# Step 11: mitc4-element-baseline

## Sprint Contract

### Objective
Implement the baseline MITC4 element utilities and stiffness path after the formulation gate is closed.

### Required Reading
- /AGENTS.md
- /PROGRESS.md
- /PLAN.md
- /docs/README.md
- /docs/HARNESS_ENGINEERING.md
- /docs/PRD.md
- /docs/ARCHITECTURE.md
- /docs/ADR.md
- /docs/NUMERICAL_CONVENTIONS.md
- /docs/MITC4_FORMULATION.md
- /phases/1-linear-static-mitc4/step10.md

### Scope
- Implement shape functions, derivatives, local basis utilities, MITC shear tying per the finalized formulation, stiffness calculation, and drilling stiffness parameter path.
- Keep the element behind runtime-polymorphic element interfaces.
- Produce a 24x24 element stiffness for four-node shell elements with six DOFs per node.

### Allowed Files
- `include/**`
- `src/**`
- `tests/**`
- `docs/MITC4_FORMULATION.md` only for errata discovered during implementation
- `PLAN.md`
- `PROGRESS.md`
- `phases/1-linear-static-mitc4/index.json`

### Explicit Non-Goals
- Do not implement S4R, reduced integration, hourglass control, nonlinear kinematics, pressure loads, composites, thermal coupling, or mesh quality checks.
- Do not implement formulas that are still placeholders in `docs/MITC4_FORMULATION.md`.
- Do not optimize element kernels before baseline benchmark behavior is established.

### Tests To Write First
- Shape function partition and nodal interpolation tests.
- Derivative and Jacobian/local basis tests.
- 24x24 dimension and symmetry tests.
- Rigid body or patch-style checks appropriate to the documented formulation.
- Drilling stiffness sensitivity tests.

### Reference Artifacts
- None required for this unit-level step. Stored-reference regression is Step 14.

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

### Evaluator Checklist
- Step 10 formulation decisions are closed before code is added.
- Element interface uses runtime polymorphism as documented.
- Stiffness output dimension, DOF order, symmetry, and drilling behavior are tested.
- No S4R or nonlinear behavior was introduced.

### Handoff Requirements
- Record implemented formulation surface and validation in `PROGRESS.md`.
- Update `PLAN.md` if benchmark or formulation risks remain.
- Update the matching phase index entry: use `completed` with a one-line `summary`, or `blocked` with `blocked_reason`, or `error` with `error_message`.

## Verification
1. Run the acceptance command.
2. Inspect tests against the finalized MITC4 formulation checklist.

## Do Not
- Do not hide formulation uncertainty in comments or TODOs inside executable code.