Pith. sign in
module module moderate

IndisputableMonolith.Materials.FatigueThresholdFromJCost

show as:
view Lean formalization →

This module defines the per-cycle fatigue J-cost on the stress ratio and related endurance concepts in the Recognition Science materials domain. Materials modelers cite it when linking J-cost to fatigue thresholds and infinite-life regimes. The module consists entirely of definitions and supporting properties with no complex proofs.

claimfatigueCost(r) denotes the per-cycle J-cost for stress ratio r; EnduranceThreshold and IsFatigueFailing mark the boundary between finite-life and infinite-life regimes under the J-cost formalism.

background

Recognition Science derives material behavior from the J-cost function satisfying the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The imported Cost module supplies the base J-cost while Constants fixes the time quantum τ₀ = 1 tick. This module applies those primitives to fatigue by introducing fatigueCost together with the predicates IsFatigueFailing and IsInfiniteLife and the EnduranceThreshold band.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the J-cost link required for fatigue analysis inside the materials domain. It directly populates the sibling declarations EnduranceThreshold, IsFatigueFailing, regimes_exclusive, endurance_threshold_band and FatigueThresholdCert that certify endurance limits.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (12)