# Two-dimensional Mechanical Metamaterials with Unusual Poisson Ratio Behavior

## TL;DR

This paper introduces 2D mechanical metamaterials capable of large deformations with minimal energy, exhibiting unusual Poisson ratio behaviors including divergence, sign change, and shape memory effects.

## Contribution

It presents novel 2D metamaterial designs that demonstrate unique Poisson ratio phenomena, expanding understanding of mechanical responses in engineered structures.

## Key findings

- Poisson ratio diverges at specific strains
- Poisson ratio changes sign and magnitude
- Structures exhibit shape memory effects

## Abstract

We design two-dimensional (2D) mechanical metamaterials that may be deformed substantially at little or no energy cost. Examples of such deformable structures are assemblies of rigid isosceles triangles hinged in their corners on the macro-scale, or polymerized phenanthrene molecules forming porous graphene on the nano-scale. In these and in a large class of related structures, the Poisson ratio $\nu$ diverges for particular strain values. $\nu$ also changes its magnitude and sign, and displays a shape memory effect.