Mechanical Design
Hertzian Contact Stress Simulator
Examine localized contact parameters and pressure fields formed between two spheres under compressive loading. Toggle materials, sweep loads, and export pressure profile coordinates.
Model
Sphere-on-Sphere
Isotropic elastic
Mesh
61 nodes
Sub-micron resolution
Output
CSV
Stress profile ready
Parameters
Sphere material preset
Animated force sweep
Hertzian Theory Formulations
Reduced Radius
R_eq = (R1 * R2) / (R1 + R2)
Reduced Modulus
1/E* = (1 - v1^2)/E1 + (1 - v2^2)/E2
Contact Radius
a = (3 * F * R_eq / (4 * E*))^(1/3)
Max pressure
P_max = 1.5 * F / (pi * a^2)
Approach (Deformation)
delta = a^2 / R_eq
Max pressure of 2463.8 MPa is achieved at the center (x = 0 mm).
The material combination has an equivalent elastic modulus E* of 109.9 GPa.
Contact radius bounds the contact zone between x = -0.440 mm and +0.440 mm.
Contact Mechanics Diagram
Max Pressure
2463.8MPa
Contact Radius
0.440mm
Deformation (Approach)
15.50µm
Equivalent Radius
12.50mm
Contact Pressure Distribution Profile
Pressure Profile Node Data
| x/a Ratio | Position x (mm) | Pressure P(x) (MPa) |
|---|---|---|
| -1.50 | -0.660 | 0.0 |
| -1.35 | -0.594 | 0.0 |
| -1.20 | -0.528 | 0.0 |
| -1.05 | -0.462 | 0.0 |
| -0.90 | -0.396 | 1073.9 |
| -0.75 | -0.330 | 1629.6 |
| -0.60 | -0.264 | 1971.0 |
| -0.45 | -0.198 | 2200.2 |
| -0.30 | -0.132 | 2350.3 |
| -0.15 | -0.066 | 2435.9 |
| 0.00 | 0.000 | 2463.8 |
| 0.15 | 0.066 | 2435.9 |
| 0.30 | 0.132 | 2350.3 |
| 0.45 | 0.198 | 2200.2 |
| 0.60 | 0.264 | 1971.0 |
| 0.75 | 0.330 | 1629.6 |
| 0.90 | 0.396 | 1073.9 |
| 1.05 | 0.462 | 0.0 |
| 1.20 | 0.528 | 0.0 |
| 1.35 | 0.594 | 0.0 |
| 1.50 | 0.660 | 0.0 |