Summary
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Accepted for publication 10 September 1996
Rights and permissions
About this article
Cite this article
Theocaris, P., Stavroulakis, G. & Panagiotopoulos, P. Negative Poisson's ratios in composites with star-shaped inclusions: a numerical homogenization approach. Archive of Applied Mechanics 67, 274–286 (1997). https://doi.org/10.1007/s004190050117
Issue Date:
DOI: https://doi.org/10.1007/s004190050117