Nonlinear scaling effects in the stiffness of soft cellular structures

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.