Large deformation mechanics of a soft elastomeric layer compressed by a finite flat rigid punch for tactile sensor applications

In this study, we develop a large deformation analytical-empirical model for a flat finite punch pinching on an incompressible, polymeric layer under plane strain conditions. The model could further advance the predictive capabilities of enhanced tactile sensor response models. The aforementioned model is developed based on the analytical model for an infinitely long layer under uniform compression which has been presented in Kalayeh and Charalambides (2015). Related non-linear finite element (FE) simulations with large strain, large deformation assumptions are carried out in this study. Using the FE finite flat punch simulations, the uniform layer compression model is properly adjusted to predicting the finite punch layer response. The mechanics of the polymeric layer in the vicinity of the symmetry plane, under the application of a flat finite rigid punch is fully analyzed and an expression for the indentation force as a function of the applied top surface deformation is developed. The relevance of this result to modeling the non-linear tactile sensor response over a broad sensing range is discussed. The reported results are compared to FE simulations for applied surface deformation levels of up to 40 percent of the layer initial thickness, and punch half-length to layer thickness ratios of 1 to 2. Great agreement is found to exist between the analytical-empirical model and the FE simulations. For completeness, this new semi-analytical model is fully summarized in the Appendix of this work.