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.

Auxetic Materials: Functional Materials and Structures from Lateral Thinking!

“…[32] The resilience of a cushion material is related to the comfort experienced by the user, and the double curvature property may be useful in ensuring mattresses, for example, provide support where it is needed for the ªdoubly curvedº human body. [33] Dynamic effects have been investigated and interesting effects on properties such as the reflection of elastic waves at surfaces have been predicted [34] for auxetic materials. Subsequent studies, [35±38] partially funded by the US Office of Naval Research, have demonstrated enhanced sound and vibration absorption for auxetic foams.…”

Auxetic compliant flexible PU foams: static and dynamic properties

“…The dynamic behaviour of auxetic materials has been investigated by several authors [7][8][9][10][11][12]. The possible use of auxetic materials for viscoelastic damping applications has been examined in [10,13], where biphasic auxetic composite showed loss tangent exceeding lower Voigt limit and close to Hashin upper bound.…”

Dynamic Response of Chiral Truss-core Assemblies

“…The mechanical properties of these alternatives to solid components have thoroughly been investigated by (Zang and Ashby, 1991;Gibson et al, 1997;Evans et al, 2001;Wicks and Hutchinson, 2001) among others. In dynamics, specific attention has been placed on surface and Rayleigh wave propagation behavior in isotropic homogeneous linear elastic solids with negative Poisson's ratios (Lipsett and Beltzer, 1988). Among the proposed innovative geometries, chiral topologies (Lakes, 1991;Prall and Lakes, 1996) feature a unique geometric configuration which can be exploited for the design of innovative structural components.…”