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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

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Several composite materials used in engineering – such as ceramic/metal matrix composites, concrete, masonry-like/geo–materials and innovative meta–materials – have internal micro-structures characterized by a random distribution of inclusions (particles) embedded in a matrix. Their structural response is highly influenced not only by the mechanical properties of components, but also by the shape, size and position of the inclusions. In this work, we adopt a statistically-based micropolar homogenization procedure, to obtain the overall elastic properties of homogeneous micropolar continua able to naturally account for scale and skew–symmetric shear effects. Attention is paid to the sensitivity to material contrast, defined as the mismatch between classical and micropolar constitutive properties of matrix and inclusions. A statistical specifically conceived convergence criterion is adopted which allow us to identify the REV (Representative Volume Element) for any value of material contrast

Many composite materials, widely used in different engineering fields, are characterized by random distributions of the constituents. Examples range from polycrystals to concrete and masonry-like materials. In this work we propose a statistically-based scale-dependent multiscale procedure aimed at the simulation of the mechanical behavior of a two-phase\ud particle random medium and at the estimation of the elastic moduli of the energy-equivalent homogeneous\ud micropolar continuum. The key idea of the procedure is to approach the so-called Representative Volume Element (RVE) using finite-size scaling of Statistical Volume Elements (SVEs). To this end properly defined Dirichlet, Neumann, and periodic-type non-classical boundary value problems are numerically solved on the SVEs defining hierarchies of constitutive bounds.\ud The results of the performed numerical simulations point out the importance of accounting for spatial randomness as well as the additional degrees of freedom of the continuum with rigid local structure

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

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 rst 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.