Comptes Rendus
no. 8
Mathematical Problems in Mechanics
Mathematical derivation of a rubber-like stored energy functional

Presented by: Philippe G. Ciarlet

Roberto Alicandro1; Marco Cicalese2; Antoine Gloria3
1 DAEIMI, Università di Cassino, via Di Biasio 43, 03043 Cassino, Italy
2 Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Università di Napoli, via Cintia, 80126 Napoli, Italy
3 CERMICS – ENPC, 6 et 8, avenue Blaise-Pascal, Champs sur Marne, 77455 Marne la Vallée cedex 2, France
Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 479-482.

In this Note, we consider a stochastic network of interacting points to which we associate an energy. We study the variational convergence of such an energy when the typical distance of the network goes to zero. We prove that the limit energy can be written as an integral functional, whose energy density is deterministic, hyperelastic and frame-invariant. This derivation allows us in particular to obtain a continuous energy density associated to cross-linked polymer networks.

Dans cette Note, nous considérons un réseau stochastique de points en interaction auquel nous associons une énergie. Nous étudions alors la convergence variationnelle de cette énergie lorsque la distance caractéristique du réseau tend vers zéro. Nous démontrons que l'énergie limite s'écrit comme l'intégrale d'une densité d'énergie déterministe, hyperélastique et objective. Cette dérivation couvre en particulier des modèles de réseau de polymères réticulés.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.10.005

Roberto Alicandro 1; Marco Cicalese 2; Antoine Gloria 3

1 DAEIMI, Università di Cassino, via Di Biasio 43, 03043 Cassino, Italy
2 Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Università di Napoli, via Cintia, 80126 Napoli, Italy
3 CERMICS – ENPC, 6 et 8, avenue Blaise-Pascal, Champs sur Marne, 77455 Marne la Vallée cedex 2, France 
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Roberto Alicandro; Marco Cicalese; Antoine Gloria. Mathematical derivation of a rubber-like stored energy functional. Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 479-482. doi : 10.1016/j.crma.2007.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.005/

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