May, S., Vignollet, J. and De Borst, R. orcid.org/0000-0002-3457-3574 (2016) A new arc-length control method based on the rates of the internal and the dissipated energy. Engineering Computations, 33 (1). pp. 100-115. ISSN 0264-4401
Abstract
Purpose - The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach - In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings - The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena. Originality/value - A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Emerald Group Publishing Limited. This is an author produced version of a paper subsequently published in Engineering Computations. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Arc-length control; Dissipation; Internal energy; Path-following technique |
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: | 09 Jun 2016 13:11 |
Last Modified: | 14 Apr 2017 03:11 |
Published Version: | http://dx.doi.org/10.1108/EC-02-2015-0044 |
Status: | Published |
Publisher: | Emerald |
Refereed: | Yes |
Identification Number: | 10.1108/EC-02-2015-0044 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:100670 |