A hybrid adaptive finite element phase‐field method for quasi‐static and dynamic brittle fracture

Abstract

SummaryThe phase‐field approach has unique advantages in describing fracture phenomena, which has received extensive attention in the past decade. Nevertheless, the phase‐field modeling of fracture is computationally demanding, due to the high temporal‐spatial resolution required for crack tracking. In this contribution, a novel hybrid adaptive finite element phase‐field method (ha‐PFM) is developed to solve brittle fracture problems under quasi‐static and dynamic loading. ha‐PFM can dynamically track the propagation of the cracks and adaptively refine the meshes based on a novel crack tip identification strategy. Afterward, the refined meshes in the noncrack progression region are reconverted into coarse meshes. This scheme prominently reduces the computational cost, eg, CPU time and memory usage. Unlike the previous adaptive phase‐field method, multilevel hybrid triangular and quadrilateral elements were developed to discretize the computational domain, which eliminates hanging nodes and ensures that the meshes in the vicinity of the crack tip are highly isotropic. Several representative benchmarks containing quasi‐static and dynamic fracture were reinvestigated with ha‐PFM, and its excellent performance is substantiated by comparison with the standard phase‐field method and literature results.