# Sprint Contract: MITC4 Material Integration

## Objective
Implement or rebuild local plane-stress material behavior, shear correction, material transformation, and `2 x 2 x 2` Gauss integration scaffolding.

## Required Reading
- /AGENTS.md
- /docs/MITC4_FORMULATION.md
- /docs/NUMERICAL_CONVENTIONS.md
- /docs/ARCHITECTURE.md

## Scope
- Implement isotropic linear elastic shell material matrix with `sigma_33 = 0` and `kappa = 5/6`.
- Define material/strain ordering tests.
- Implement or verify convected-to-local material transformation for Phase 1 cases.
- Add `2 x 2 x 2` integration point and weight infrastructure.

## Allowed Files
- `include/`
- `src/`
- `tests/`
- `PLAN.md`
- `PROGRESS.md`

## Explicit Non-Goals
- Do not add composite sections.
- Do not add stress/strain output recovery as mandatory output.
- Do not switch to analytic thickness integration without equivalence tests and doc update.

## Tests To Write First
- Isotropic matrix value tests for known `E`, `nu`, and `kappa`.
- Shear row ordering tests.
- Integration point count and weights tests.
- Flat element material transform identity/equivalence tests.
- Invalid material/thickness diagnostic tests if not covered earlier.

## Reference Artifacts
- None.

## Acceptance Commands
```bash
python scripts/validate_workspace.py
```

## Evaluator Checklist
- `2 x 2 x 2` integration is the active baseline.
- Material transform behavior is tested.
- No reduced integration or hourglass logic is introduced.

## Handoff Requirements
- Record material and integration readiness in `PROGRESS.md`.

## Do Not
- Do not make S4R assumptions in material or integration code.