A note on undistorted states of isotropic elastic solids

Abstract

Non-homogeneous conformal deformations are shown to be possible in an isotropic elastic material in the absence of body forces if and only if the material satisfies a certain condition which renders it incapable of obeying the classical pressure-compression inequality. The undistorted states of materials in this class (which are obtained by subjecting an undistorted state called reference configuration to all possible conformal deformations) are shown to be at best neutrally stable when subject to hydrostatic loading everywhere on the boundary.