Universal Deformations in Compressible Isotropic Cauchy Elastic Solids with Residual Stress
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915446182117376 |
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| author | Yavari, Arash Merodio, José Shariff, Mohd H. B. M. |
| author_facet | Yavari, Arash Merodio, José Shariff, Mohd H. B. M. |
| contents | We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the associated residual stresses must also be homogeneous. Since a non-trivial residual stress cannot be homogeneous, it follows that residual stress must vanish. Thus, a compressible Cauchy elastic solid with a non-trivial distribution of residual stress cannot admit universal deformations. These findings are consistent with the results of \citet{YavariGoriely2016}, who showed that in the presence of eigenstrains, universal deformations are covariantly homogeneous and in the case of simply-connected bodies the universal eigenstrains are zero-stress (impotent). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Deformations in Compressible Isotropic Cauchy Elastic Solids with Residual Stress Yavari, Arash Merodio, José Shariff, Mohd H. B. M. Mathematical Physics We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the associated residual stresses must also be homogeneous. Since a non-trivial residual stress cannot be homogeneous, it follows that residual stress must vanish. Thus, a compressible Cauchy elastic solid with a non-trivial distribution of residual stress cannot admit universal deformations. These findings are consistent with the results of \citet{YavariGoriely2016}, who showed that in the presence of eigenstrains, universal deformations are covariantly homogeneous and in the case of simply-connected bodies the universal eigenstrains are zero-stress (impotent). |
| title | Universal Deformations in Compressible Isotropic Cauchy Elastic Solids with Residual Stress |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2508.10179 |