# Reversible signal transmission in an active mechanical metamaterial

## TL;DR

This paper presents a theoretical active mechanical metamaterial that uses a biological reaction mechanism to enable reversible signal transmission, overcoming limitations of passive metamaterials and allowing controllable signal propagation.

## Contribution

It introduces a biologically inspired reaction mechanism into mechanical metamaterials, enabling reversible signal transmission and providing analytical insights into signal speed control.

## Key findings

- Signals propagate via traveling waves in the material.
- Parameter space analysis reveals conditions for signal transmission.
- Explicit formulas relate reaction timescale to signal speed.

## Abstract

Mechanical metamaterials are designed to enable unique functionalities, but are typically limited by an initial energy state and require an independent energy input to function repeatedly. Our study introduces a theoretical active mechanical metamaterial that incorporates a biological reaction mechanism to overcome this key limitation of passive metamaterials. Our material allows for reversible mechanical signal transmission, where energy is reintroduced by the biologically motivated reaction mechanism. By analysing a coarse grained continuous analogue of the discrete model, we find that signals can be propagated through the material by a travelling wave. Analysis of the continuum model provides the region of the parameter space that allows signal transmission, and reveals similarities with the well-known FitzHugh-Nagumo system. We also find explicit formulae that approximate the effect of the timescale of the reaction mechanism on the signal transmission speed, which is essential for controlling the material.