The auxetic properties of a network of bending beams

Abstract

The mechanical response of an aggregate of bending beams in two dimensions is investigated. The special mission of this paper is to find auxetic properties (negative Poisson's ratio). A formal correspondence between a contacting granular material and a medium consisting of bending beams is established. The former has already been studied in previous papers and the results can be taken over quite readily. Among the results it is reported that networks of beams that are stubby auxetic behaviour is naturally present, even in a mean field approach. For heterogeneous materials the role of local anisotropies is highlighted as a possible mechanism underlying an overall negative Poisson ratio. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulated optimisation of disordered structures with negative Poisson’s ratios

“…The results from these may correlate fairly well with experimental data but since their geometries often bear little resemblance to the reality of the internal microstructure of the materials there remains a gap in understanding between theorised ideals and the heterogeneous structures seen in auxetic materials (Gaspar et al 2005b). This disparity leads to difficulties in predicting properties when considering the manufacture of such materials since it is currently very difficult to accurately account for heterogeneity in microstructure and resulting Poisson's ratios (Gaspar et al 2005b;Koenders and Gaspar 2008). The issue of control over the nature and extent of heterogeneity is relatively unexplored and indeed may prove difficult to achieve in practice.…”

“…Koenders and Gaspar (Koenders and Gaspar 2008) P > term. However, this partial correction is based on the assumption that all the ribs are long and slender.…”

“…The following techniques are based on analyses of randomly packed granular materials that have been adapted to bending beam networks (Koenders and Gaspar 2008). …”

“…However, due to the heterogeneity in the structures, the global properties are not the same as an average of the local properties (Gaspar et al 2003), therefore, an additional term based on the geometrical differences must be included. The analysis follows that of Koenders and Gaspar (2008) in which each node is considered subject to force and force moments from the displacements of its neighbours. Neighbours ν are located a vector c μν from node μ.…”

“…These questions are tackled via numerical optimisation of 2D grids and statistical analysis of results in the context of the homogenisation approach of Gaspar and co-workers (Gaspar et al 2003;Koenders and Gaspar 2008).…”