# The giant increase of stiffness of inhomogeneous rods and beams

## TL;DR

This paper shows that inhomogeneous beams can have significantly increased stiffness when using materials with a negative Poisson's ratio.

## Contribution

The novelty is identifying conditions under which inhomogeneous beams exhibit a giant increase in stiffness due to varying Poisson’s ratios.

## Key findings

- Stiffness of inhomogeneous beams matches classical theories only when specific Poisson’s ratio conditions are met.
- Using materials with negative Poisson’s ratios can lead to a significant increase in beam stiffness.
- The difference in Poisson’s ratios between beam components is critical for the observed stiffness increase.

## Abstract

We demonstrate that stiffnesses of an inhomogeneous beam of coaxial structure coincide with the ones predicted by classical Bernoulli–Euler and Saint-Venant theories if and only if the indicated below conditions on the local Poisson’s ratio are satisfied. If the conditions are not satisfied, the stiffnesses of the inhomogeneous beam exceed the stiffnesses predicted by classical theories. The difference in Poisson’s ratios of the components of the rod/beam can result in a giant increase in stiffness when using materials possessing a negative Poisson’s ratio.