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Published December 1, 2021 | Submitted
Journal Article Open

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


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.

Additional Information

© 2021 Elsevier B.V. Received 26 January 2021, Revised 13 July 2021, Accepted 24 July 2021, Available online 14 August 2021. MO gratefully acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060 and project 390685813 - GZ 2047/1 - HCM. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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August 22, 2023
October 23, 2023