OS-V: 0291 Hertzian Contact - Elastic Sphere and Rigid Half-space
Hertzian contact is demonstrated using OptiStruct for an elastic sphere and rigid half-space problem.
Hertzian contact (Hertz 1881, 1882) refers to the frictionless contact between two
non-conforming bodies.
Model Files
Before you begin, copy the file(s) used in this problem
to your working directory.
Benchmark Model
The properties are:
- Material Properties
- Value
- Young's modulus (E)
- 210000
- Poisson's ratio ( )
- 0.3
- R
- 30
- d
- 0.1 (enforced z-displacement)
Analytical Results:
The analytical solutions are provided by Popov, 2010. The derivation of the analytical solution is beyond the technical scope of this document. Some key variables of the analytical solution are as follows:
The contact area is calculated as:
Where,
- Radius of the sphere.
- Depth of indentation.
The applied force is calculated as:
Where,
- Young's modulus.
- Poisson's ratio.
The maximum contact pressure/stress is calculated as:
Results
Pressure/Stress (Magnitude) | r/a | |
---|---|---|
Analytical Result | OptiStruct (S2S)-Contact Pressure | |
8482 | 8525 | 0 |
8350 | 8300 | 0.2 |
7700 | 7675 | 0.4 |
6800 | 6990 | 0.6 |
5100 | 5200 | 0.8 |
0 | 1345 | 1 |
The results from FEA are in good agreement with the analytical solution.