Many natural structures are cellular solids at millimetre scale and fibre-reinforced composites at micrometre scale. For these structures, mechanical properties are associated with cell strength, and phenomena such as cell separation through debonding of the middle lamella in cell walls are key in explaining some important characteristics or behaviour. To explore such phenomena, we model cellular structures with non-linear hyperelastic cell walls under large shear deformations, and incorporate cell wall material anisotropy and unilateral contact between neighbouring cells in our models. Analytically, we show that, for two cuboid walls in unilateral contact and subject to generalised shear, gaps can appear at the interface between the deforming walls. Numerically, when finite element models of periodic structures with hexagonal cells are sheared, significant cell separation is captured diagonally across the structure. Our analysis further reveals that separation is less likely between cells with high internal cell pressure (e.g. in fresh and growing fruit and vegetables) than between cells where the internal pressure is low (e.g. in cooked or ageing plants).

For stretch-dominated cellular structures with arbitrarily oriented cell walls made from a homogeneous isotropic hyperelastic material, recently, continuum isotropic hyperelastic models were constructed analytically, at a mesoscopic level, from the microstructural architecture and the material properties at the cell level. Here, the nonlinear elastic properties of these models for structures with neo-Hookean cell components are derived explicitly from the strain-energy function and the finite deformation of the cell walls. First, the nonlinear shear modulus is calculated under simple shear superposed on finite uniaxial stretch. Then, the nonlinear Poisson's ratio is computed under uniaxial stretch and the nonlinear stretch modulus is obtained from a universal relation involving the shear modulus as well. The role of the nonlinear shear and stretch moduli is to quantify stiffening or softening in a material under increasing loads. Volume changes are quantified by the nonlinear bulk modulus under hydrostatic pressure. Numerical examples are presented to illustrate the behaviour of the nonlinear elastic parameters under large strains.

For cellular structures with uniform geometry, cell size and distribution, made from a neo-Hookean material, we demonstrate experimentally that large stretching causes nonlinear scaling effects governed by the microstructural architecture and the large strains at the cell level, which are not predicted by the linear elastic theory. For this purpose, three honeycomb-like structures with uniform square cells in stacked distribution were designed, where the number of cells varied, while the material volume and the ratio between the thickness and the length of the cell walls were fixed. These structures were manufactured from silicone rubber and tested under large uniaxial tension in a bespoke test fixture. Optical strain measurements were used to assess the deformation by capturing both the global displacements of the structure and the local deformations in the form of a strain map. The experimental results showed that, under sufficiently large strains, there was an increase in the stiffness of the structure when the same volume of material was arranged as many small cells compared to when it was organized as fewer larger cells. Finite element simulations confirmed our experimental findings. This study sheds light upon the nonlinear elastic responses of cellular structures in large-strain deformations, which cannot be captured within the linear elasticity framework.

No abstract