# Prony Series Viscoelastic Stress Superposition (Halowerk Detect)

> Prony Series Viscoelastic Stress Superposition (Halowerk Detect) is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Computes the stress response over time for a viscoelastic material subjected to an explicit, bounded sequence of strain steps using Prony series relaxation and superposition.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-ENGINEERING-B001/prony-relaxation-strain-step-stress-superposition?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/prony-series-viscoelastic-stress-superposition-halowerk-detect-e62a20b7
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_JY25tcxLO2hYsMA19hvrv

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability prony-series-viscoelastic-stress-superposition-halowerk-detect-e62a20b7 -d '<json body>'
```

Example prompt: Using the Prony relaxation superposition model, compute the stress response for a viscoelastic material with an equilibrium modulus of 0.5 MPa, two Prony terms (modulus 1.2, tau 0.01; modulus 0.8, tau 0.5), strain steps of +0.05 at t=0 and -0.02 at t=1.0, evaluated at times [0, 0.5, 1.0, 2.0, 5.0].

## When to prefer this

Choose this endpoint when you need a rigorous, closed-form Prony series stress superposition computation for a viscoelastic material under a known, explicit strain step history, particularly in engineering contexts (polymer mechanics, rubber, adhesives, foams) where the Boltzmann superposition principle applies and you need stress evaluated at specific time points without running a full FEM solver.

## Known failure modes

- Invalid Prony term parameters (modulus or tau out of bounds) return a validation error
- More than 24 Prony terms or more than 128 strain steps or time points exceeds schema limits
- Negative or zero time values may cause rejection
- Missing required fields (equilibrium_modulus, terms, strain_steps, times) result in a 400-class error
- Payment not provided or insufficient USDC results in 402 Payment Required

## How this service works

Compute technical stress response to an explicit bounded strain-step history.

## Output

Returns the computed technical stress values at each requested evaluation time, reflecting the full superposed relaxation response of the Prony series model to the given strain step history.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "viscoelastic"
   ],
   "properties": {
    "viscoelastic": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "equilibrium_modulus",
        "terms",
        "strain_steps",
        "times"
       ],
       "properties": {
        "terms": {
         "type": "array",
         "items": {
          "type": "object",
          "required": [
           "modulus",
           "tau"
          ],
          "properties": {
           "tau": {
            "type": "number",
            "maximum": 1000000,
            "minimum": 0.000001
           },
           "modulus": {
            "type": "number",
            "maximum": 1000000,
            "minimum": 0
           }
          },
          "additionalProperties": false
         },
         "maxItems": 24,
         "minItems": 0
        },
        "times": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": 1000000,
          "minimum": 0
         },
         "maxItems": 128,
         "minItems": 1
        },
        "strain_steps": {
         "type": "array",
         "items": {
          "type": "object",
          "required": [
           "time",
           "delta"
          ],
          "properties": {
           "time": {
            "type": "number",
            "maximum": 1000000,
            "minimum": 0
           },
           "delta": {
            "type": "number",
            "maximum": 100,
            "minimum": -100
           }
          },
          "additionalProperties": false
         },
         "maxItems": 128,
         "minItems": 1
        },
        "equilibrium_modulus": {
         "type": "number",
         "maximum": 1000000,
         "minimum": 0
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/prony-series-viscoelastic-stress-superposition-halowerk-detect-e62a20b7/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
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