Calculation Reference

1. K. L. Johnson, Contact Mechanics, Cambridge University Press, 1985, Chapter 4, "Normal contact of elastic solids - Hertz theory," DOI: 10.1017/CBO9781139171731.005.

Assumptions

• Hertz elastic contact: smooth, frictionless, homogeneous, isotropic bodies with small strains.
• The contact patch is small compared with the body radii and nearby geometry.
• Point contact uses a circular contact radius a; line contact uses half-width b over a specified contact length.
• Point-contact deflection uses delta = a^2 / R*, with incremental stiffness k = dF / ddelta = 2 E* a.
• Line-contact deflection and stiffness are local Hertz estimates: delta_local = b^2 / (2 R*), k_local = pi E* L / 2, and k'_local = pi E* / 2.
• Surface finish, coating layers, plasticity, tangential loading, adhesion, lubrication, and subsurface fatigue life are not modeled.