Roadmap

Shipped

• Mean-field schemes: Voigt/Reuss bounds, dilute, Mori–Tanaka, Maxwell, Ponte-Castañeda–Willis, self-consistent (Anderson + Newton), asymmetric self-consistent, differential.
• Representative volume element (RVE) assembly and effective-property pipelines mirroring the reference C++ RVE assembly.
• Concentric multi-layer sphere (LayeredSphere via AbstractLayeredInclusion): Hervé-Zaoui bulk / shear / conductivity recurrences, five interface types (perfect, spring, membrane, Kapitza, surface-conductive), volume-average and pointwise localization fields.
• Ageing linear viscoelasticity (ALV): time-domain Volterra pipeline for every scheme, structured ISO/TI/ortho fast paths, ALV cracks and the ALV layered sphere (bulk and shear recurrences).
• Exact rotation-group symmetrization (ISO / TI) of concentration tensors, preserving non-major-symmetric content (TensTI{4,T,8}), for arbitrary multi-axis orientation distributions inside every scheme kernel.
• User-defined inclusions and algorithms: a levelled, documented contract (Adding a new inclusion), the neutral AbstractCustomInclusion branch, the callback-driven CustomInclusion, the check_inclusion_interface conformance checker, and shape_trait-based inheritance of the crack algebra (a user crack needs only cod_tensor).
• Real-space Kelvin Green gradient and dipole far field for an isotropic matrix (green_gradient_iso, dipole_displacement_iso) — the boundary correction that makes a finite numerical Eshelby cell behave like an infinite medium.
• ForwardDiff sensitivities across all elastic and ALV schemes (fractions, moduli, and inclusion geometry).
• NonlinearSolve.jl backend for the self-consistent fixed point (MeanFieldHomNonlinearSolveExt): any SciML algorithm (NewtonRaphson, TrustRegion, …) can solve SelfConsistent / AsymmetricSelfConsistent, through an implicit-function-theorem lift that keeps derivative/gradient/jacobian exact and free of nested ForwardDiff.Duals regardless of algorithm.

Open

• Extended-COD crack model in conduction: resistive cracks (linear-spring analog) and conductive cracks (elastic-membrane analog), via a tensorial conduction COD.
• Multi-layer extensions: coated cylinders, anisotropic per-layer moduli, excentered spheres.
• PairwiseDistribution (Willis 1982) envelope for the PCW scheme.
• Native Anderson acceleration with memory > 1, replacing the current AndersonDefault (currently Picard with relaxation, memory = 1).
• Optional structured TensTI{4,T,8} fast path for the ALV TI schemes.
• Viscoelastic constitutive laws in the Laplace–Carson domain.
• Finite-element inclusions, behind the FEBackend contract (MeanFieldHomFerriteExt, MeanFieldHomGridapExt), both with the first-order corrected boundary condition of [6] and an isotropic reference medium: the elliptical crack in 3-D tetrahedra (3 + 3 crack declination) and the sphere with an off-centre core in axisymmetric Fourier elements (the general polarization fixed point). Open extensions — anisotropic reference medium (Pan-Chou or Barnett-Willis Green gradient); more than one inclusion, or a non-spherical envelope, in the axisymmetric cell.
• Neural-surrogate inclusions (NeuralHillInclusion, NeuralLocalizationInclusion), with the sampling, fitting and serialization machinery; the optimizer is the weak-dependency extension MeanFieldHomLuxExt, evaluation needs nothing extra. Four models ship, validated against the analytic ellipsoid. This is also the answer to "automatic differentiation through the solve", which the finite-element inclusions cannot offer: a surrogate is differentiable in the morphology. Open extensions — a surrogate trained on fe_axi_localization (gate B, the heterogeneous case the second type exists for); an anisotropic reference medium, which needs a feature set describing it.