Phase field fracture over quadtrees using the Virtual Element Method

Predictive modelling of fracture in materials is critical for understanding progressive failure at the material or structure scale.Traditional fracture modeling techniques often require laborious algorithms to track propagating cracks.Conversely, the phase field method has been established as an appealing alternative, mainly due to its favorable implementational features.Yet, criticism to the phase field method involves its ability to accurately resolve crack nucleation and its associated computational costs.In this work, we integrate adaptive quadtree meshing with the Virtual Element Method with the objective of significantly reducing the computational costs of phase field simulations.Quadtree meshing is a hierarchical grid-based technique used for adaptive mesh refinement in 2D simulations.Using the VEM, hanging nodes in the quadtree decomposition are naturally treated and a conforming mesh is always established in contrast to conventional methods.This optimizes computational resources by refining the mesh locally, improving accuracy in complex regions while maintaining coarser elements elsewhere.Different adaptivity criteria are explored and benchmarks pertaining to mode I and mode II brittle fracture are examined in terms of accuracy and efficiency when compared to the standard finite element method.