Shear Correction Factor for Porous Eco-Materials:Mechanical Characterization of a Heterogeneous Medium

Porous eco-materials—such as perlite, pumice composites, foamed concretes, and bio-derived cellular solids—are increasingly used in sustainable construction due to their low density, thermal insulation capacity, and reduced environmental impact. However, their mechanical characterization remains incomplete, particularly with respect to transverse shear behavior. Classical formulas for the shear correction factor ks, typically derived for homogeneous continua, are unsuitable for porous media exhibiting local density gradients, irregular pore morphologies, and spatially varying stiffness. This paper presents a generalized analytical–numerical methodology for evaluating the shear correction factor in a wide class of porous eco-materials. The approach is based on the strain-energy equivalence principle and uses a continuous stiffness model that reflects density-dependent elastic properties. A voxel-based microstructural representation is employed to validate the analytical predictions and to quantify the influence of heterogeneity on the shear stress distribution. Perlite is used as a representative case study, demonstrating how classical homogeneous formulas may produce errors exceeding 40%, while the proposed method provides significantly improved agreement with numerical benchmarks. The framework is applicable to a broad range of porous materials and offers a consistent basis for predicting transverse shear stiffness in lightweight fillers, thermal barriers, and fire-protective building components where shear deformation is critical.