Abstract
Poisson's ratio, ν, was measured for four materials, a rubbery polymer, a conventional soft foam, and two auxetic foams. We find that for the first two materials, having ν ≥ 0.2, the experimental determinations of Poisson's ratio are in good agreement with values calculated from the shear and tensile moduli using the equations of classical elasticity. However, for the two auxetic materials (ν < 0), the equations of classical elasticity give values significantly different from the measured ν. We offer an interpretation of these results based on a recently published analysis of the bounds on Poisson's ratio for classical elasticity to be applicable.
Highlights
The classical theory of elasticity for infinitesimal linear strain (i.e., Lame’s theory)[4] links ν of an isotropic solid to the other elastic constants, including the moduli and Lameconstants.[5,6]
We find that for two materials for which ν ≥ 0.2, the equations of classical elasticity are accurate
The deformation mechanism of the auxetic foams involves de-buckling of the cell ribs, which causes their modulus to be lower than that of the precursor material.[11,8]
Summary
For a mechanically isotropic material, Poisson’s ratio is unique, having but one value.[1,2,3] The classical theory of elasticity for infinitesimal linear strain (i.e., Lame’s theory)[4] links ν of an isotropic solid to the other elastic constants, including the moduli and Lameconstants.[5,6] Because of the appeal of representing strain as the sum of a volumetric and a deviatoric (shear) strain, the most common expression involves the bulk, B, and shear, G, moduli[7 ] G B
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