# hertz_contact

Family 14: a cylinder pressed on a block (frictionless line contact, plane strain, built-in contact solver).

Exact anchor for a shallow contact on a deep block: Hertz, p0 = sqrt(P' E* / (pi R)), a = sqrt(4 P' R / (pi E*)), with
1/E* = 2 (1 - nu^2) / E. The load is set through a/R. A block of finite depth (h/R, with h fixed at the template's 8 mm)
carries the contact a little differently, which is the part no formula gives. Both bodies share the elastic constants.
The mesh is Studio's own graded contact mesh at its three sizes (element size at the contact = a/5 x 1.6, 1, 0.625).

## Parameters (nondimensional)

| parameter | range |
|---|---|
| `a_over_R` | 0.005 - 0.03 |
| `h_over_R` | 0.1 - 0.4 |
| `nu` | 0.2 - 0.35 |

## Answers and their error bands

| answer | error band (median / 95 % / max) | similarity x2 / x4 | CalculiX (same mesh) |
|---|---|---|---|
| `p_over_hertz` | 0.83 % / 0.83 % / 0.83 % | max 0 % | max - |
| `a_over_hertz` | 6.1 % / 6.1 % / 6.1 % | max 0 % | max - |

## Checks

- points: 18 solved, 6 failed
- three-mesh studies: 2 (every 4th point); the band of each point is 1.25 x the largest standard-mesh error among its 3 nearest studies
- symmetry check (max): 0 %
- neighbour check: flagged 0, re-solved on a finer mesh 0, unresolved 0
- direction checks: 

## Columns of points.csv

parameters, the answers, `<answer>_band` (relative), the hand-theory ratios, `mirror_err`, `equilibrium_err` (where a single reaction exists), `<answer>_loo_err` / `_neighbour_flag` (leave-one-out prediction from all other points), `<answer>_recheck_diff` / `_flag_resolved` (finer re-solve of a flagged point), `has_gci` / `has_similarity` / `has_calculix`, `nodes`, `solve_s`, `studio` (version).

Solved with NovaSolver Studio through the same commands an AI client uses over MCP; the first section says which solver and mesh. The claim is verification (the equations are solved within the band), not validation against tests.

## License

This data is licensed under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/
Credit: NovaSolver, https://novasolver.jp/studio/verified/
Provided as is, without warranty. Design decisions remain the user's responsibility.