EQUIVALENT ELASTIC MODULI FOR BRICK MASONRY: A COMPARATIVE STUDY OF PERIODIC HOMOGENIZATION APPROACHES

Abstract

The mechanical characterisation of masonry remains a central challenge in structural analysis due to its heterogeneous composition of bricks and mortar joints. This study conducts a comprehensive comparative assessment of four approaches for determining the equivalent elastic properties of masonry: finite element modelling (FEM), the two-step homogenization method, the one-step Fourier-based scheme, and the interface-joint model. FEM simulations of a two-dimensional brick–mortar assemblage with varying mortar thicknesses serve as the benchmark. Analytical predictions are compared with FEM results for longitudinal and transverse Young's moduli, shear modulus, and Poisson’s ratio. The two-step method achieves excellent agreement with FEM, with errors typically below 3% across all parameters. In contrast, the one-step method consistently overestimates transverse and shear stiffnesses by up to 50-60%, while the interface approach underestimates them by 20-55%. These deviations grow with mortar thickness, reflecting the different modelling assumptions. Overall, the FEM results are bounded by the stiffer predictions of the one-step method and the more compliant interface model, while the two-step method aligns most closely with the reference values. The study concludes that the two-step scheme is most suitable for engineering design, while the interface model is valuable for nonlinear mortar analyses.