# Contact of a spherical probe with a stretched rubber substrate

In a recently published paper, we report on a theoretical and experimental investigation of the normal contact of stretched neo-Hookean substrates with rigid spherical probes. Starting from a published formulation of surface Green’s function for incremental displacements on a pre-stretched, neo-Hookean, substrate (L.H. Lee \textitJ. Mech. Phys. Sol. \textbf56 (2008) 2957-2971), a model is derived for both adhesive and non-adhesive contacts. The shape of the elliptical contact area together with the contact load and the contact stiffness are predicted as a function of the in-plane stretch ratios $\lambda_x$ and $\lambda_y$ of the substrate. The validity of this model is assessed by contact experiments carried out using an uniaxally stretched silicone rubber. For stretch ratio below about 1.25, a good agreement is observed between theory and experiments. Above this threshold, some deviations from the theoretical predictions are induced as a result of the departure of the mechanical response of the silicone rubber from the neo-Hokeean description embedded in the model.

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