Geodesic
Mathematical problems in mechanics
Motion of an incompressible solid with large deformations
[Solide incompressible en grande déformation]

Présenté par : Philippe G. Ciarlet

Bonetti, Elena1, 2 ; Frémond, Michel3
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, Tome 356 (2018) no. 3, pp. 345-350.

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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.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2018.01.016

Bonetti, Elena 1, 2 ; Frémond, Michel 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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Bonetti, Elena; Frémond, Michel. Motion of an incompressible solid with large deformations. Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 345-350. doi : 10.1016/j.crma.2018.01.016. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2018.01.016/

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

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

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

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

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

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

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

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