Hertz Contact Mechanics

Two elastic spheres · contact radius a = (3RF/4E*)^(1/3)

Parameters

Results

Contact radius a
Peak pressure p₀
Indentation δ
E* (reduced)
Max shear stress

About

Hertz contact (1882) describes two elastic spheres pressing together. Contact radius grows as a=(3RF/4E*)^(1/3). Pressure profile is semi-ellipsoidal: p(r)=p₀√(1−r²/a²). The reduced modulus E*=[(1−ν₁²)/E₁+(1−ν₂²)/E₂]⁻¹ captures material compliance. Max shear stress occurs at ~0.47a depth below surface.