In this work, a masonry prismatic structure made of alternating layers of mortar and bricks is modeled as a periodic two-phase elastic composite with one-dimensional heterogeneity along the layering direction. The prediction of its mechanical behavior (failure mainly) is important to estimate the allowable stress and stiffness used in the masonry design. At the mortar-brick interfaces, both ideally perfect contact and spring-type imperfect contact are considered. In order to model both classical and failure behaviors simultaneously, a nonlinear constitutive relation, which results from limiting the classical Hookean energy by inserting it into the so-called softening hyperelasticity energy representation, is adopted. The model is a two-point boundary value problem, which is stated by subjecting the resulting mechanical equilibrium nonlinear differential equation to the contact conditions at the interfaces and the mixed boundary conditions corresponding to uniaxial compression in the layering direction. The masonry structure exhibits separation of scales, as its size is generally much greater than the size of the mortar-brick periodicity cell, so its mechanical properties are rapidly oscillating, and also the equivalent homogeneity is guaranteed, justifying the application of the asymptotic homogenization method. Here, the effective law, that is, the constitutive relation of the equivalent homogeneous structure, is obtained via the asymptotic homogenization method. Finally, comparisons with experimental results from the literature are provided, which show qualitative agreement and that the model with imperfect contact is more accurate than the one with perfect contact.
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