May, S., Vignollet, J. and De Borst, R. (2015) A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations. European Journal of Mechanics, A/Solids, 52. pp. 72-84. ISSN 0997-7538
Abstract
Recently, phase-field approaches have gained popularity as a versatile tool for simulating fracture in a smeared manner. In this paper we give a numerical assessment of two types of phase-field models. For the case of brittle fracture we focus on the question whether the functional that describes the smeared crack surface approaches the functional for the discrete crack in the limiting case that the internal length scale parameter vanishes. By a one-dimensional example we will show that Γ-convergence is not necessarily attained numerically. Next, we turn attention to cohesive fracture. The necessity to have the crack opening explicitly available as input for the cohesive traction-relative displacement relation requires the independent interpolation of this quantity. The resulting three-field problem can be solved accurately on structured meshes when using a balanced interpolation of the field variables: displacements, phase field, and crack opening. A simple patch test shows that this observation does not necessarily extend to unstructured meshes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Elsevier Masson SAS. This is an author produced version of a paper subsequently published in European Journal of Mechanics - A/Solids. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Phase-field model; Fracture; Γ-Convergence |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 02 Feb 2016 13:15 |
Last Modified: | 09 Mar 2016 13:53 |
Published Version: | http://dx.doi.org/10.1016/j.euromechsol.2015.02.00... |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.euromechsol.2015.02.002 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94438 |