Maria Laura De Bellis

Auxetic behavior and acoustic properties of microstructured piezoelectric strain sensors

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.

A Statistically-Based Homogenization Approach for Particle Random Composites as Micropolar Continua

This article is focused on the identification of the size of the representative volume element (RVE) and the estimation of the relevant effective elastic moduli for particulate random composites modeled as micropolar continua. To this aim, a statistically-based scale-dependent multiscale procedure is adopted, resorting to a homogenization approach consistent with a generalized Hill’s type macrohomogeneity condition. At the fine level the material has two phases (inclusions/matrix). Two different cases of inclusions, either stiffer or softer than the matrix, are considered. By increasing the scale factor, between the size of intermediate control volume elements (Statistical Volume Elements, SVEs) and the inclusions size, series of boundary value problems are numerically solved and hierarchies of macroscopic elastic moduli are derived. The constitutive relations obtained are grossly isotropic and are represented in terms of classical bulk, shear and micropolar bending moduli. The “finite size scaling” of these relevant elastic moduli for the two different material contrasts (ratio of inclusion to matrix moduli) is reported. It is shown that regardless the scaling behavior, which depends on the material phase contrast, the RVE size is statistically detected. The results of the performed numerical simulations also highlight the importance of taking into account the spatial randomness of inclusions which intersect the SVEs boundary.

An Enriched 2D Multi-Scale Model Based on a Cosserat Continuum for the Analysis of Regular Masonry

A multi-scale nonlinear homogenization procedure is presented for the analysis of the in-plane structural response of masonry panels characterized by a regular texture. A Cosserat continuum model is adopted at the macroscopic level, while a classical Cauchy model is employed at the microscopic scale; proper bridging conditions are stated to connect the two scales. The constitutive behaviour of bricks and mortar at the microscopic level is based on a scalar damage model, non symmetric in tension and compression. As for the regularization of the strain softening response, the standard fracture energy method is used at micro-level, while at the macro-level the inner capabilities of Cosserat continuum are exploited. A numerical example is presented and a comparison with an experimental test is performed.