Modeling Electronic Skin Response to Normal Distributed Force

The reference electronic skin is a sensor array based on PVDF (Polyvinylidene fluoride) piezoelectric polymers, coupled to a rigid substrate and covered by an elastomer layer. It is first evaluated how a distributed normal force (Hertzian distribution) is transmitted to an extended PVDF sensor through the elastomer layer. A simplified approach based on Boussinesq's half-space assumption is used to get a qualitative picture and extensive FEM simulations allow determination of the quantitative response for the actual finite elastomer layer. The ultimate use of the present model is to estimate the electrical sensor output from a measure of a basic mechanical action at the skin surface. However this requires that the PVDF piezoelectric coefficient be known a-priori. This was not the case in the present investigation. However, the numerical model has been used to fit experimental data from a real skin prototype and to estimate the sensor piezoelectric coefficient. It turned out that this value depends on the preload and decreases as a result of PVDF aging and fatigue. This framework contains all the fundamental ingredients of a fully predictive model, suggesting a number of future developments potentially useful for skin design and validation of the fabrication technology.