Walking Sheets: Locomotion in chemo-mechanically driven, non-Euclidean elastic plates

Spatio-temporally varying chemical patterns are an essential mechanism for coordinating force generation in biological systems. Inspired by this, the use of active materials driven by self-oscillating reaction-diffusion equations is increasingly being explored for engineering applications. This talk describes recent investigations into the locomotion of chemically-driven, deformable surfaces from the perspective of non-Euclidean elastic plate theory. Through a combination of numerical and analytical results, we examine the geometric and mechanical characteristics which optimize gait velocity in an elastic sheet driven along a frictional surface. Further, locomotion on non-uniform terrain is considered, in particular the conditions in which external geometry can inhibit or promote robust motion. Overall, we develop insights into how best to utilize incompatible geometry in the design of soft robotics and other applications.