Calculus of Variations and Geometric Measure Theory

R. Alicandro - M. Cicalese - A. Gloria

Mathematical derivation of a rubber-like stored energy functional

created by cicalese on 18 Feb 2008


Published Paper

Inserted: 18 feb 2008

Journal: C. R. Acad. Sci. Paris, Sér. I
Volume: 345
Pages: 479-482
Year: 2007


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.

Keywords: $\Gamma$-convergence, discrete systems, stochastic networks, rubber elasticity