Mathematical derivation of a rubber-like stored energy functional

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).