The Poisson ratio can be defined for solid materials as the negative ratio of the relative diameter change in the transverse direction (negative for contraction) and the relative length change in the direction of tension (positive). When Poisson introduced this ratio in the 1820es, he came to the conclusion that it should be 025 for all materials and should therefore not be considered as a material property.' This is indeed the case when the solid is composed of particles atoms or molecules governed by spherically symmetric potentials.~2 In this case the so-called Cauchy relations hold and the elastic behavior of isotropic solids is governed by only one elastic constant, e.g. the Young's modulus, Forexample, quasi-isotropic polycrystalline solids made up of alkali halides (cubic) and certain glasses may be expected to approach to this type of behavior to a certain extent.~(4,5) In general, however, isotropic materials are characterized by two elastic constants, concomitant with the fact that (linear) elasticity is a fourth-order tensor property.~6 The Poisson ratio may be chosen as one of these. From the positivity of elastic moduli (assumption of thermodynamic stability) it follows that the Poisson ratio of an isotropic material must lie in the range — 1 < v < 0.5, and although it has been frequently claimed in textbooks that isotropic materials with negative Poisson ratios do not exist, their existence has been definitely proved and the first auxetic materials have been produced in the 1980es.~(7-9) It is clear, therefore, that the possibility of auxetic behavior has to be taken into account when the porosity dependence of the Poisson ratio is to be discussed. The Poisson ratio of porous materials is a topic of constant interest,~(10-17)since — in combination with one of the elastic moduli (typically the Young's modulus) it determines the linear elastic response of isotropic materials completely and is therefore of practical importance for many problems of wave propagation and acoustics. However, up to now there is still no agreement on the "most realistic" porosity dependence of the Poisson ratio. Nevertheless, based on published literature values and the results of several popular models, most authors seem to recognize only a "slight" porosity dependence, with a converging trend to some asymptotic limit value when the porosity approaches 100 %. In this paper we summarize and discuss the known relations and show that only power-law relations and certain types of exponential relations result, under certain conditions (sufficiently high porosity and appropriate Poisson ratio of the solid phase), in predictions that allow for negative Poisson.
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