A Hybrid-High Order method for fracture modelling

TL;DR

This paper presents a novel Hybrid High-Order method for simulating fracture propagation using phase-field models, offering flexible mesh handling and improved numerical stability.

Contribution

It introduces a new hybrid high-order approach supporting polygonal meshes and fully discontinuous spaces for fracture modeling, with efficient algebraic solution strategies.

Findings

Supports general polygonal/polyhedral meshes

Demonstrates accurate fracture propagation simulation

Outperforms standard finite element schemes in validation

Abstract

In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides great flexibility in mesh design and adaptation, and can accommodate large variations of both the displacement and damage variables thanks to the use of fully discontinuous spaces. The resolution of the corresponding algebraic problem is based on a staggered time stepping scheme which takes advantage of static condensation for each subproblem. We provide extensive numerical validation of the method on classical two-dimensional fracture propagation problems, including a comparison with a more standard finite element scheme.