Negative Poisson's ratios in composites with star-shaped inclusions: A numerical homogenization approach

Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This result has been proved for continuum materials by analytical methods in previous works of the first author, among others [1]. Furthermore, it also has been shown to be valid for certain mechanisms involving beams or rigid levers, springs or sliding collars frameworks and, in general, composites with voids having a nonconvex microstructure. Recently microstructures optimally designed by the homogenization approach have been verified. For microstructures composed of beams, it has been postulated that nonconvex shapes with re-entrant corners are responsible for this effect [2]. In this paper, it is numerically shown that mainly the shape of the re-entrant corner of a non-convex, star-shaped microstructure influences the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids or for composities with irregular shapes of inclusions, even if the individual constituents are quite usual materials. Elements of the numerical homogenization theory are reviewed and used for the numerical investigation.