# Analytic analysis of auxetic metamaterials through analogy with rigid link systems

## TL;DR

This paper introduces an analytical approach to study auxetic metamaterials by drawing analogies with rigid link systems, providing accurate predictions of elastic instability and post-buckling behavior to aid design.

## Contribution

It presents a novel analytical methodology linking lattice mechanisms with mechanical behavior, improving understanding and design of auxetic metamaterials.

## Key findings

- Excellent agreement with finite element simulations
- Accurate prediction of elastic instability onset
- Insight into lattice mechanisms and mechanical responses

## Abstract

Recent progress in advanced additive manufacturing techniques has stimulated the growth of the field of mechanical metamaterials. One area particular interest in this subject is the creation of auxetic material properties through elastic instability. This paper focuses on a novel methodology in the analysis of auxetic metamaterials through analogy with rigid link lattice systems. Our analytic methodology gives extremely good agreement with finite element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson's ratio. The insight into the relationships between mechanisms within lattices and their mechanical behaviour has the potential to guide the rational design of lattice based metamaterials.