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Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2023

Souriau's Relativistic general covariant formulation of hyperelasticity revisited

Boris Kolev

Résumé

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. We focus as much as possible on the Continuum Mechanics point of view and describe the general covariant formulation of Hyperelasticity in (Variational) General Relativity. At this level of generality, different relativistic strain and stress tensors are formulated and discussed. Then, the choice of an observer, through the introduction of a spacetime structure allows us to make deeper insights into the foundations of Continuum Mechanics. We extend Souriau’s calculations, initially performed in the flat Minkowski spacetime, to the Schwarzschild spacetime accounting for gravitation. Finally, we recover the Classical Galilean Hyperelasticity with gravity, as the Newton–Cartan infinite light speed limit of this formulation.
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Dates et versions

hal-03861444 , version 1 (19-11-2022)
hal-03861444 , version 2 (17-01-2023)

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Boris Kolev, Rodrigue Desmorat. Souriau's Relativistic general covariant formulation of hyperelasticity revisited. Journal of the Mechanics and Physics of Solids, inPress, pp.105463. ⟨10.1016/j.jmps.2023.105463⟩. ⟨hal-03861444v2⟩
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