The flow of forces through cellular materials

TL;DR

This paper introduces a force flow visualization method for cellular materials that helps understand how their geometry influences elastic properties, especially in disordered structures, by analyzing force paths and stress distribution.

Contribution

It presents a novel force flow-based approach to analyze elastic properties of cellular materials, extending previous models to disordered structures.

Findings

Reproduces known Poisson's ratio expressions for regular honeycombs

Extends analysis to disordered honeycombs and foams

Highlights the importance of force paths with greatest stress

Abstract

Describing and measuring the elastic properties of cellular materials such as honeycombs and foams can be a difficult problem when the cell structure is disordered. This paper suggests that tracking the flow of forces through the material can help in visualizing and understanding how the geometry of the cell structure affects the elastic behaviour. The mean strain tensor for a sample of material can be calculated by summing over the force paths, weighted by the strengths of the paths. This method emphasizes the paths with the greatest stress, which can have the most dynamic effect. The path averaging technique reproduces previous expressions for the Poisson's ratio of regular honeycombs, but easily extends to disordered honeycombs and foams.