[petlenz]

Closes #95, closes #103. First PR of the uvwmaterial port (#94); stacked on #93 because it uses core/tensor_identities.h from there and the composites that follow ship reports.

core/elastic_constants.h: bulk_modulus(E, nu), shear_modulus, youngs_modulus(K, G), poisson_ratio, lame_lambda, isotropic_stiffness<T, Dim>(K, G) (the K I⊗I form of plasticity_utils), rotate for rank 2 (R A Rᵀ) and rank 4 (one tmech expression through otimesu(R, R)), rotation(axis, angle) (Rodrigues, with [axis]ₓ = −(ε · axis) from tmech's permutation tensor) and rotation_to(direction) (e₁ onto a direction; the parallel and antiparallel branches are taken at 8 ε of the scalar type). All pure helpers are [[nodiscard]].

Elliptic integrals: the Carlson port of the first version is gone; the Eshelby tensors (#128) and the orientation average (#132) call Boost.Math's ellint_rd directly, and #128 adds that dependency where it is first used.

Tests (test_elastic_constants, 7): round trips, invariance of an isotropic tensor, a fibre tensor moving from e₁ to e₂, axis–angle against the explicit z rotation, orthogonality and rotation_to typed over float and double for the parallel, antiparallel and generic directions.

736/736 tests pass (GCC 14, reports on).

[petlenz]

Rebased: the first commit had dropped the five test targets of the base branch (drivers, report, core utilities) from tests/CMakeLists.txt while resolving a conflict; they are restored in a second commit, and every PR of the stack is rebased on it. Test counts in the PR texts below #138 are from before the restore; the top of the stack runs 885 tests.

[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.

elliptic integrals + elastic constants — needs changes

• [must] core/elliptic_integrals.h:106 T{0.75} * c1 * ed → T{0.75} * c3 * ed (Carlson/NR3 C5 = 0.75·C3 = 9/88). Effect: 4th- instead of 6th-order truncation, ≈4e-12 worst case; tests pass because Carlson's table points exit early.
• [must] rf/rc/rd/rj hang on inf or near-overflow input (rf(inf,1,1), rf(1e308,1e308,1) verified); orientation.h feeds exp() into rd. Add isfinite + sum bound to require.
• [must] core/elastic_constants.h:66,69 c > 1 - T{1e-14} is c > 1 for float → rotation_to<float>(±e1) all-NaN. Use 8·eps<T>; std::numbers::pi_v<T>.
• [should] rotation matrix built component-wise → cos·I − sin·(levi_civita<T,3>() * axis) + (1−cos)·otimes(axis,axis) (verified to 0.0).
• [should] DRY: umat::rotate (8-deep loop, comment claims no single-call spelling) duplicates the new one-liner; plasticity_utils.h:38 builds isotropic stiffness by hand.
• [should] rotate/rotation/rotation_to belong in core/rotation.h, not elastic_constants.h; template <typename T> void require with unused T → inline; [[nodiscard]] missing; two Dim=2 isotropic-stiffness conventions (K I⊗I vs 3K Pvol) coexist.
• [nit] NR3 double tolerances for all T; magic 166666.67 in tests; no float instantiation, no rotation_to(−e1), no complete_k(1).

[petlenz]

Review findings addressed in 17946ba:

• must, R_J coefficient / must, hangs on inf: the Carlson port is removed altogether; Boost.Math (ellint_rd) takes over where the integrals are used (Eshelby tensors as materials: sphere, cylinder, spheroid and ellipsoid nodes #128, Orientation averaging with the angular central Gaussian distribution #132). No numsim code to get wrong.
• must, rotation_to<float>: tolerance is 8 * numeric_limits<T>::epsilon(); with the old T{1e-14} a float instantiation did not even compile under -Wconversion -Werror. Typed test over float and double for ±e₁ and generic directions.
• should, rotation matrix by components: cos·I − sin·(levi_civita<T,3>() * axis) + (1 − cos)·axis⊗axis.
• should, [[nodiscard]]: on every pure helper; std::numbers::pi_v<T> for the half turn.

Left for a follow-up: umat::rotate and plasticity_utils reusing these helpers (files of the base branch), and a separate core/rotation.h.