L1 ⚛ L1-216 ⊙ Testnet

J2 Plasticity — von Mises rate-independent

Structural Mechanics · Rate-independent J2 plasticity with hardening

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⬇ L1-216.md

# ⚛ L1 Principle — J2 Plasticity — von Mises rate-independent **ID:** `L1-216` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Rate-independent J2 plasticity with hardening* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** plastic strain history > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554011 --- ## 🧠 1. Introduction **J2 Plasticity — von Mises rate-independent** is a **nonlinear inverse problem** whose unknown lives in **plastic strain history** space, within the **Rate-independent J2 plasticity with hardening** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **strain dic** sensing mechanism. The forward operator applies, in order: L · yield function operator; L · flow rule operator; L · return map 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 · yield function → L · flow rule → L · return map → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.return_map` `L.flow_rule` `L.yield_function` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.yield_function` | L · yield function operator | | `L.flow_rule` | L · flow rule operator | | `L.return_map` | L · return map operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Rate-independent J2 plasticity with hardening | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | plastic_strain_history | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 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:** `j2_plasticity` · **Forward operator:** `j2_plasticity_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 10000 | | N inc | — | 100 | | Snr db | dB | 30 | | E error | — | 0 | | Sigma y error | — | 0 | | H hardening error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 100 – 1000000 | | N inc | — | 10 – 10000 | | Snr db | dB | 0 – 40 | | E error | — | 0.0 – 0.1 | | Sigma y error | — | 0.0 – 0.1 | | H hardening error | — | 0.0 – 0.2 | ## 🎯 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 = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7cf079535ee747807bea71e90d7972e19dab8114e9632ff3b9aee893c8de0d3b` - **Chain tx hash:** `0x71fb0538e397a396213ac0359a3643505e90f9fd13901d2938ab1fd918c86513` - **Chain block:** `41554011` --- ## File Mapping This bundle consists of: `L1-216.md`, `L1-216.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-216.md` | Source of truth — edit this | Human or LLM | | `L1-216.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 `L1-216`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-216.md).
Regenerate L1-216.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-216-001 J2 Plasticity — von Mises rate-independent Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554011,
  "chain_hash": "0x7cf079535ee747807bea71e90d7972e19dab8114e9632ff3b9aee893c8de0d3b",
  "chain_tx_hash": "0x71fb0538e397a396213ac0359a3643505e90f9fd13901d2938ab1fd918c86513",
  "domain": "Structural Mechanics",
  "hardness_fn": {
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    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
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    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Structural Mechanics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
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    "sensing_mechanism": "strain_dic",
    "solution_space": "plastic_strain_history",
    "sub_domain": "Rate-independent J2 plasticity with hardening",
    "title": "J2 Plasticity \u2014 von Mises rate-independent"
  },
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      "omega": {
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    "epsilon_bounds": {
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      "H_hardening_error": [
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      ],
      "SNR_dB": [
        0,
        40
      ],
      "sigma_y_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Rate-independent J2 plasticity with hardening",
  "title": "J2 Plasticity \u2014 von Mises rate-independent"
}

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