Homogenization estimates for hyperelastic composites and particle-reinforced rubbers

This Note is concerned with the development of variational estimates for th e effective stored-energy function of hyperelastic composites undergoing fi nite deformations. It makes use of a suitable generalization of the "second -order procedure" of Ponte Castaneda, the key idea being the introduction o f an optimally chosen "linear thermoelastic comparison composite", which ca n then be used to convert available homogenization estimates for linear sys tems directly into new estimates for hyperelastic composites. The resulting estimates are known to be exact to second order in the contrast. An applic ation is given for particle-reinforced rubbers. (C) 1999 Academie des scien ces/Editions scientifiques et medicales Elsevier SAS.