A comparative accuracy and convergence study of eigenerosion and phasefield models of fracture
Abstract
We compare the accuracy, convergence rate and computational cost of eigenerosion (EE) and phasefield (PF) methods. For purposes of comparison, we specifically consider the standard test case of a centercrack 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 oneorderofmagnitude computational speedup over PF.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 December 2021
 DOI:
 10.1016/j.cma.2021.114078
 arXiv:
 arXiv:2101.12520
 Bibcode:
 2021CMAME.386k4078P
 Keywords:

 Mathematics  Numerical Analysis;
 7410;
 74S10;
 74R10
 EPrint:
 20 pages, 6 figures