Section: New Results

Derivation of nonlinear elasticity from polymer-physics

In [10] , 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 [57] 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, https://www.lri.fr/ hansen/cmaesintro.html).

In [34] , M. Duerinckx and A. Gloria succeeded in relaxing one of the two unphysical assumptions made in [1] on the growth of the energy of polymer chains. In particular, [34] deals with the case when the energy of the polymer chain is allowed to blow up at finite deformation.