THE HOMOGENIZATION METHOD FOR THE STUDY OF VARIATION OF POISSONS RATIO IN FIBER COMPOSITES

Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This fact has been shown to be valid for certain mechanisms, composites with voids and frameworks and has recently been verified for microstructures opti mally designed by the homogenization approach. For microstructures com posed of beams, it has been postulated that nonconvex shapes (with ree ntrant corners) are responsible for this effect. In this paper, it is numerically shown that mainly the shape, but also the ratio of shear-t o-bending rigidity of the beams do influence the apparent (phenomenolo gical) Poisson's ratio. The same is valid for continua with voids, or for composites with irregular shapes of inclusions, even if the consti tuents are quite usual materials, provided that their porosity is stro ngly manifested. Elements of the numerical homogenization theory and f irst attempts towards an optimal design theory are presented in this p aper and applied for a numerical investigation of such types of materi als.