Mechanics of encapsulated three-dimensional structures for simultaneous sensing of pressure and shear stress

Flexible, large-area tactile sensors capable of simultaneously measuring in real time both the normal pressure and the tangential shear stress have many important applications, including those in artificial skin for uses in robotics, medicine and rehabilitation. Previously reported sensors exhibit responses to pressure and shear stress that are coupled, mainly due to nonlinearities, in ways that can be difficult to separate. A recently developed sensor based on techniques in mechanics-guided, deterministic three-dimensional (3D) assembly provides a route to decouple these responses such that the pressure and the shear stress can be determined explicitly and linearly from the change in resistance of multiple strain gauges integrated at carefully selected locations on the 3D structure. A clear understanding of the mechanics of this 3D structure-based sensor is essential for its optimization and application. Here analytic models, validated by finite element analysis, are presented for the deformation of such structures under pressure and shear stress. Analytic solutions in concise forms are derived for a buckled wavy ribbon encapsulated in a soft elastomer, which reveal the effect of the geometry and material parameters on the sensitivity, therefore establishing design guidelines for these devices.