A new variational estimate for the effective response of hyperelastic composites

A variational method for predicting the effective properties of hyperelastic composites in terms of available estimates for “hyperelastic comparison composites” is proposed. In some cases this estimate can produce a lower bound on the effective energy-density function. This nonlinear-comparison variational procedure is specialized to classes of fiber and statistically isotropic composites with the aid of appropriate choices of comparison composites with neo-Hookean phases. The end results are given in terms of closed-form expressions for the effective strain energy-density functions, from which the stress–strain relations can be extracted analytically. Explicit analytical estimates for the overall responses of composites whose phases behaviors are governed by the Gent model are obtained. The results for the fiber composites are compared with corresponding finite element simulations of periodic fiber composites as well as with other available estimates. A fine agreement between the predictions obtained via the various estimates is revealed even in the limit of infinite contrast between the properties of the phases.