# ⚛  L1 Principle — Crystal Plasticity — slip-system resolved plasticity

**ID:** `L1-217` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Structural Mechanics — *Dislocation slip-system crystal plasticity FE*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** grain scale stress strain
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554011

---

## 🧠 1. Introduction

**Crystal Plasticity — slip-system resolved plasticity** is a **nonlinear inverse problem** whose unknown lives in **grain scale stress strain** space, within the **Dislocation slip-system crystal plasticity FE** sub-domain of **Structural Mechanics**.

Measurements consist of mechanical vibrations or strain signals via a **ebsd dic** sensing mechanism.

The forward operator applies, in order: L · slip systems operator; L · rate dependent operator; L · grain assembly operator; pixel-level spatial averaging on the detector.

Observations are corrupted by additive Gaussian noise. Stiff, nonlinear; texture-dependent; expensive at sub-grain resolution.

## ⚙ 2. Forward Model

Physical chain: **x** → L · slip systems → L · rate dependent → L · grain assembly → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.grain_assembly` `L.rate_dependent` `L.slip_systems` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.slip_systems` | L · slip systems operator |
| `L.rate_dependent` | L · rate dependent operator |
| `L.grain_assembly` | L · grain assembly operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Structural Mechanics |
| Sub domain | Dislocation slip-system crystal plasticity FE |
| Carrier | mechanical |
| Problem class | nonlinear_inverse |
| Solution space | grain_scale_stress_strain |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 10 |
| L dag | 3.8 |

## 📡 4. Measurement Model

Stiff, nonlinear; texture-dependent; expensive at sub-grain resolution.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `crystal_plasticity` · **Forward operator:** `crystal_plasticity_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N dof | — | 100000 |
| Snr db | dB | 25 |
| N grains | — | 100 |
| N slipsys | — | 12 |
| Tau 0 error | — | 0 |
| Texture error | — | 0 |
| H hardening error | — | 0 |
| Grain boundary error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N dof | — | 1000 – 10000000 |
| Snr db | dB | 0 – 40 |
| N grains | — | 1 – 10000 |
| N slipsys | — | 3 – 48 |
| Tau 0 error | — | 0.0 – 0.1 |
| Texture error | — | 0.0 – 0.3 |
| H hardening error | — | 0.0 – 0.2 |
| Grain boundary error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 18.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1000` and δ = `10`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x3467af012ebed5859c268511f2efbe624f08056b131942fbb0024d7dfd66204b`
- **Chain tx hash:** `0xf31247b08a8d80789daf0a9cf3e343ea6850db65b3e4e4b9cdb1d31ecdb80afe`
- **Chain block:** `41554011`

---

## File Mapping

This bundle consists of: `L1-217.md`, `L1-217.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-217.md` | Source of truth — edit this | Human or LLM |
| `L1-217.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-217`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._