L1 ⚛ L1-215 ⊙ Testnet

Hyperelasticity — large-deformation rubber-like

Structural Mechanics · Neo-Hookean / Mooney-Rivlin / Ogden

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⬇ L1-215.md

# ⚛ L1 Principle — Hyperelasticity — large-deformation rubber-like **ID:** `L1-215` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Neo-Hookean / Mooney-Rivlin / Ogden* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** strain energy params > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554011 --- ## 🧠 1. Introduction **Hyperelasticity — large-deformation rubber-like** is a **nonlinear inverse problem** whose unknown lives in **strain energy params** space, within the **Neo-Hookean / Mooney-Rivlin / Ogden** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **dic strain stress** sensing mechanism. The forward operator applies, in order: L · deformation gradient operator; L · strain energy operator; L · piola stress 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 · deformation gradient → L · strain energy → L · piola stress → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.piola_stress` `L.strain_energy` `L.deformation_gradient` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.deformation_gradient` | L · deformation gradient operator | | `L.strain_energy` | L · strain energy operator | | `L.piola_stress` | L · piola stress operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Neo-Hookean / Mooney-Rivlin / Ogden | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | strain_energy_params | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 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:** `hyperelastic` · **Forward operator:** `hyperelastic_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 10000 | | Snr db | dB | 30 | | Mu error | — | 0 | | N sensors | — | 64 | | Bulk modulus error | — | 0 | | Param choice error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 100 – 1000000 | | Snr db | dB | 0 – 40 | | Mu error | — | 0.0 – 0.1 | | N sensors | — | 4 – 4096 | | Bulk modulus error | — | 0.0 – 0.1 | | Param choice error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3896d044280d4fe3f825228b36fa7b6c9a47aaf806f5cf3d5d9318fe9b491015` - **Chain tx hash:** `0x803a6d2bce102c7ac849af4a9be3c67e9240a1fbfbec85d901d11a115a2d0018` - **Chain block:** `41554011` --- ## File Mapping This bundle consists of: `L1-215.md`, `L1-215.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-215.md` | Source of truth — edit this | Human or LLM | | `L1-215.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 `L1-215`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-215.md).
Regenerate L1-215.json so every field matches the Markdown.
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L2-215-001 Hyperelasticity — large-deformation rubber-like Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-215",
  "chain_block": 41554011,
  "chain_hash": "0x3896d044280d4fe3f825228b36fa7b6c9a47aaf806f5cf3d5d9318fe9b491015",
  "chain_tx_hash": "0x803a6d2bce102c7ac849af4a9be3c67e9240a1fbfbec85d901d11a115a2d0018",
  "domain": "Structural Mechanics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "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": 3.2,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Structural Mechanics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.deformation_gradient",
      "L.strain_energy",
      "L.piola_stress",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "dic_strain_stress",
    "solution_space": "strain_energy_params",
    "sub_domain": "Neo-Hookean / Mooney-Rivlin / Ogden",
    "title": "Hyperelasticity \u2014 large-deformation rubber-like"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "hyperelastic_forward"
    ],
    "allowed_omega_dimensions": [
      "N_DOF",
      "N_sensors",
      "SNR_dB",
      "mu_error",
      "bulk_modulus_error",
      "param_choice_error",
      "mu_error",
      "bulk_modulus_error",
      "param_choice_error"
    ],
    "allowed_problem_classes": [
      "hyperelastic"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "hyperelastic_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_DOF": 10000,
        "N_sensors": 64,
        "SNR_dB": 30,
        "bulk_modulus_error": 0.0,
        "mu_error": 0.0,
        "param_choice_error": 0.0
      },
      "problem_class": "hyperelastic"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_DOF": [
        100,
        1000000
      ],
      "N_sensors": [
        4,
        4096
      ],
      "SNR_dB": [
        0,
        40
      ],
      "bulk_modulus_error": [
        0.0,
        0.1
      ],
      "mu_error": [
        0.0,
        0.1
      ],
      "param_choice_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Neo-Hookean / Mooney-Rivlin / Ogden",
  "title": "Hyperelasticity \u2014 large-deformation rubber-like"
}

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