Crack propagation simulation without crack tracking algorithm: embedded discontinuity formulation with incompatible modes

TL;DR

This paper introduces a novel embedded discontinuity finite element method that simulates crack propagation in 2D solids without crack tracking algorithms, enabling complex crack patterns including branching with high accuracy and efficiency.

Contribution

The work presents a new local crack nucleation criterion within an embedded discontinuity framework, allowing multiple cracks to propagate independently without tracking algorithms.

Findings

Accurately predicts complex crack patterns including branching.

Matches experimental and previous numerical results in fracture energy and load-displacement.

Efficiently simulates crack propagation in static and dynamic cases.

Abstract

We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element that has incompatible modes. Even more importantly, we demonstrate that these results can be obtained without using a crack tracking algorithm. Therefore, the simulation of crack patterns with several cracks, including branching, becomes possible. The avoidance of a tracking algorithm is mainly enabled by the application of a novel, local (Gauss-point based) criterion for crack nucleation, which determines the time of embedding the localisation line as well as its position and orientation. We treat the crack evolution in terms of a thermodynamical framework, with softening variables describing internal dissipative mechanisms of material degradation. As presented by numerical examples, many elements in the mesh may develop a crack, but only some of them actually open and/or slide, dissipate fracture energy, and eventually form the crack pattern. The novel approach has been implemented for statics and dynamics, and the results of computed difficult examples (including Kalthoff's test) illustrate its very satisfying performance. It effectively overcomes unfavourable restrictions of the standard embedded strong discontinuity formulations, namely the simulation of the propagation of a single crack only. Moreover, it is computationally fast and straightforward to implement. Our numerical solutions match the results of experimental tests and previously reported numerical results in terms of crack pattern, dissipated fracture energy, and load-displacement curve.