Auxetic laminates composed of plies with special orthotropy

Abstract

This paper focuses on the conditions for obtaining auxetic, i.e. with a negative Poisson's ratio, composite laminates made of specially orthotropic layers. In particular, the layers considered are of three types: R1-orthotropic, i.e. square-symmetric plies, like those reinforced by balanced fabrics, R0-orthotropic layers, like those that can be obtained with balanced fabrics having warp and weft forming an angle of 45 degrees, and finally r0-orthotropic layers, like common paper. All these types of orthotropy have mathematical and mechanical properties different by common orthotropy. As a consequence of this, the conditions of auxeticity for anisotropic composite laminates made of such special plies change from the more common case of unidirectional plies. These conditions are analyzed in this paper making use of the polar formalism, a mathematical method particularly suited for the study of two-dimensional anisotropic elasticity.