This paper presents a multi-scale model for the analysis of the in-plane structural response of regular masonry. It is based on a computational periodic homogenization technique and is characterized by the adoption of the Cosserat continuum model at the macroscopic structural level, taking into account the influence of the microstructure on the global response and correctly describing the localization phenomena; at the microscopic representative volume element (RVE) level, where the nonlinear constitutive behavior, geometry, and arrangement of the masonry constituents are modeled in detail, a standard Cauchy model is employed. An isotropic nonsymmetric damage model is adopted for the bricks and mortar joints. The solution algorithm is based on a parallelization strategy and on the finite-element method. Some numerical applications on typical masonry structures are reported, showing both the global response curves and the stress and damage distributions on the RVEs.

The use of multifunctional composite materials adopting piezo-electric periodic cellular lattice structures with auxetic elastic behavior is a recent and promising solution in the design of piezoelectric sensors. In the present work, periodic anti-tetrachiral auxetic lattice structures, characterized by different geometries, are taken into account and the mechanical and piezoelectrical response are investigated. The equivalent piezoelectric properties are obtained adopting a first order computational homogenization approach, generalized to the case of electro-mechanical coupling, and various polarization directions are adopted. Two examples of in-plane and out-of-plane strain sensors are proposed as design concepts. Moreover, a piezo-elasto-dynamic dispersion analysis adopting the Floquet–Bloch decomposition is performed. The acoustic behavior of the periodic piezoelectric material with auxetic topology is studied and possible band gaps are detected.

We present a two–steps multiscale procedure suitable to describe the constitutive behavior of hierarchically structured particle composites. The complex material is investigated considering three nested scales, each one provided by a characteristic length. At the lowest scale (micro), a periodic lattice system describes in detail the mechanical response governed by interactions between rigid grains connected through elastic interfaces. At the intermediate scale (meso), the material is perceived as heterogeneous and characterized by deformable particles randomly distributed into a base matrix, either stiffer or softer. At the macroscopic scale, the material is represented as a micropolar continuum. The micro/meso transition is governed by an energy equivalence procedure, based on a generalized Cauchy–Born correspondence map between the discrete degrees of freedom and the continuum kinematic fields. The meso/macro equivalence exploits a statistically–based homogenization procedure, allowing us to estimate the equivalent micropolar elastic moduli. A numerical example illustrating the integrated multiscale procedure complements the paper