Note on a random isotropic granular material with negative Poisson's ratio
type: Item
instance of: scholarly article
title: Note on a random isotropic granular material with negative Poisson's ratio
zbMATH Open document ID: 0634.73004
DOI: 10.1016/0020-7225(88)90116-4
author: Richard J. Bathurst
author: Leo Rothenburg
published in: International Journal of Engineering Science
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74A40
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 4033191
zbMATH Keywords: tangential forces
zbMATH Keywords: normal contact forces
zbMATH Keywords: constitutive stress-strain relationships
zbMATH Keywords: macroscopic behaviour
zbMATH Keywords: idealized bonded granular materials
zbMATH Keywords: three-dimensional random isotropic assemblies of bonded spheres
zbMATH Keywords: analogous expression for Poisson's ratio
MaRDI profile type: Publication
full work available at URL: 0020-7225(88)90116-4
OpenAlex ID: W2027190822
cites work: Q5844404
cites work: A Micromechanical Description of Granular Material Behavior
cites work: On statistical description of stress and fabric in granular materials
cites work: Q5791941
description: scientific article; zbMATH DE number 4033191