IndisputableMonolith.Materials.FractureMechanicsFromJCost
Module applying J-cost to the strain energy over surface energy ratio to derive fracture mechanics quantities in Recognition Science. Materials researchers modeling crack propagation cite fractureCost, parisLawExponent, and FractureCert. It consists of definitions together with nonnegativity and positivity lemmas for the derived objects.
claimDefines fractureCost as the J-cost of the strain-energy to surface-energy ratio, surfaceEnergyFactor as the associated J-value, parisLawExponent, and FractureCert as the certification object for the derived fracture properties.
background
Recognition Science obtains all physics from the J-cost function satisfying the Recognition Composition Law. The imported Constants module supplies the fundamental RS time quantum τ₀ = 1 tick. The imported Cost module supplies the J-cost definition itself. This module specializes that J-cost to the ratio of strain energy to surface energy.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
Supplies the fracture-mechanics layer of the Materials domain, connecting J-cost directly to crack-growth models that sit downstream of T5 J-uniqueness. The FractureCert object provides a certified interface that later theorems can invoke for material-failure statements.
scope and limits
- Does not derive numerical fracture-toughness values for specific materials.
- Does not treat dynamic or rate-dependent fracture.
- Does not prove the Paris law from the Recognition Composition Law.
- Does not address three-dimensional crack-front geometry.
depends on (2)
declarations in this module (12)
-
def
fractureCost -
theorem
fractureCost_at_threshold -
theorem
fractureCost_nonneg -
def
surfaceEnergyFactor -
theorem
surfaceEnergyFactor_eq_Jph -
theorem
surfaceEnergyFactor_pos -
def
parisLawExponent -
theorem
parisLawExponent_eq -
theorem
parisLawExponent_pos -
structure
FractureCert -
def
cert -
theorem
cert_inhabited