Comptes Rendus
no. 3
Mathematical problems in mechanics
Motion of an incompressible solid with large deformations

Presented by: Philippe G. Ciarlet

Elena Bonetti1, 2; Michel Frémond3
1 Laboratorio Lagrange, Dipartimento di Matematica “Federigo Enriques”, Università di Milano, Via Saldini, 50, 20133 Milano, Italy
2 IMATI–CNR, Via Ferrata 1, 27100, Pavia, Italy
3 Laboratorio Lagrange, Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, Via del Politecnico, 1, 00163 Roma, Italy
Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 345-350.

We study the motion of a visco-elastic solid with large deformations. We prove the existence of a local-in-time motion and of a non-negative pressure, which is a measure reaction to the incompressibility condition.

On étudie le mouvement d'un solide viscoélastique incompressible en grande déformation. On démontre l'existence d'un mouvement local en temps et d'une pression positive qui est une mesure, réaction à la condition d'incompressibilité.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.01.016

Elena Bonetti 1, 2; Michel Frémond 3

1 Laboratorio Lagrange, Dipartimento di Matematica “Federigo Enriques”, Università di Milano, Via Saldini, 50, 20133 Milano, Italy
2 IMATI–CNR, Via Ferrata 1, 27100, Pavia, Italy
3 Laboratorio Lagrange, Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, Via del Politecnico, 1, 00163 Roma, Italy 
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Elena Bonetti; Michel Frémond. Motion of an incompressible solid with large deformations. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 345-350. doi : 10.1016/j.crma.2018.01.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.01.016/

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[2] E. Bonetti; P. Colli; M. Frémond 2D motion with large deformations, Boll. UMI, Volume 7 (2014), pp. 19-44

[3] E. Bonetti; P. Colli; M. Frémond The 3D motion of a solid with large deformations, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014), pp. 183-187

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[5] M. Frémond Collisions, Edizioni del Dipartimento di Ingegneria Civile dell'Università di Roma Tor Vergata, Roma, 2007 (ISBN: 978-88-6296-000-7)

[6] M. Frémond Virtual Work and Shape Change in Solid Mechanics, Springer Ser. Solid Struct. Mech., vol. 7, Springer-Verlag, Berlin, Heidelberg, Germany, 2017

[7] J.J. Moreau Principes extrémaux pour le problème de la naissance de la cavitation, J. Méc., Volume 5 (1966), pp. 439-470

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