The optimal density of cellular solids in axial tension

A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

Cellular Materials and Topology Optimization use a structured distribution of material to achieve specific mechanical properties. The controlled distribution of material often leads to several advantages including the customization of the resulting mechanical properties; this can be achieved following these two approaches. In this work, a review of these two as approaches used with compliance purposes applied at flexure level is presented. The related literature is assessed with the aim of clarifying how they can be used in tailoring stiffness of flexure elements. Basic concepts needed to understand the fundamental process of each approach are presented. Further, tailoring stiffness is described as an evolutionary process used in compliance applications. Additionally, works that used these approaches to tailor stiffness of flexure elements are described and categorized. Finally, concluding remarks and recommendations to further extend the study of these two approaches in tailoring the stiffness of flexure elements are discussed.

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.

Microstructure-based hyperelastic models for closed-cell solids

For cellular bodies involving large elastic deformations, mesoscopic continuum models that take into account the interplay between the geometry and the microstructural responses of the constituents are developed, analysed and compared with finite-element simulations of cellular structures with different architecture. For these models, constitutive restrictions for the physical plausibility of the material responses are established, and global descriptors such as nonlinear elastic and shear moduli and Poisson's ratio are obtained from the material characteristics of the constituents. Numerical results show that these models capture well the mechanical responses of finite-element simulations for three-dimensional periodic structures of neo-Hookean material with closed cells under large tension. In particular, the mesoscopic models predict the macroscopic stiffening of the structure when the stiffness of the cell-core increases.