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

Pandolfi, A. and Weinberg, K. and Ortiz, M. (2021) A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210225-132738559

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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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2101.12520arXivDiscussion Paper
ORCID:
AuthorORCID
Pandolfi, A.0000-0002-7084-7456
Ortiz, M.0000-0001-5877-4824
Additional Information:Attribution 4.0 International (CC BY 4.0). MO gratefully acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060 and project 390685813 - GZ 2047/1 - HCM.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SFB 1060
Hausdorff Center for MathematicsGZ 2047/1
Record Number:CaltechAUTHORS:20210225-132738559
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210225-132738559
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108210
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Mar 2021 15:31
Last Modified:01 Mar 2021 15:31

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