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Run npx skillmds@latest add ashfordeou/failure-criteria in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

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Is Failure Criteria free to use?

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Who published Failure Criteria?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Failure Criteria by ashfordeou — Agent Skill

Name: Failure Criteria
Author: ashfordeOU

Failure Criteria

Use when you must evaluate a composite lamina against strength failure criteria: compute the Tsai-Wu, Tsai-Hill, and max-stress failure indices from the in-plane stresses and the ply allowables, and return the failure verdict. Produces each criterion index, the governing criterion, and the pass or fail verdict for the ply stress state. Trigger: lamina failure, tsai wu, tsai hill, max stress, failure index, composite ply strength, in plane stress.

ashfordeOU Updated Sep 17, 2026

File contents

Lamina Failure Criteria (structures/composites/failure-criteria)

Use when the task is lamina failure assessment for a composite ply: Tsai-Wu, Tsai-Hill, and max-stress failure indices under in-plane stress.

Domain quick reference

A lamina has strength allowables in material axes: fiber tension Xt, fiber compression Xc, transverse tension Yt, transverse compression Yc, and in-plane shear S.
A failure index compares the applied stress state with the allowables; an index at or above 1.0 means the ply fails that criterion.
Max-stress checks each stress component independently against its own allowable, so it ignores interaction between components.
Tsai-Hill couples the two normal stresses with an interaction term and uses the tensile allowables in its classic form.
Tsai-Wu is a quadratic interaction criterion whose linear terms capture tension and compression asymmetry.
Composite airframe certification under FAR-25 relies on statistically based ply allowables; these criteria evaluate the ply stress state against them.

Workflow

Collect the lamina in-plane stresses s1, s2, t12 and the allowables Xt, Xc, Yt, Yc, S, all in MPa.
Compute the Tsai-Wu index with tsai_wu_index.
Compute the Tsai-Hill index with tsai_hill_index.
Compute the max-stress index with max_stress_index.
Combine the three with failure_verdict; the ply fails when any index is at or above 1.0.

Pitfalls

Mixing units: keep every stress and allowable in MPa (the Pa/MPa mix is the classic bug class here).
Using the compression allowables in the classic Tsai-Hill form, which is written for tension.
Reading an index of exactly 1.0 as pass; 1.0 is the failure boundary, so treat index >= 1.0 as failure.
Forgetting that max-stress checks components independently while Tsai-Wu and Tsai-Hill include interaction terms.
Missing the sign convention: s1 and s2 are signed, so max-stress must pick Xt or Xc (Yt or Yc) by the stress sign.

Behavior contract (gate 3)

The Tsai-Wu, Tsai-Hill, max-stress, and verdict logic is exercised by the gate 3 contract test: scripts/test_failure_criteria_logic.py against scripts/failure_criteria_logic.py (stdlib unittest, offline). Run: python3 scripts/test_failure_criteria_logic.py

Compliance

Standards referenced, not reproduced: FAR-25 (14 CFR Part 25) is US government work (public domain); the failure criteria are common strength-of-materials knowledge, summary-only per standards-map.yaml.
compliance: STANDARDS-REF, gated: false.

---name: failure-criteriadescription: Use when you must evaluate a composite lamina against strength failure criteria: compute the Tsai-Wu, Tsai-Hill, and max-stress failure indices from the in-plane stresses and the ply allowables, and return the failure verdict. Produces each criterion index, the governing criterion, and the pass or fail verdict for the ply stress state. Trigger: lamina failure, tsai wu, tsai hill, max stress, failure index, composite ply strength, in plane stress.license: Apache-2.0---# Lamina Failure Criteria (structures/composites/failure-criteria)Use when the task is lamina failure assessment for a composite ply:Tsai-Wu, Tsai-Hill, and max-stress failure indices under in-planestress.## Domain quick reference- A lamina has strength allowables in material axes: fiber tension Xt, fiber compression Xc, transverse tension Yt, transverse compression Yc, and in-plane shear S.- A failure index compares the applied stress state with the allowables; an index at or above 1.0 means the ply fails that criterion.- Max-stress checks each stress component independently against its own allowable, so it ignores interaction between components.- Tsai-Hill couples the two normal stresses with an interaction term and uses the tensile allowables in its classic form.- Tsai-Wu is a quadratic interaction criterion whose linear terms capture tension and compression asymmetry.- Composite airframe certification under FAR-25 relies on statistically based ply allowables; these criteria evaluate the ply stress state against them.## Workflow1. Collect the lamina in-plane stresses s1, s2, t12 and the allowables Xt, Xc, Yt, Yc, S, all in MPa.2. Compute the Tsai-Wu index with tsai_wu_index.3. Compute the Tsai-Hill index with tsai_hill_index.4. Compute the max-stress index with max_stress_index.5. Combine the three with failure_verdict; the ply fails when any index is at or above 1.0.## Pitfalls- Mixing units: keep every stress and allowable in MPa (the Pa/MPa mix is the classic bug class here).- Using the compression allowables in the classic Tsai-Hill form, which is written for tension.- Reading an index of exactly 1.0 as pass; 1.0 is the failure boundary, so treat index >= 1.0 as failure.- Forgetting that max-stress checks components independently while Tsai-Wu and Tsai-Hill include interaction terms.- Missing the sign convention: s1 and s2 are signed, so max-stress must pick Xt or Xc (Yt or Yc) by the stress sign.## Behavior contract (gate 3)The Tsai-Wu, Tsai-Hill, max-stress, and verdict logic is exercised bythe gate 3 contract test: scripts/test_failure_criteria_logic.pyagainst scripts/failure_criteria_logic.py (stdlib unittest, offline).Run:python3 scripts/test_failure_criteria_logic.py## Compliance- Standards referenced, not reproduced: FAR-25 (14 CFR Part 25) is US government work (public domain); the failure criteria are common strength-of-materials knowledge, summary-only per standards-map.yaml.- compliance: STANDARDS-REF, gated: false.

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