Hertz Sphere Contact

Hertzian contact theory describes the stresses and deformations that occur when two solid, curved bodies are pressed together. This module specifically models a nonadhesive, elastic sphere of radius R indenting into a flat elastic half-space, which is a fundamental case in mechanics. The result is a non-linear load-indentation relationship, distinct from the simple linear behavior of a Hookean spring.

Experiment

Use the Hertz Sphere Contact module to observe how the contact mechanics evolve.

1. Start with the default settings: Effective modulus of 10 GPa, Sphere radius of 4 mm, and Indentation of 4 micrometers. Confirm the calculated values match the worked example above.
2. Observe the visual representation. The red line represents the contact radius, and the shaded red region illustrates the semi-elliptical pressure distribution. The force-indentation graph on the left shows your current state on the non-linear curve.
3. Change the Indentation micrometers to 9. Notice how the normal force and contact radius increase, and observe the point moving along the stiffening force-indentation curve.
4. Change the Effective modulus GPa to 100. Observe the significant increase in normal force and peak pressure required to maintain the same indentation into a stiffer material.