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Comptes Rendus Mathématique
Volume 345, n° 8
pages 479-482 (octobre 2007)
Doi : 10.1016/j.crma.2007.10.005
Received : 22 May 2007 ;  accepted : 28 September 2007
Mathematical derivation of a rubber-like stored energy functional
Dérivation mathématique dʼune densité dʼénergie hyperélastique pour des polymères réticulés
 

Roberto Alicandro a , Marco Cicalese b , Antoine Gloria c
a DAEIMI, Università di Cassino, via Di Biasio 43, 03043 Cassino, Italy 
b Dipartimento di Matematica e Applicazioni R. Caccioppoli', Università di Napoli, via Cintia, 80126 Napoli, Italy 
c CERMICS - ENPC, 6 et 8, avenue Blaise-Pascal, Champs sur Marne, 77455 Marne la Vallée cedex 2, France 

Abstract

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. To cite this article: R. Alicandro et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

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Résumé

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 lʼénergie limite sʼécrit comme lʼintégrale dʼune densité dʼénergie déterministe, hyperélastique et objective. Cette dérivation couvre en particulier des modèles de réseau de polymères réticulés. Pour citer cet article : R. Alicandro et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.


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