NEGATIVE POISSON-RATIOS IN COMPOSITES WITH STAR-SHAPED INCLUSIONS - ANUMERICAL HOMOGENIZATION APPROACH

Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This result h as been proved for continuum materials by analytical methods in previo us works of the first author, among others [1]. Furthermore, it also h as been shown to be valid for certain mechanisms involving beams or ri gid levers, springs or sliding collars frameworks and, in general, com posites with voids having a nonconvex microstructure. Recently microst ructures optimally designed by the homogenization approach have been v erified. For microstructures composed of beams, it has been postulated that nonconvex shapes with re-entrant corners are responsible for thi s effect [2]. In this paper, it is numerically shown that mainly the s hape of the re-entrant corner of a non-convex, star-shaped microstruct ure influences the apparent (phenomenological) Poisson's ratio. The sa me is valid for continua with voids or for composities with irregular shapes of inclusions, even if the individual constituents are quite us ual materials. Elements of the numerical homogenization theory are rev iewed and used for the numerical investigation.