Multiscale Homogenization Analysis of the Effective Elastic Properties of Masonry Structures

The asymptotic homogenization method of differential equations with rapidly oscillating coefficients is used to evaluate the effective elastic stiffness of masonry structures. The equilibrium equations as well as the constitutive relationships at different scales are determined from the asymptotic expansion of the displacement field. The formulation is developed for a general three-dimensional problem. It is then particularized for a simple one-dimensional (1D) model that is applicable to available experimental results of a masonry prism. Key concepts of the method such as periodicity of the fields are highlighted in this 1D problem. A multiscale finite-element model was developed for a two-dimensional unit cell to solve the canonical cell equation that arises in homogenization, which provides numerical solution of the effective elastic moduli. In particular, the numerical study focuses on the in-plane action of the masonry panels that are used as the experimental specimens in laboratory tests. Comparing experimental and analytical (from classical computational homogenization) results, the multiscale homogenization model for linear elastic masonry structures is validated. The main advantage of this model is its straightforward extension for the study of the dynamic homogenization of masonry structures. Furthermore, the developed model is suitable for a comprehensive study of the stress localization in masonry structures for the determination of its strength-based limiting properties.