Journal article
The anelastic Ericksen problem: universal deformations and universal eigenstrains in incompressible nonlinear anelasticity
- Abstract:
- Ericksen’s problem consists of determining all equilibrium deformations that can be sustained solely by the application of boundary tractions for an arbitrary incompressible isotropic hyperelastic material whose stress-free configuration is geometrically flat. We generalize this by first, using a geometric formulation of this problem to show that all the known universal solutions are symmetric with respect to Lie subgroups of the special Euclidean group. Second, we extend this problem to its anelastic version, where the stress-free configuration of the body is a Riemannian manifold. Physically, this situation corresponds to the case where nontrivial finite eigenstrains are present. We characterize explicitly the universal eigenstrains that share the symmetries present in the classical problem, and show that in the presence of eigenstrains, the six known classical families of universal solutions merge into three distinct anelastic families, distinguished by their particular symmetry group. Some generic solutions of these families correspond to well-known cases of anelastic eigenstrains. Additionally, we show that some of these families possess a branch of anomalous solutions, and demonstrate the unique features of these solutions and the equilibrium stress they generate.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 3.0MB, Terms of use)
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- Publisher copy:
- 10.1007/s10659-020-09797-2
Authors
- Publisher:
- Springer
- Journal:
- Journal of Elasticity More from this journal
- Volume:
- 142
- Pages:
- 291-381
- Publication date:
- 2020-10-07
- Acceptance date:
- 2020-09-16
- 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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1132593
- Local pid:
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pubs:1132593
- Deposit date:
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2020-09-17
- ARK identifier:
Terms of use
- Copyright holder:
- Goodbrake et al.
- Copyright date:
- 2020
- Rights statement:
- Copyright © 2020 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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