Comptes Rendus
no. 3
Mathematical problems in mechanics
Motion of an incompressible solid with large deformations
[Solide incompressible en grande déformation]

Présenté par : 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.

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.

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.

Reçu le :
Accepté le :
Publié le :
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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     title = {Motion of an incompressible solid with large deformations},
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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/

[1] E. Bonetti; P. Colli; M. Frémond The motion of a solid with large deformations, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013), pp. 579-583

[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

[4] E. Bonetti; E. Rocca; R. Scala; G. Schimperna On the strongly damped wave equation with constraint, Commun. Partial Differ. Equ., Volume 42 (2017) no. 7, pp. 1042-1064

[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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