On the Extremal Properties of Hashin’s Hollow Cylinder Assemblage in Nonlinear Elasticity

Abstract

Counterexamples are given of 2D isotropic porous nonlinear elastic solids whose responses under hydrostatic loading are stiffer than that of the corresponding hollow cylin- der assemblage. In addition to disproving existing conjectures in the literature, the results serve to illustrate that radially symmetric deformation—contrary to common belief—is not necessarily the stiffest possible deformation mechanism to accommodate hydrostatic load- ing. Instead, depending on the growth conditions of the material at hand, other types of deformations may lead to stiffer responses.