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International audience; Composite adhesive bonded joints are widely used in various industrial and technological applications, including aerospace, electronics, biomedical, automotive, ship building and construction. In this paper, the attention is focused on layered structures consisting of two adherent beams bonded together by an adhesive layer. For such structures, a modeling approach based on the classical Timoshenko beam theory in conjunction with an adhesive model of imperfect interface is introduced. This imperfect interface approach, recently proposed by the authors in the contest of linear elastic adhesive and adherents materials, small strains and small displacements theory, models the asymptotic behavior of a thin interphase at higher orders for both the cases of hard and soft interface materials in a unified approach (Rizzoni et al., 2014). Accounting for higher order terms of the asymptotic expansions in the adhesive, the proposed approach generalizes simpler models based on the classical spring-type interface law or on the case of perfect contact between the adherent layers.The proposed methodology is used to evaluate stresses in two adhesive bonded joint configurations subjected to bending moment and transverse shear loading. Numerical simulations are produced and the results show good agreements with those obtained through finite element analysis.

The paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. The macromechanical equivalent Cosserat medium, which naturally accounts for the absolute size of the constituents, is derived by a rational homogenization procedure based on the Transformation Field Analysis. The micromechanical analysis is developed considering a Cauchy model for masonry components. In particular, a linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is adopted for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Some numerical applications are performed on a Representative Volume Element characterized by a selected commonly used texture, without per- forming at this stage structural analyses. A comparison between the results obtained adopting the proposed procedure and a nonlinear micromechanical Finite Element Analysis is presented. Moreover, the substantial differences in the nonlinear behavior of the homogenized Cosserat material model with respect to the classical Cauchy one, are illustrated.

In this paper, several variational principles for the evaluation of the overall properties of composite materials with periodic microstructure are introduced. The two classical homogenization problems corresponding to assigned average strain or assigned average stress are considered. The periodicity of the variables governing the problem is enforced either by considering special representations (i.e. Fourier series) of the periodic part of the displacement and stress fields or by adopting appropriate boundary conditions on the unit cell. In particular, the boundary conditions ensuring the periodicity of the governing variable are introduced in the functionals by using Lagrangian multipliers. Once the variational principles are introduced, the Fourier series technique and the finite element method are adopted to obtain rational approximation procedures. Finally, numerical applications are carried out in order to assess the performances of the proposed methods in the computation of estimates or bounds on the overall elastic properties of a composite material, and in the determination of the displacement and stress distribution in the unit cell.