  Localized deformation patterns are a common motif in morphogenesis and are
increasingly finding widespread applications in materials science, for instance
as memory devices. Here we describe the emergence of spatially localized
deformations in a minimal mechanical system by exploring the impact of growth
and shear on the conformation of a semi-flexible filament connected to a
pliable shearable substrate. We combine numerical simulations of a discrete rod
model with theoretical analysis of the differential equations recovered in the
continuum limit to quantify (in the form of scaling laws) how geometry,
mechanics, and growth act together to give rise to such localized structures in
this system. We find that spatially localized deformations along the filament
emerge for intermediate shear modulus and increasing growth. Finally, we use
experiments on a 3D printed multi-material model system to demonstrate that
external control of the amount of shear and growth regulates the spatial extent
of the localized strain texture.
