New Results on the Poisson Ratio Behavior in Matrix-Inclusion Planar Composites
Shmuel Vigdergauz*
The Israel Electric Corp. Ltd, PO Box 10, 31000, Haifa, Israel
* To whom correspondence should be addressed.
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Abstract |
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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.
