Elastic smooth-contact screen
Hertzian sphere-on-flat contact
Inputs
Positive compressive normal load; tangential force is excluded.
Nominal radius of the sphere against one locally flat body.
Declared linear-elastic modulus for the spherical body.
Declared isotropic elastic ratio in the range 0 through less than 0.5.
Declared linear-elastic modulus for the locally flat body.
Declared isotropic elastic ratio in the range 0 through less than 0.5.
Results
Reduced elastic modulus
58.605
Contact radius
0.42504
Contact diameter
0.85007
Peak Hertz pressure
1,321.5
Elastic approach
15.055
1/E* = (1−ν₁²)/E₁ + (1−ν₂²)/E₂; a = [3FR/(4E*)]^(1/3); p₀ = 3F/(2πa²)
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion
Method
Formula, when it applies, and when it does not
Calculate reduced modulus, contact radius, indentation, and peak contact pressure for one elastic sphere-on-flat normal contact.
1/E* = (1−ν₁²)/E₁ + (1−ν₂²)/E₂; a = [3FR/(4E*)]^(1/3); p₀ = 3F/(2πa²)
When
- Smooth frictionless contact
- Elastic isotropic homogeneous materials
- Sphere on flat
- Normal load only
Don’t
- This is a smooth, frictionless, elastic, isotropic, homogeneous sphere-on-flat normal-contact screen. It excludes roughness, friction, plasticity, coatings, fatigue, thermal effects, surface finish, material selection, life, safety, and approval.