RELAXATION OF SOME TRANSVERSALLY ISOTROPIC ENERGIES AND APPLICATIONS TO SMECTIC A ELASTOMERS

Abstract

We determine the relaxation of some transversally-isotropic energy densities, i.e. functions W : R-3x3 -> [0,infinity] with the property W(QFR) = W(F) for all Q is an element of SO(3) and all R is an element of SO(3) such that Rn-0 = n(0), where n(0) is a fixed unit vector. One physically relevant example is a model for smectic A elastomers. We discuss the implications of our result for the computation of macroscopic stress-strain curves for this material and compare with experiment.