On material-uniform elastic bodies with disclinations and their homogenization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912789543518208 |
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| author | Maor, Cy |
| author_facet | Maor, Cy |
| contents | In this note, we define material-uniform hyperelastic bodies (in the sense of Noll) containing discrete disclinations and dislocations, and study their properties. We show in a rigorous way that the size of a disclination is limited by the symmetries of the constitutive relation; in particular, if the symmetry group of the body is discrete, it cannot admit arbitrarily small, yet non-zero, disclinations. We then discuss the application of these observations to the derivations of models of bodies with continuously-distributed defects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On material-uniform elastic bodies with disclinations and their homogenization Maor, Cy Mathematical Physics Differential Geometry Classical Physics 74A20, 74Q05, 53Z05, 74B20 In this note, we define material-uniform hyperelastic bodies (in the sense of Noll) containing discrete disclinations and dislocations, and study their properties. We show in a rigorous way that the size of a disclination is limited by the symmetries of the constitutive relation; in particular, if the symmetry group of the body is discrete, it cannot admit arbitrarily small, yet non-zero, disclinations. We then discuss the application of these observations to the derivations of models of bodies with continuously-distributed defects. |
| title | On material-uniform elastic bodies with disclinations and their homogenization |
| topic | Mathematical Physics Differential Geometry Classical Physics 74A20, 74Q05, 53Z05, 74B20 |
| url | https://arxiv.org/abs/2412.14319 |