Energy consistent framework for continuously evolving 3D crack propagation

TL;DR

This paper introduces an energy consistent, mesh-adaptive finite element framework for 3D crack propagation in brittle materials, enabling continuous crack evolution without face splitting or enrichment techniques.

Contribution

It develops a novel formulation based on configurational mechanics that allows for continuous crack front evolution and incorporates mesh smoothing and hierarchical basis functions.

Findings

Accurate simulation of 3D crack growth demonstrated

Mesh quality maintained during crack evolution

Robustness shown through numerical examples

Abstract

This paper presents a formulation for brittle fracture in 3D elastic solids within the context of configurational mechanics. The local form of the first law of thermodynamics provides a condition for equilibrium of the crack front. The direction of the crack propagation is shown to be given by the direction of the configurational forces on the crack front that maximise the local dissipation. The evolving crack front is continuously resolved by the finite element mesh, without the need for face splitting or the use of enrichment techniques. A monolithic solution strategy is adopted, solving simultaneously for both the material displacements (i.e. crack extension) and the spatial displacements, is adopted. In order to trace the dissipative loading path, an arc-length procedure is developed that controls the incremental crack area growth. In order to maintain mesh quality, smoothing of the mesh is undertaken as a continuous process, together with face flipping, node merging and edge splitting where necessary. Hierarchical basis functions of arbitrary polynomial order are adopted to increase the order of approximation without the need to change the finite element mesh. Performance of the formulation is demonstrated by means of three representative numerical simulations, demonstrating both accuracy and robustness.