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.