Note on a random isotropic granular material with negative Poisson's ratio
Poisson's ratio in generalized Hooke's law for an isotropic continuum is subject to the restriction -1\(\leq \nu \leq 0.5\). With the exception of recently developed low-density polymer foams, solids including granular materials have not been known to exhibit negative Poisson's ratio. This paper is concerned with the verification of constitutive stress- strain relationships proposed by the second author [Micromechanics of idealized granular systems. Ph. D. thesis, Carleton University (1980)] which describe macroscopic behaviour of idealized bonded granular materials by elastic parameters (K and \(\nu)\) that are formulated explicitly in terms of microstructural parameters such as interparticle stiffness, contact density and average interparticle distance. The theory includes an expression for Poisson's ratio which is a function only of the ratio of tangential (shear) to normal contact stiffness \(\lambda\). A negative Poisson's ratio is predicted for both planar and three- dimensional random isotropic systems when the tangential stiffness is greater than the normal stiffness (i.e. \(\lambda >1)\). The results of numerical simulation of bonded disc assemblies used to verify constitutive relationships show that systems with \(\lambda >1\) do exhibit negative Poisson's ratio. Similar theoretical developments are summarized for three-dimensional random isotropic assemblies of bonded spheres and an analogous expression for Poisson's ratio is presented for these systems. It is noted that while a negative Poisson's ratio is theoretically possible, the micromechanical condition for \(\lambda >1\) is physically unlikely for particles of natural materials.
constitutive stress-strain relationships
three-dimensional random isotropic assemblies of bonded spheres
analogous expression for Poisson's ratio
scientific article; zbMATH DE number 4033191