Fig. 1

Schematic illustration of the spherical contact model, where Z is the gross displacement controlled by the experimental apparatus, k is the equivalent stiffness of the measurement system, R ₁ is the radius of curvature of the spherical rigid tip, R ₂ is the radius of curvature of the elastic body surface, F is the applied force between the spherical rigid tip and the elastic body, δ is the penetration depth of the spherical rigid tip into the elastic body, and a is the radius of the contact area