On a discrete model for rubber and its continuous limit

In this talk I will present a discrete model for rubber at a mesoscopic scale, based on statistical physics arguments and on a minimization principle. I will emphasize the differences with other more classical models and address the question of the derivation of a continuum limit when the mesoscopic scale is sent to zero. In particular, using the concept of stochastic lattices, I will prove the convergence towards a nonlinear elasticity model and study its mechanical properties, such as hyperelasticity, frame-invariance, isotropy and natural states. At the end, I will quickly mention related work in homogenization theory.