Estimations homogénéisées pour les composites hyperélastiques et applications aux élastomères renforcés

This Note is concerned with the development of variational estimates for the effective stored-energy function of hyperelastic composites undergoing finite deformations. It makes use of a suitable generalization of the “second-order procedure” of Ponte Castañeda, the key idea being the introduction of an optimally chosen “linear thermoelastic comparison composite”, which can then be used to convert available homogenization estimates for linear systems directly into new estimates for hyperelastic composites. The resulting estimates are known to be exact to second order in the contrast. An application is given for particle-reinforced rubbers.