{"uid":"cap_JY25tcxLO2hYsMA19hvrv","slug":"prony-series-viscoelastic-stress-superposition-halowerk-detect-e62a20b7","name":"Prony Series Viscoelastic Stress Superposition (Halowerk Detect)","description":"Compute technical stress response to an explicit bounded strain-step history.","url":"https://detect.halowerk.com/v1/F-TD2000-ENGINEERING-B001/prony-relaxation-strain-step-stress-superposition?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"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}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_IZs4w0JRqF02pTGxNY3aG","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"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].","exampleUseCases":[{"title":"Polymer seal stress relaxation analysis","prompt":"I have a rubber seal modeled with a Prony series: equilibrium modulus 0.3, two terms with moduli 2.0 and 1.0 and taus of 0.005 and 0.2. It gets a strain step of +0.1 at t=0. Can you compute the stress response at times [0, 0.01, 0.05, 0.1, 0.5, 1.0, 5.0]?"},{"title":"Multi-step loading viscoelastic simulation","prompt":"Simulate the stress history of a viscoelastic foam with equilibrium modulus 0.1, Prony terms (modulus 0.9, tau 0.1) and (modulus 0.5, tau 1.0), subjected to strain steps: +0.08 at t=0, +0.04 at t=2, and -0.06 at t=5. Evaluate at times [0, 1, 2, 3, 5, 7, 10]."},{"title":"Adhesive layer stress after load reversal","prompt":"For a structural adhesive with equilibrium modulus 10, two Prony terms (modulus 50, tau 0.001) and (modulus 20, tau 0.01), apply a strain step of +0.02 at t=0 and a reversal of -0.02 at t=0.1, then compute stress at times [0, 0.001, 0.01, 0.05, 0.1, 0.2, 1.0]."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:37:16.803Z","isFirstParty":false,"canonicalSlug":"prony-series-viscoelastic-stress-superposition-halowerk-detect-e62a20b7"}