A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture

TL;DR

This study compares eigenerosion and phase-field fracture models, showing eigenerosion's superior accuracy, convergence rate, and computational efficiency in a standard test case.

Contribution

It provides a detailed comparison of eigenerosion and phase-field models, highlighting eigenerosion's faster convergence and lower computational cost.

Findings

Eigenerosion converges at twice the rate of phase-field.

Eigenerosion achieves an order of magnitude faster computation.

Enhanced eigenerosion with Richardson extrapolation improves accuracy.

Abstract

We compare the accuracy, convergence rate and computational cost of eigenerosion (EE) and phase-field (PF) methods. For purposes of comparison, we specifically consider the standard test case of a center-crack panel loaded in biaxial tension and assess the convergence of the energy error as the length scale parameter and mesh size tend to zero simultaneously. The panel is discretized by means of a regular mesh consisting of standard bilinear or Q1 elements. The exact stresses from the known analytical linear elastic solution are applied to the boundary. All element integrals over the interior and the boundary of the domain are evaluated exactly using the symbolic computation program Mathematica. When the EE inelastic energy is enhanced by means of Richardson extrapolation, EE is found to converge at twice the rate of PF and to exhibit much better accuracy. In addition, EE affords a one-order-of-magnitude computational speed-up over PF.