New Results on the Poisson Ratio Behavior in Matrix-Inclusion Planar Composites

Abstract

This study is motivated by a consistent set of numerical and experimental observations reported in various papers on the effective Poisson ratio (EPR) of 2D granular structures. Here, we uniformly explain them with the novel closed-form expression for EPR obtained as a rational function in the matrix Poisson ratio and the easily computable inverses to the effective bulk and shear moduli. Particularly, the EPR of a perforated plate is proved to be independent of the matrix Young modulus. On this basis, the existence of the EPR fixed points is studied both analytically and numerically. Finally, some numerical example are given for illustration. The proposed approach is based on using the complex-valued Kolosov–Muskhelishvili potentials which perform well in plane elasticity.

Keywords

2D elasticity perforated plates effective Poisson ratio circular inclusions

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