Hertz Contact
hertz_contactCalculates Hertzian contact peak pressure, contact radius, and approach for sphere-on-flat or sphere-sphere geometry, indicating when linear theory is valid or nonlinear FEM is required.
Instructions
Exact Hertzian point-contact peak pressure (NO solver) — the screening twin
of a frictional CONTACT PAIR solve. Sphere of radius_mm on a flat (default)
or on a second sphere radius2_mm (negative for a conforming socket). Each
body's elastics from youngs#_gpa+poisson# or a Materials-DB material#; body 2
defaults to body 1. Reduced modulus 1/E = (1−ν₁²)/E₁ + (1−ν₂²)/E₂, effective
radius 1/R = 1/R₁ + 1/R₂; contact radius a = (3FR/4E*)^(1/3), peak pressure
p₀ = 3F/(2πa²) = 1.5× mean, approach δ = a²/R. Half-space theory: valid while
a ≪ R and p₀ below first sub-surface yield (~1.6·σ_y) — past that escalate to
the nonlinear fem_set_nonlinear_material contact path.
Returns {e_star_mpa, effective_radius_mm, contact_radius_mm, peak_pressure_mpa, mean_pressure_mpa, approach_mm, a_over_R, fidelity, band_pct, valid_range_ok, warnings, escalate_to}.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| load_n | Yes | ||
| poisson1 | No | ||
| poisson2 | No | ||
| material1 | No | ||
| material2 | No | ||
| radius_mm | Yes | ||
| radius2_mm | No | ||
| youngs1_gpa | No | ||
| youngs2_gpa | No |