L1 ⚛ L1-223 ⊙ Testnet

Phase-Field Fracture — regularized crack model

Structural Mechanics · Variational phase-field (AT1/AT2) fracture

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⬇ L1-223.md

# ⚛ L1 Principle — Phase-Field Fracture — regularized crack model **ID:** `L1-223` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Variational phase-field (AT1/AT2) fracture* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** phase field and displacement > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554022 --- ## 🧠 1. Introduction **Phase-Field Fracture — regularized crack model** is a **nonlinear inverse problem** whose unknown lives in **phase field and displacement** space, within the **Variational phase-field (AT1/AT2) fracture** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **dic** sensing mechanism. The forward operator applies, in order: L · psi split operator; L · phase field evolve operator; L · coupled solve operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · psi split → L · phase field evolve → L · coupled solve → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.coupled_solve` `L.phase_field_evolve` `L.psi_split` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.psi_split` | L · psi split operator | | `L.phase_field_evolve` | L · phase field evolve operator | | `L.coupled_solve` | L · coupled solve operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Variational phase-field (AT1/AT2) fracture | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | phase_field_and_displacement | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `phase_field_fracture` · **Forward operator:** `phase_field_fracture_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 10000 | | Snr db | dB | 30 | | Ell mm | mm | 0.1 | | G c error | — | 0 | | Degradation func error | — | 0 | | Ell regularization error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 1000 – 10000000 | | Snr db | dB | 0 – 40 | | Ell mm | mm | 0.001 – 10 | | G c error | — | 0.0 – 0.2 | | Degradation func error | — | 0.0 – 0.2 | | Ell regularization error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 21.5 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb7d9fde3e0672fb05cebda4145f0e41ac165a8a3aa604f5352a500e3a412c03d` - **Chain tx hash:** `0x3224b6bcb02f445fe5cac667e807ed5348584bbac58387632dcc20b4078b2a14` - **Chain block:** `41554022` --- ## File Mapping This bundle consists of: `L1-223.md`, `L1-223.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-223.md` | Source of truth — edit this | Human or LLM | | `L1-223.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 `L1-223`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-223.md).
Regenerate L1-223.json so every field matches the Markdown.
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L2-223-001 Phase-Field Fracture — regularized crack model Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-223",
  "chain_block": 41554022,
  "chain_hash": "0xb7d9fde3e0672fb05cebda4145f0e41ac165a8a3aa604f5352a500e3a412c03d",
  "chain_tx_hash": "0x3224b6bcb02f445fe5cac667e807ed5348584bbac58387632dcc20b4078b2a14",
  "domain": "Structural Mechanics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Structural Mechanics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.psi_split",
      "L.phase_field_evolve",
      "L.coupled_solve",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "dic",
    "solution_space": "phase_field_and_displacement",
    "sub_domain": "Variational phase-field (AT1/AT2) fracture",
    "title": "Phase-Field Fracture \u2014 regularized crack model"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "phase_field_fracture_forward"
    ],
    "allowed_omega_dimensions": [
      "N_DOF",
      "ell_mm",
      "SNR_dB",
      "ell_regularization_error",
      "G_c_error",
      "degradation_func_error",
      "ell_regularization_error",
      "G_c_error",
      "degradation_func_error"
    ],
    "allowed_problem_classes": [
      "phase_field_fracture"
    ],
    "center_spec": {
      "epsilon_fn_center": "21.5",
      "forward_operator": "phase_field_fracture_forward",
      "input_format": "measurement_only",
      "omega": {
        "G_c_error": 0.0,
        "N_DOF": 10000,
        "SNR_dB": 30,
        "degradation_func_error": 0.0,
        "ell_mm": 0.1,
        "ell_regularization_error": 0.0
      },
      "problem_class": "phase_field_fracture"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "G_c_error": [
        0.0,
        0.2
      ],
      "N_DOF": [
        1000,
        10000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "degradation_func_error": [
        0.0,
        0.2
      ],
      "ell_mm": [
        0.001,
        10
      ],
      "ell_regularization_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Variational phase-field (AT1/AT2) fracture",
  "title": "Phase-Field Fracture \u2014 regularized crack model"
}

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