The effective Poisson ratio of random cellular matter having bending dominated architecture

Aeronautics & Astronautics, School of Engineering Sciences, University of Southampton - SO17 1BJ, Southampton, UK, EU

Corresponding author: A.Bhaskar@soton.ac.uk

Received: 10 February 2009
Accepted: 16 June 2009

Abstract

We argue that the effective Poisson ratio of cellular and porous solids is independent of the material of the solid phase, if the mechanism of the cell wall deformation is dominated by beam bending —thus rendering it to be a purely kinematic quantity. Introducing a kinematic simplification and requiring statistical isotropy, we prove a result of remarkable generality that the effective Poisson ratio of irregular planar structures equals 1 for all bending dominated random architectures. We then explore a deeper connection of this behavior with area-preserving deformation of planar closed elastic cells. We show that thin sheets and films made of such microstructured material afford physical realizations of the two-dimensional analogue of incom- pressible matter. We term such non-stretchable sheet material as well as deformations as isoektasic.