Analytical modeling for suction cup designs for skin-interfaced wearable devices

Stable mounting is a central requirement for skin-interfaced wearable biomedical devices, because accurate and long-term measurements with clinical utility typically demand intimate contact with the skin, whereas practical use also requires gentle removal to minimize skin irritation and damage. Existing mounting strategies often struggle to satisfy these competing requirements simultaneously, especially under prolonged wear or in the presence of sweat and moisture. Suction-based mounting has recently emerged as a promising alternative because it can provide strong, reversible, and adhesive-free attachment, yet its underlying mechanics remain insufficiently understood. Here, we establish analytical models for the deformation and force of suction cups in a fully explicit form, covering both the cone suction cup and an optimized ring suction cup design. Unlike previous approaches that rely on indirect quantities such as the pressure difference and contact radius, which are not available before experiments and therefore cannot serve as controllable design variables, the present framework yields direct relations between suction performance and geometry parameters, material properties, and loading conditions, including the maximum push down displacement and the subsequent pull up displacement. The resulting formulas agree closely with accurate numerical solutions and lead to compact scaling laws that clearly identify how geometry and material parameters govern suction performance. These results provide a quantitative and physically transparent foundation for the design of suction-based mounting strategies in wearable devices.