Materials Composite Failure Modes From Config Dim Composite Failure Mode

The five failure channels

Fiber-reinforced composites fail through a small set of recognizable channels. Materials engineers name five canonical modes: fiber fracture, when the reinforcing fibers snap; matrix cracking, when the surrounding polymer resin splits; delamination, when layers separate; fiber pull-out, when fibers are drawn out of the matrix; and interfacial debonding, when the bond between fiber and matrix fails. These five are the standard damage channels for fiber-reinforced composites, the categories engineers use when inspecting a failed part and deciding what went wrong.

The Recognition Science framework's machine-checked library of formal theorems contains a declaration, CompositeFailureMode, that names exactly these five modes as an inductive type: a formal list of five distinct symbols. A companion theorem in the same file proves, by direct computation, that the count of these modes is five. The declaration also carries a certificate structure that packages this count as a single object. The framework's contribution is to pin the number five to a formal list, so that any later argument about composite failure modes can refer to a fixed, machine-checked enumeration rather than an informal list.

What the declaration does not do matters as much as what it does. It does not say that real composites fail only in these five ways, nor that every composite failure must be classified into one of them. It does not assert anything about the physics of crack propagation, the strength of interfaces, or the conditions under which one mode dominates another. The declaration is a definitional choice: it establishes a vocabulary of five modes and proves their count. Whether those five modes are the right ones for a given material system is an engineering question, not a theorem in the library.

The practical consequence is modest but real. When a framework argument needs to refer to composite failure modes, it can do so against a fixed, enumerated list with a machine-checked count. The list matches the standard engineering categories, so the formal object and the working vocabulary line up. What remains open is everything else about composite failure: the mechanics, the triggers, the interactions between modes. The declaration fixes the names; it does not fix the behavior.

inductive CompositeFailureMode where
  | fiberFracture
  | matrixCracking
  | delamination
  | fiberPullout
  | interfacialDebonding
  deriving DecidableEq, Repr, BEq, Fintype

theorem compositeFailureMode_count : Fintype.card CompositeFailureMode = 5 := by decide

What this page does not claim

The declaration does not assert that real composites fail only in these five ways. The declaration does not claim any physics about crack propagation, interface strength, or mode dominance conditions. The declaration does not derive the five modes from first principles; it names them as a definitional choice.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Materials/CompositeFailureModesFromConfigDim.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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