Hertzian contact refers to the frictionless contact between two nonconforming bodies.

For example, contact between two spheres, a sphere and the surface of a half space, two cylinders, a cylinder and
the surface of a half space etc.

In the case of the sphere, the initial contact occurs at a point and in the case of the cylinder, the initial contact occurs
along a line. Such point and line contact prior to loading can occur in other applications as well.

As the bodies deform, the contact occurs over an area and hence the stresses are not infinite. But the stresses can
still be very high.

The assumptions of the Hertzian theory are as follows:
The surfaces are nonconforming, smooth and frictionless.
The contact area is small compared to the size of the bodies.
The bodies are isotropic, elastic and the strains are small.

In this document, Hertzian contact is demonstrated using Altair OptiStruct for the following problems
Rigid sphere and elastic half space
Elastic sphere and rigid half space
Rigid sphere and elastic sphere