element method (FEM) or the boundary element method (BEM).