[Dérivation mathématique d'une densité d'énergie hyperélastique pour des polymères réticulés]
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.
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.
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@article{CRMATH_2007__345_8_479_0,
author = {Roberto Alicandro and Marco Cicalese and Antoine Gloria},
title = {Mathematical derivation of a rubber-like stored energy functional},
journal = {Comptes Rendus. Math\'ematique},
pages = {479--482},
publisher = {Elsevier},
volume = {345},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.10.005},
language = {en},
}
TY - JOUR AU - Roberto Alicandro AU - Marco Cicalese AU - Antoine Gloria TI - Mathematical derivation of a rubber-like stored energy functional JO - Comptes Rendus. Mathématique PY - 2007 SP - 479 EP - 482 VL - 345 IS - 8 PB - Elsevier DO - 10.1016/j.crma.2007.10.005 LA - en ID - CRMATH_2007__345_8_479_0 ER -
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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