Constitutive properties of contacting materials with a finite-sized microstructure

Materials consisting of macro-molecules that are set in a structure and interact via contact interactions are investigated. The analysis is analytical, based on the methodology developed for granular materials by Jenkins J. T. and Koenders M. A. "The incremental response of random aggregates of round particles" European Physics Journal E., 13, 2004 113 - 123. The stiffness tensor is obtained and the results are screened for auxetic properties. Two-dimensional materials are investigated. For regular packings isotropic and anisotropic structures are examined. It is demonstrated that isotropic materials in this category are never auxetic. Heterogeneous materials are also analysed. It is shown that auxetic behaviour is enhanced when structural variation is present. By contrast, auxetic behaviour is suppressed when constitutive heterogeneity is present. The results of the analysis may be employed to scrutinize numerical simulations.