Microstructure of isotropic materials with negative Poisson's ratio

Abstract

MATERIALS that expand in the transverse direction under uniaxial extension, or that contract laterally when compressed, are said to have a negative Poisson's ratio, v. For an isotropic elastic material, v is the negative of the ratio of lateral to axial strain under uniaxial extension or compression. Despite the apparently counterintuitive nature of this behaviour, v<0 has been observed for some anisotropic crystals¹ and materials comprised of fibrous networks^2,3, when loaded in a specific direction. Lakes⁴ has described a class of foams that constitute perhaps the only known isotropic materials with negative v. Materials of this sort are expected to have interesting mechanical properties, such as high energy absorption and fracture resistance, which may be useful in some applications⁴. Here we describe a general class of microstructures that lead to a negative Poisson's ratio, and show that some existing and hypothetical materials with this property share features common to this class. Our microstructural model provides insight into why natural materials of this kind are rare, and suggests a general methodology for designing such materials.