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Mathematical derivation of a rubber-like stored energy functional

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.
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Submitted on : Tuesday, December 18, 2012 - 5:50:25 PM
Last modification on : Tuesday, November 22, 2022 - 2:26:15 PM
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Roberto Alicandro, Marco Cicalese, Antoine Gloria. Mathematical derivation of a rubber-like stored energy functional. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2007, 345 (8), pp.479-482. ⟨10.1016/j.crma.2007.10.005⟩. ⟨hal-00766739⟩



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