A novel adaptive mesh refinement scheme for the simulation of phase-field fracture using trimmed hexahedral meshes

In this article, a novel adaptive mesh refinement scheme based on trimmed hexahedral (TH) meshes is proposed to simulate phase-field fracture in brittle materials. A regular hexahedral background mesh is adaptively refined using a balanced octree algorithm to resolve the length scale in phase-field fracture models. Adaptively refined TH meshes are created by cutting octree background meshes with the boundary of an analysis domain. A multithreshold criterion for mesh refinement is proposed to accurately capture the evolution of the damage phase field. Shape functions for transition TH elements are developed to satisfy the compatibility across the interelement boundaries between TH elements with different refinement levels. Numerical results show that the present scheme is very efficient and effective to trace arbitrary evolving phase-field cracks in three dimensions.