[petlenz]

Closes #106. Part of the uvwmaterial port (#94); stacked on #132.

short_fibre_composite: Mori–Tanaka stiffness of fibres in an isotropic matrix averaged over the fibre orientation distribution, as a tangent producer over phase nodes (#130). The orientation enters as the second-order tensor orientation [a11, a22, a33, a12, a13, a23]; the ACG distribution with that second moment (#132) gives the quadrature directions, Lebedev precision (default 23) the weights. Two averagings as in uvwmaterial: concentration (the orientation average of the dilute concentration inside Mori–Tanaka) and stiffness (the average of the unidirectional Mori–Tanaka stiffness).

Matrix and fibre are phases (matrix, fibre: produced tangent and fraction; the fibre's eshelby is an eshelby_spheroid or eshelby_cylinder along x₁ consuming the matrix Poisson's ratio — #128, #130). The composite consumes their properties and nothing else. Everything is formed once in the fibre frame — the dilute concentration T₁ = (I + S₁ : Cₘ⁻¹ : (C_f − Cₘ))⁻¹, the unidirectional stiffness and (C_f − Cₘ) : T₁ — and rotated onto the directions with otimesu(R, R) fixed per direction at construction. One rank-4 inverse per update instead of one per direction, and a transversely isotropic fibre tangent given in the fibre frame is rotated with the rest. Outputs tangent, concentration_matrix, concentration_fibre; the stress is a linear_stress on the tangent. The two fractions must sum to one.

Tests (test_short_fibre_composite, 6): aligned fibres equal the unidirectional mean_field_tangent to 1e-12 for both averagings (tangent and concentrations); the isotropic orientation gives an isotropic tangent; Σ c A = I and the linear_stress gives C : ε; stiffness ordering aligned > mostly aligned > random along x₁; a wrong orientation trace, averaging and Lebedev degree are rejected; JSON.

Report docs/materials/short_fibre_composite/report.json: aligned, injection-moulded (0.7, 0.25, 0.05) and random orientation on one point, the aligned case checked against the unidirectional composite.

889/889 tests pass (GCC 14, reports on).

JSON input

New material type: short_fibre_composite. A json_model document that loads (the FromJson test of the PR):

{"materials": [
  {"type": "external_strain_source", "name": "strain"},
  {"type": "constant_scalar", "name": "Km", "value": 3.0},  {"type": "constant_scalar", "name": "Gm", "value": 1.0},
  {"type": "constant_scalar", "name": "Kf", "value": 60.0}, {"type": "constant_scalar", "name": "Gf", "value": 30.0},
  {"type": "isotropic_tangent", "name": "Cm", "K_source": "Km", "G_source": "Gm"},
  {"type": "isotropic_tangent", "name": "Cf", "K_source": "Kf", "G_source": "Gf"},
  {"type": "isotropic_moduli", "name": "moduli", "tangent_source": "Cm"},
  {"type": "eshelby_spheroid", "name": "shape", "nu_source": "moduli", "nu_property": "poisson_ratio", "aspect_ratio": 10.0},
  {"type": "constant_scalar", "name": "c", "value": 0.2},
  {"type": "constant_scalar", "name": "cm", "value": 0.8},
  {"type": "phase", "name": "fibres", "tangent_source": "Cf", "eshelby_source": "shape", "fraction_source": "c"},
  {"type": "phase", "name": "matrix", "tangent_source": "Cm", "fraction_source": "cm"},
  {"type": "short_fibre_composite", "name": "sf", "matrix": "matrix", "fibre": "fibres",
   "orientation": [0.8, 0.1, 0.1, 0, 0, 0], "averaging": "concentration", "precision": 23},
  {"type": "linear_stress", "name": "composite", "tangent_source": "sf", "strain_source": "strain"}
]}

The fibre's Eshelby node lies along x₁ (the fibre frame; a transversely isotropic fibre tangent is given in that frame); orientation = [a11, a22, a33, a12, a13, a23] of the second-order orientation tensor; averaging concentration | stiffness; precision a Lebedev degree (3 … 23). Outputs tangent, concentration_matrix, concentration_fibre.

[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.

short_fibre_composite — needs changes

• [must] only the Eshelby tensor is rotated; a transversely isotropic Cf is used unrotated and nothing checks it. Compute T1 = inv(Is + S1:M) once in the fibre frame and rotate(T1, R_q) per node (also replaces 26–194 inverses per update by one and makes averaging: stiffness literally ⟨C_UD⟩). Add an anisotropic-fibre test.
• [should] default precision 15 → 1–2 % tangent error (see Orientation averaging with the angular central Gaussian distribution #132).
• [should] cache keyed on ν only, but m_aspect_ratio is a parameter reference → stale m_S after set_parameter.
• [should] / cm with volume_fraction ≤ 1 accepted → inf at c = 1.
• [nit] views::zip(m_nodes, m_S); redundant (void)lebedev::rule; negative precision cast in message.

[petlenz]

Rebased on the Eshelby-node refactor (#128): the fibre shape is an eshelby_spheroid/_cylinder node along x₁ named by eshelby; aspect_ratio left the composite. Of the review findings this covers:

• must, anisotropic fibre used unrotated: T₁, the unidirectional stiffness and (C_f − Cₘ) : T₁ are formed in the fibre frame and rotated per direction; a transversely isotropic C_f in that frame is rotated with them. One inverse per update (was one per direction).
• should, default precision 15: now 23.
• should, cache keyed on ν while aspect_ratio can change: the cache is gone — the Eshelby node owns the tensor and the rotations are fixed per direction.
• should, c = 1 → division by zero: the fraction must lie in [0, 1).
• should, poisson_of duplicate: gone, the node checks its matrix.

Not added: an anisotropic-fibre test — the repo has no transversely isotropic linear material to feed it yet.

[petlenz]

Producer/consumer pass: the fibre is one inclusion node (inclusion parameter) — material, produced fraction and Eshelby node along x₁ — instead of fibre/volume_fraction/eshelby spelled out again on the composite; the fraction bound (< 1) is checked per update on the produced value.