[petlenz]

Closes #119. Part of the uvwmaterial port (#94); stacked on #137.

Of uvwmaterial's propagation laws, linear and damage_exponential2 already exist (linear_damage_law, exponential_damage_law). Added, all reading kappa of a yield_source and producing damage, d_damage:

• power_damage_law: d = K (κ − κ₀)ᵐ, capped at d_max (0.999).
• saturation_damage_law: d = K (1 − e^(−m(κ − κ₀))) (exponential_law of the original).
• peerlings_damage_law: d = 1 − κ₀/κ (1 − α + α e^(β(κ₀ − κ))), capped at d_max (damage_exponential3, without its hard-coded 0.99 factor). damage_exponential1 (1 − e^(β(κ₀ − κ))) is not carried over; it is Peerlings' law without the κ₀/κ factor and was unused.

Tests (test_damage_laws, 6): each law's value and derivative against the formula and against finite differences of the real chain (strain → von Mises state → threshold yield → law), the threshold, the cap and the saturation limit; creation from JSON.

Report docs/materials/isotropic_damage/report.json: the full damage chain with the exponential law as the point and all laws recorded; checks: σ = (1 − d) σ_elastic, κ monotone, no damage below the threshold, every law monotone in κ, Peerlings and saturation against their formulas, and the tangent check. The report point now takes stress_property / tangent_property (damaged_stress, damaged_tangent).

What the report found: the consistent tangent of isotropic_damage is correct (2e-11 against central differences on damaging and elastic steps; the existing test only verified elastic steps), but a central difference straddles the kink wherever the strain state lies exactly on the damage surface — the first threshold step and the load reversals of a symmetric cycle. The tangent check now skips those steps (|ε_eq − κₙ| > 1e-9). To make that possible an include's named entry (check, case, figure) can be replaced by a local entry of the same name instead of being appended.

Review follow-up: the plumbing lives once in the CRTP detail::scalar_damage_law<Derived> — κ from yield_source, kappa_0, d_max (default 0.999, validated in (0, 1]), the threshold, the cap with a zero slope, the two outputs; a law is its parameters(), its own checks and evaluate(κ) → {d, dd}. The two older laws (exponential_damage_law, linear_damage_law) sit on the same base, so the cap is d_max everywhere (their 0.999 was hard-coded) and the derivative is zero at it. Parameters are validated: power K > 0, m > 0; saturation 0 < K ≤ 1 (K is the final damage — K > 1 gave negative stiffness), m > 0; Peerlings κ₀ > 0, 0 ≤ α ≤ 1, β ≥ 0; exponential κ₀ > 0, β ≥ 0; linear κ_f ≥ κ₀ (equal stays legal: full damage right past the threshold, as the existing test pins). report_spec.h reads name with at(); the report's tangent check excludes loading steps through the recorded yield::is_yielding (report columns now read int flags) and the on-surface steps — threshold step and path reversals, where the central-difference stencil straddles the C⁰ kink — through eq ≠ κ. New tests: every rejection, the cap's zero slope, the older laws on the shared cap.

945/945 tests pass (GCC 14, reports on).

JSON input

New material types: power_damage_law, saturation_damage_law, peerlings_damage_law. A json_model document that loads (the FromJson test of the PR):

{"materials": [
  {"type": "external_strain_source", "name": "strain"},
  {"type": "von_mises_state_function", "name": "state", "strain_source": "strain"},
  {"type": "strain_threshold_yield", "name": "yield", "state_source": "state", "kappa_critical": 0.002},
  {"type": "power_damage_law", "name": "pow", "yield_source": "yield", "K": 200.0, "m": 1.5, "kappa_0": 0.002},
  {"type": "saturation_damage_law", "name": "sat", "yield_source": "yield", "K": 0.9, "m": 300.0, "kappa_0": 0.002},
  {"type": "peerlings_damage_law", "name": "peer", "yield_source": "yield", "kappa_0": 0.002, "alpha": 0.95, "beta": 200.0}
]}

Each law consumes kappa of its yield_source and produces damage, d_damage for isotropic_damage ("damage_source": "pow"). Power: D = K (κ − κ₀)ᵐ; saturation: D = K (1 − exp(−m (κ − κ₀))); Peerlings: D = 1 − κ₀/κ (1 − α + α exp(−β (κ − κ₀))); d_max caps (default 0.999).

[petlenz]

Review findings (design, tmech expressions instead of component loops, modern C++, comments, tests, correctness). Severity: must = wrong result, hang, build break or unreachable feature; should = design, duplication, accuracy; nit = style.

damage laws — needs changes

• [must] saturation_damage_law.h:113-115 no cap, no check: K > 1 → D > 1 → negative stiffness. Validate 0 < K ≤ 1 or apply d_max.
• [should] plumbing copied three times (plus twice in existing laws) → CRTP scalar_damage_law<Derived> owning κ, κ₀, d_max, threshold/cap and compute(); Derived::evaluate(x) → {D, dD}.
• [should] no parameter validation (power m > 0, Peerlings κ₀ > 0, 0 ≤ α ≤ 1, β ≥ 0, saturation m > 0).
• [nit] 170-char comment; four members per declarator; report_spec.h:21 e["name"] on const json; test comment wrong about von Mises strain; d_damage == 0 at cap untested. Report where exclusion is principled (C⁰ kinks), but a recorded is_yielding predicate would be more robust than a 1e-9 float equality.