Walking on a membrane: how to measure ground contact forces for small animals

Measuring spatially distributed forces is crucial to study and understand animal locomotion. For animals like humans, piezo or capacitive pressure mats are readily available, but when it comes to lighter animals that weigh under 100g we lack similar sensors. Optical methods that use photoelastic materials have been developed previously but with limited success. We show a new method to measure spatially distributed in vivo loads that uses the deformation of a thin sheet to back-calculate the applied traction; reminiscent of traction force microscopy but with some notable differences. The substrate is a pre-stressed thin sheet that behaves like a membrane rather than a shell. When the pre-stress dominates the behavior, the deformed curvature is proportional to the normal load according to the Young-Laplace approximation, i.e. -T▽²w=q, with pre-tension T, normal deformation w, and force q to be estimated. In numerical studies, we show the viability of this approach and propose an experimental realization using a non-contact digital image correlation system. Finally, based on analytical models, we develop material selection criteria to satisfy constraints like spatial resolution, minimum load detection thresholds, and animal comfort.