Journal article
Universality in anisotropic linear anelasticity
- Abstract:
- In linear elasticity, universal displacements for a given symmetry class are those displacements that can be maintained by only applying boundary tractions (no body forces) and for arbitrary elastic constants in the symmetry class. In a previous work, we showed that the larger the symmetry group, the larger the space of universal displacements. Here, we generalize these ideas to the case of anelasticity. In linear anelasticity, the total strain is additively decomposed into elastic strain and anelastic strain, often referred to as an eigenstrain. We show that the universality constraints (equilibrium equations and arbitrariness of the elastic constants) completely specify the universal elastic strains for each of the eight anisotropy symmetry classes. The corresponding universal eigenstrains are the set of solutions to a system of second-order linear PDEs that ensure compatibility of the total strains. We show that for three symmetry classes, namely triclinic, monoclinic, and trigonal, only compatible (impotent) eigenstrains are universal. For the remaining five classes universal eigenstrains (up to the impotent ones) are the set of solutions to a system of linear second-order PDEs with certain arbitrary forcing terms that depend on the symmetry class.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.0MB, Terms of use)
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- Publisher copy:
- 10.1007/s10659-022-09910-7
Authors
- Publisher:
- Springer
- Journal:
- Journal of Elasticity More from this journal
- Volume:
- 150
- Pages:
- 241-259
- Publication date:
- 2022-07-13
- Acceptance date:
- 2022-06-16
- DOI:
- EISSN:
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1573-2681
- ISSN:
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0374-3535
- Language:
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English
- Keywords:
- Pubs id:
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1265200
- Local pid:
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pubs:1265200
- Deposit date:
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2022-06-24
- ARK identifier:
Terms of use
- Copyright holder:
- Yavari and Goriely
- Copyright date:
- 2022
- Rights statement:
- Copyright © 2022, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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