Geometric localization in supported elastic struts

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.