Souriau's Relativistic general covariant formulation of hyperelasticity revisited
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866912001227227136 |
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| author | Kolev, Boris Desmorat, Rodrigue |
| author_facet | Kolev, Boris Desmorat, Rodrigue |
| contents | We present and modernize Souriau's 1958 geometric framework for Relativistic continuous media, and enlighten the necessary and the ad hoc modeling choices made since, focusing as much as possible on the Continuum Mechanics point of view. We describe the general covariant formulation of Hyperelasticity in General Relativity, and then in the particular case of a static spacetime. Finally, we apply this formalism for the Schwarzschild's metric, and recover the Classical Galilean Hyperelasticity with gravity, as the Newton-Cartan infinite light speed limit of this formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09437 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Souriau's Relativistic general covariant formulation of hyperelasticity revisited Kolev, Boris Desmorat, Rodrigue General Relativity and Quantum Cosmology Mathematical Physics We present and modernize Souriau's 1958 geometric framework for Relativistic continuous media, and enlighten the necessary and the ad hoc modeling choices made since, focusing as much as possible on the Continuum Mechanics point of view. We describe the general covariant formulation of Hyperelasticity in General Relativity, and then in the particular case of a static spacetime. Finally, we apply this formalism for the Schwarzschild's metric, and recover the Classical Galilean Hyperelasticity with gravity, as the Newton-Cartan infinite light speed limit of this formulation. |
| title | Souriau's Relativistic general covariant formulation of hyperelasticity revisited |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2301.09437 |