Influence of Prestretch on Planar Indentation of Elastomers: Insights from Experiments and Theory

Abstract

Elastomers exhibit a stiffer mechanical response and anisotropy when stretched in a specific direction, which has led to numerous applications in biomechanics, surgery, tactile sensors, and more. This study introduces a comprehensive, experimentally validated analytical framework to investigate the effects of prestretch on the planar contact between a rigid indenter and a hyperelastic substrate. By linearizing the equilibrium equation for incremental deformation, we adapt the superposition principle to reveal how prestretch modifies the mechanical response, which is reflected in a simple prefactor in the surface Green's function. This modification facilitates precise calculation of contact mechanics properties, including indentation pressure distributions and displacement profiles, which are essential for assessing both global and local properties, e.g., force-displacement responses. We further support our theoretical findings with numerical simulations and validate them through cylindrical indentation tests across various stretch ratios. These outcomes emphasize the feasibility of using our first-order approximation theory in practical settings, especially for the mechanical characterization of materials involving residual stress analysis and the development of advanced, model-based adaptive tactile sensors.