A Bound-Respecting and Interpretable Machine-Learning Framework for the Micromechanical Homogenisation and Inverse Design of Aligned-Spheroid Two-Phase Composites

Analytical micromechanical schemes predict the effective stiffness of two-phase composites accurately and cheaply, yet they are opaque to the influence of individual descriptors, are not analytically invertible for target-driven design, and grow onerous as the fine-scale solver in multiscale analysis. This study develops a rigorously validated, physically bounded and interpretable machine-learning framework for composites reinforced by aligned spheroidal inclusions. An Eshelby–Mori–Tanaka engine, in full fourth-order tensor form, is validated against eight independent closed-form limits, reproducing the spherical and cylindrical Eshelby tensors and the exact scalar Mori–Tanaka moduli to machine precision and coinciding with the Hashin–Shtrikman lower bound. A dimensionless five-parameter design space, with every bound anchored to real material systems, is sampled by a Latin-hypercube design under a bound-admissibility screen, and the responses are perturbed with a small, disclosed level of noise emulating finite-RVE scatter. Among four surrogates, Gaussian process regression is the champion (mean test R2 ≈ 0.994) and reaches it from roughly an order of magnitude fewer samples than the ensembles. A Shapley analysis attributes axial stiffness chiefly to aspect ratio and transverse response to volume fraction, and reveals the near-irrelevance of the inclusion Poisson ratio within the sampled ranges. A genetic-algorithm inverse design, refined and verified against the true engine, attains the feasible property targets to numerical tolerance.