Nonlinear Poisson effects in soft honeycombs

We examine solid cellular structures within the theoretical framework of finite elasticity, whereby we assume that the cell wall material is nonlinear elastic. This enables us to identify new mechanical effects that appear in cellular materials when elastically deformed, and to explore the physical properties that influence them. We find that, when a honeycomb structure of hyperelastic material and standard geometry, such as rectangular-, hexagonal- or diamond-shaped cells, contains walls which are inclined relative to an applied uniaxial tensile load, these walls tend to expand both in the direction of the load and in the perpendicular direction, producing an apparent negative Poisson's ratio at local cell level. Moreover, we show that this (negative) Poisson ratio decreases as the magnitude of the tensile load increases. For these structures, Poisson's ratios greater than 0.5 are obtained in uniaxial compression. Similar effects in structures with linearly elastic cell walls do not occur.