A frame-indifferent model for a thermo-elastic material beyond the three-dimensional Eulerian and Lagrangian descriptions

Panicaud, Benoît; Rouhaud, Emmanuelle

doi:10.1007/s00161-013-0291-z

Cited by 17 publications

(4 citation statements)

References 28 publications

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“…In his relativistic thermodynamics ( [23,24]), Souriau proposed to generalize the second principle as ∇ α S α ≥ 0 and introduced the friction tensor f αβ = 1 2 (∇ α b β + ∇ β b α ) that merges the temperature gradient and the strain rate tensor, allowing to extend Fourier's conduction law and viscous flow rules to Relativity, as proposed by Vallée [25,26]. By the way, Relativity is a consistent framework for the hypoelastic, hyperelastic and dissipative constitutive laws [27][28][29].…”

Section: Relativistic Dynamics and Thermodynamicsmentioning

confidence: 99%

Lie groups and continuum mechanics: where do we stand today?

de Saxcé,

Razafindralandy

2024

Comptes Rendus. Mécanique

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Section: Relativistic Dynamics and Thermodynamicsmentioning

confidence: 99%

Lie groups and continuum mechanics: where do we stand today?

de Saxcé,

Razafindralandy

2024

Comptes Rendus. Mécanique

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“…The constant C 1 is homogeneous to a stress and has a weight equal to 1 (Panicaud and Rouhaud 2014). This leads to the fact that Lie derivative of C 1 does not vanish in general, but is equal to…”

Section: Incompressible Neo-hookean Hypoelastic Modelmentioning

confidence: 99%

Viscoelastic models with consistent hypoelasticity for fluids undergoing finite deformations

Altmeyer

Rouhaud

Panicaud

et al. 2015

Mech Time-Depend Mater

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Constitutive models of viscoelastic fluids are written with rate-form equations when considering finite deformations. Trying to extend the approach used to model these effects from an infinitesimal deformation to a finite transformation framework, one has to ensure that the tensors and their rates are indifferent with respect to the change of observer and to the superposition with rigid body motions. Frame-indifference problems can be solved with the use of an objective stress transport, but the choice of such an operator is not obvious and the use of certain transports usually leads to physically inconsistent formulation of hypoelasticity. The aim of this paper is to present a consistent formulation of hypoelasticity and to combine it with a viscosity model to construct a consistent viscoelastic model. In particular, the hypoelastic model is reversible.A methodology is proposed in this paper to model hypoelasticity as an equivalent incremental formulation of hyperelasticity. This method is based on the use of Lie derivative to write an equivalent hypoelastic model and simultaneously to respect the general covariance principle. By associating these hypoelastic models with viscous behaviors, a physically re-B E. Rouhaud Mech Time-Depend Mater alistic model is obtained and can be used to represent the behavior of viscoelastic solids or fluids that are submitted to finite transformations or large rates of deformation. The validity of this approach is illustrated with the construction of a model for a Maxwell-like viscoelastic fluid. The model is implemented in the Z-set® numerical package and solved.

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“…Attempts to formulate Relativistic Elasticity in the General Relativity framework go back to 1916 with the pioneering work of Nordström [68], in Dutch. Since then, several authors have first aimed at proposing constitutive equations for Relativistic fluids [87,54,14,60] and, then, at modeling Relativistic continuous media, most often at the astrophysics scale [80,86,19,74,82,5,70,50,43,44,4,27,90,36,10], for instance for the modeling of the solid crust of neutron stars, but also at a local scale [57,58,59,72,72,73,63], for mechanical engineering applications.…”

Section: Introductionmentioning

confidence: 99%

Souriau's Relativistic general covariant formulation of hyperelasticity revisited

Kolev¹,

Desmorat²

2023

Preprint

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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 (Variational) General Relativity, and then in the particular case of a static spacetime. Different relativistic strain and stress tensors are formulated and discussed. Finally, we apply Souriau's formalism to Schwarzschild's metric, and recover the Classical Galilean Hyperelasticity with gravity, as the Newton-Cartan infinite light speed limit of this formulation.

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A frame-indifferent model for a thermo-elastic material beyond the three-dimensional Eulerian and Lagrangian descriptions

Cited by 17 publications

References 28 publications

Lie groups and continuum mechanics: where do we stand today?

Lie groups and continuum mechanics: where do we stand today?

Viscoelastic models with consistent hypoelasticity for fluids undergoing finite deformations

Souriau's Relativistic general covariant formulation of hyperelasticity revisited

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