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A spatially adaptive phase-field model of fracture

Phansalkar, Dhananjay and Weinberg, Kerstin and Ortiz, Michael and Leyendecker, Sigrid (2022) A spatially adaptive phase-field model of fracture. Computer Methods in Applied Mechanics and Engineering, 395 . Art. No. 114880. ISSN 0045-7825. doi:10.1016/j.cma.2022.114880.

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Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter ϵ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying spatial resolution where needed while simultaneously keeping the computational size of the model as small as possible. Here, a variational-based spatial adaptivity is proposed for a phase-field model of fracture. An extension of the conventional phase-field model is achieved by allowing spatial variation of the regularisation length ϵ in the energy functional. Similar to the displacement and phase fields, the optimal regularisation length is obtained by minimising the energy functional. This extended phase-field model serves as the foundation for an adaptive mesh refinement strategy, in which the mesh size is determined locally by the optimal regularisation length. The resulting solution procedure is implemented in the framework of the finite element library FEniCS. According to the selected numerical experiment, the spatially adaptive phase-field model converges marginally faster than the conventional phase-field model but with a vastly superior constant, resulting in significant computational savings.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Phansalkar, Dhananjay0000-0001-7870-1446
Weinberg, Kerstin0000-0002-2213-8401
Ortiz, Michael0000-0001-5877-4824
Additional Information:© 2022 The Authors. Published by Elsevier Under a Creative Commons license. Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Received 21 September 2021, Revised 28 January 2022, Accepted 10 March 2022, Available online 16 May 2022, Version of Record 16 May 2022. The German Research Foundation (DFG) is gratefully acknowledged for funding this research within the research training group GRK2423 FRASCAL. KW and MO gratefully acknowledge the support of the DFG within the Priority Program 2256 “Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials”, project number 422730790. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Dhananjay Phansalkar reports financial support was provided by German Research Foundation. Kerstin Weinberg, Michael Ortiz reports travel was provided by German Research Foundation.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)GRK2423
Deutsche Forschungsgemeinschaft (DFG)422730790
Subject Keywords:Brittle fracture; Phase-field model; Spatial variation of the regularisation length; Adaptive mesh refinement
Record Number:CaltechAUTHORS:20220517-424411000
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Official Citation:Dhananjay Phansalkar, Kerstin Weinberg, Michael Ortiz, Sigrid Leyendecker, A spatially adaptive phase-field model of fracture, Computer Methods in Applied Mechanics and Engineering, Volume 395, 2022, 114880, ISSN 0045-7825,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114772
Deposited By: George Porter
Deposited On:18 May 2022 14:50
Last Modified:18 May 2022 14:50

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