Resilience & toughness moduli API

Computes modulus of resilience σy²/(2E), modulus of toughness from the stress-strain curve, and the absolute strain energy of a loaded bar. Answers 'How much elastic energy can this material store to yield?', 'What is its toughness modulus?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/strain-energy-resilience

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

materialstrain-energyresiliencemodulus-of-toughnesselastic-energystress-strainyieldmachine-design

API URLhttps://x402.hexl.dev/v1/engineering/strain-energy-resilience

Integration docs

Example request

{
  "youngsModulusGpa": 200,
  "yieldStrengthMpa": 250,
  "ultimateStrengthMpa": 400,
  "fractureStrain": 0.2
}

Example response

{
  "modulusOfResilienceMjm3": 0.15625,
  "modulusOfResilienceKjm3": 156.25,
  "formula": "Ur = σy²/(2E); Ut ≈ ½(σy+σu)·εf; U_bar = F²L/(2AE)",
  "interpretation": "Resilience is recoverable elastic energy to yield; toughness adds the plastic area to fracture.",
  "modulusOfToughnessMjm3": 65
}

Input schema

{
  "type": "object",
  "required": [
    "youngsModulusGpa",
    "yieldStrengthMpa"
  ],
  "properties": {
    "youngsModulusGpa": {
      "type": "number",
      "examples": [
        200
      ]
    },
    "yieldStrengthMpa": {
      "type": "number",
      "examples": [
        250
      ]
    },
    "ultimateStrengthMpa": {
      "type": "number",
      "examples": [
        400
      ]
    },
    "fractureStrain": {
      "type": "number",
      "examples": [
        0.2
      ]
    },
    "forceN": {
      "type": "number",
      "examples": [
        5000
      ]
    },
    "lengthM": {
      "type": "number",
      "examples": [
        1
      ]
    },
    "areaMm2": {
      "type": "number",
      "examples": [
        100
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}