Reexamination of dynamic problems of elasticity for negative Poisson’s ratio

Abstract

Recently, isotropic elastic materials with a negative Poisson’s ratio have been manufactured. Since most of the theoretical results of linear elasticity focus on a positive Poisson’s ratio, the need arises for their extension and reexamination. The above materials may have a variety of technological applications so the motivation for this study is not purely academic. The article deals first with some of the limit cases arising when Poisson’s ratio takes on an extreme value. For models represented by these limit cases, the material and structure responses may not be treated independently from each other. Then such basic dynamic elasticity problems as reflection from a free surface, propagation of Rayleigh waves, and lateral vibrations of beams and plates are reconsidered for the case of a negative Poisson’s ratio. It is shown, in particular, that the static definition of the shear factor in Timoshenko beam theory may not be satisfactory in all cases. Extensive numerical results are also given.