Architecture of cylinders with implications for materials with negative Poisson ratio

It is known that auxetic properties (for example, negative Poisson ratios, that is, when a solid experiences lateral expansion under stretching instead of lateral contraction) start showing themselves in materials where there is a certain kind of geometrical orientational correlations between “rigid” constituents. Properly arranged orientational degrees of freedom of building blocks govern the characteristic distances in auxetic materials and thus determine the way in which the materials contract or expand. Very often the building blocks are filamentous. We suggest a way to arrange filamentous objects into highly interwoven regular structures which may exhibit auxetic properties with negative Poisson ratio. Our purely geometrical consideration can be extended to an irregular positional arrangement. This implies that a solid of sufficiently dense “random” arrangements of filaments (for example, “wool” of nanowires or of carbon nanotubes) may become auxetic. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)