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Covariant spacetime formalism for applications to thermo-hyperelasticity

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Abstract

The principle of material objectivity used in classical continuum mechanics states that the description of material behaviors has to be frame-invariant. Moreover, geometric considerations show that objectivity can be extended by use of a covariant principle. Covariance can be naturally expressed using a four-dimensional spacetime. We thus propose to consider a thermodynamic approach within this framework to obtain covariant constitutive models in the case of finite deformation. A four-dimensional form of the Clausius–Duhem inequality is thus derived for continuum thermomechanics applications. In this article, we are able to propose a new thermo-hyperelastic constitutive model from such a generalized thermodynamics approach with the implementation of the spacetime Lie derivative. The resulting model is then illustrated for different mechanical or thermal loadings with numerical simulations.

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Acknowledgements

We thank the Scientific Council of the Université de Technologie de Troyes and the Région Grand Est for their trust and financial supports.

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Authors and Affiliations

  1. Life Assessment of Structures, Materials, mechanics and Integrated Systems (LASMIS), Université de Technologie de Troyes (UTT), 12, rue Marie Curie, CS 42060 10004, Troyes cedex, France

    Roula Al Nahas, Benoît Panicaud & Alexandre Charles

  2. Sino-French Engineer School, Nanjing University of Science and Technology, Jiangsu 210094, Nanjing, China

    Mingchuan Wang

  3. Automatic Mesh Generation & Advanced Methods (GAMMA3), Université de Technologie de Troyes (UTT), 12, rue Marie Curie, CS 42060 10004, Troyes cedex, France

    Emmanuelle Rouhaud

  4. Safran Tech, Safran, Rue des Jeunes Bois, Châteaufort, 78114, Magny-Les-Hameaux, France

    Alexandre Charles

  5. Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Universié, Place Jussieu, 75252, Paris cedex 05, France

    Richard Kerner

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  1. Roula Al Nahas
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  2. Mingchuan Wang
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  3. Benoît Panicaud
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  4. Emmanuelle Rouhaud
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Correspondence to Benoît Panicaud.

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Al Nahas, R., Wang, M., Panicaud, B. et al. Covariant spacetime formalism for applications to thermo-hyperelasticity. Acta Mech 233, 2309–2334 (2022). https://doi.org/10.1007/s00707-022-03218-2

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