How does the microstructure impact softwood stiffness? Hybrid multiscale homogenisation and neural network-based sensitivity analyses

Abstract This study addresses the complex hierarchical nature of softwood by establishing quantitative links between its multiscale microstructure and macroscopic stiffness. A hybrid multiscale modelling framework is developed that combines analytical continuum micromechanics with a numerical finite-element unit-cell approach, within the scope of linear elasticity. The unit cell enables a more nuanced description of the cellular architecture, including cell misalignment, corner roundness, and cell wall heterogeneity. After the model has been benchmarked against independent experimental data, a neural network-based surrogate model is trained to map the 15 morphological microscale inputs to the macroscale engineering stiffness constants. This surrogate enables instantaneous predictions of material properties and a systematic assessment of sensitivities in the structure–property relationships. A Coefficient of Prognosis analysis provides quantitative measures of the relative contribution of each morphological input parameter to each engineering constant. The Coefficient of Prognosis analyses corroborate the dominant influence of density and microfibril orientation on the macroscopic stiffness moduli, while geometric cell features, such as lumen aspect ratio and radial cell wall alignment, emerge as critical second-order parameters for the transverse Young’s moduli and the rolling shear modulus. In contrast, the transverse Poisson’s ratios are predominantly controlled by cell geometry; density is only a secondary contributor. Furthermore, the role of rays in stiffening the radial direction is quantified and ranked within a unified parameter ranking, complementing earlier work. These findings provide a better understanding of the structure–property relationships of softwood, offering a computationally efficient tool for future utilisation, development, and optimisation of wood products.