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.Comment: 20 pages, 7 figure