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hertz_contact

Calculate Hertzian point-contact peak pressure, contact radius, and approach from load and radii, so you can screen designs before running a full frictional contact solve.

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

TableJSON Schema
NameRequiredDescriptionDefault
load_nYes
poisson1No
poisson2No
material1No
material2No
radius_mmYes
radius2_mmNo
youngs1_gpaNo
youngs2_gpaNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

A5/5.0
Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden and does so well: it discloses that no solver is used, the half-space assumptions, the validity limit, the yield-based escalation condition, and the exact output fields including warnings, fidelity, band_pct, valid_range_ok, and escalate_to.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is dense but front-loaded, opening with the core purpose before adding formulas, validity, and return fields. Every sentence earns its place for a calculation tool with 9 parameters and no schema descriptions.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a complex, no-annotation, no-output-schema tool with 9 parameters, this is complete: it explains the physics, parameter mapping, validity limits, escalation behavior, and all returned fields. Nothing critical for correct invocation is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate, and it does: it explains radius2_mm as a second sphere or negative conforming socket, body 2 defaulting to body 1, elastic sourcing from youngs#_gpa+poisson# or a Materials-DB material#, and the reduced modulus / effective radius formulas that tie parameters to the calculation.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific calculation—Hertzian point-contact peak pressure—and explicitly distinguishes it as a no-solver screening twin of a frictional contact-pair solve. It also names the escalation path, fem_set_nonlinear_material, so the agent can differentiate it from solver-based siblings.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

It gives clear when-to-use context as a screening calculation and an explicit when-not-to-use boundary: valid while a ≪ R and p0 is below first sub-surface yield, past which the agent should escalate to the nonlinear FEM contact path. The alternative tool is named directly.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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