Gower, A.L. orcid.org/0000-0002-3229-5451, Shearer, T. orcid.org/0000-0001-7536-5547, Ciarletta, P. orcid.org/0000-0002-1011-5587 et al. (1 more author) (2025) The elastic stored energy of initially strained, or stressed, materials: restrictions and third-order expansions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481 (2307). 20240272. ISSN 1471-2946
Abstract
A large variety of engineering and biological materials have a non-zero internal stress distribution, even in the absence of applied forces. These stresses can arise from thermal expansion or volumetric growth, for example, in the production of the material. There are two approaches to modelling such materials that appear similar but are, in fact, distinct. The first defines a function, associated with a fixed reference configuration, where each value of τ corresponds to the initial stress in a different elastic material that occupies (each with a different elastic constitutive equation, effectively). The second defines a function, τ W ~ (F, τ) B , , say, B W , associated with a single, fixed, initially stressed, elastic material (with a single constitutive equation), where each value of (F, τ) represents the stress in a different configuration of that material. Here, we discuss why stored energy functions of the latter type, and similar functions that are written in terms of an initial strain, need to satisfy some restrictions to avoid unphysical behaviours. To illustrate their need, we perform an asymptotic expansion to prove that these restrictions are required for consistency with strain energy functions of classical third-order weakly nonlinear elasticity.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 The Author(s). Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
Keywords: | initial stress; initial strain; nonlinear elasticity; residual stress; residual strain; third-order elasticity |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > School of Mechanical, Aerospace and Civil Engineering |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 19 Feb 2025 16:44 |
Last Modified: | 19 Feb 2025 16:44 |
Status: | Published |
Publisher: | The Royal Society |
Refereed: | Yes |
Identification Number: | 10.1098/rspa.2024.0272 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:223450 |