Section: New Results

Derivation of nonlinear elasticity from polymer-physics

In [15] , A. Gloria, P. Le Tallec (Mechanics department, Ecole polytechnique), and M. Vidrascu (Project-team REO, Inria) numerically investigated the nonlinear elasticity model obtained in [1] by discrete stochastic homogenization, and compared it to the standard measurements by Treloar on natural rubber. The implementation was realized in the Modulef software. These results are in rather good agreement, which shows that the approach seems to be promising.

In [25] , M. de Buhan (CNRS, Univ. Paris Descartes), A. Gloria, P. Le Tallec and M. Vidrascu proposed a numerical method to produce analytical approximations (that can be used in practical nonlinear elasticity softwares) of the numerical approximations obtained in [15] of the discrete-to-continuum energy density derived theoretically in [1] . This numerical method is based on the parametrization of the set of polyconvex Ogden laws and on the combination of a least square method and a genetic algorithm (cf. CMA-ES).