Stability of elastic material with negative stiffness and negative Poisson's ratio

Abstract

Abstract Stability of cuboids and cylinders of an isotropic elastic material with negative stiffness under partial constraint is analyzed using an integral method and Rayleigh quotient. It is not necessary that the material exhibit a positive definite strain energy to be stable. The elastic object under partial constraint may have a negative bulk modulus K and yet be stable. A cylinder of arbitrary cross section with the lateral surface constrained and top and bottom planar surfaces is stable provided the shear modulus G > 0 and – G /3 < K < 0 or K > 0. This corresponds to an extended range of negative Poisson's ratio, –∞ < ν < –1. A cuboid is stable provided each of its surfaces is an aggregate of regions obeying fully or partially constrained boundary conditions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)