Hertz Contact Mechanics

Problem Specification

Consider a simple problem that illustrates a comparison between the analytical and numerical results.  As shown in the diagram below, consider a problem where we apply a downward force (F) of 60π N to a spherical object with a radius (R1) of 8 mm.  This isotropic sphere has an axial modulus (E1) of 1 GPa and a Poisson's ratio (ν1) of 0.3.  In addition, this sphere is fixed vertically at the contact interface with a rigid wall.  Since we are modeling the wall as a rigid body, we assume axial modulus (E2) equals +∞ and Poisson's ratio (ν2) equals 0.  Also, the radius of curvature of the wall (R2) can be assumed to be zero.

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