The idea behind this paper is to present a numerical procedure for the analysis of masonry walls, based on the application of an asymptotic homogenization method. In this paper, a masonry wall, obtained by the regular repetition of blocks between which mortar is laid, is modelled as a periodic body in the two plane directions. The local problem is formulated for a base cell tied to the geometry of the body and in a position to generate it entirely through some law of its internal composition. Two homogenized models are formulated: the first envisages that both phases, block and mortar, behave in linear elastic fashion; the other envisages that the mortar behaves in linear elastic fashion, while the block is infinitely stiff. The two models are described theoretically and the construction of the model according to the characteristic module is numerically defined. In the case where the infinitely stiff (rigid) block is assumed, not only is the formulation of the model made extremely simple, but any numerical problems tied to great differences in the numerical values characterizing the constitutive modules of the two phases are overcome. In this regard, the domain of applicability of this model is sought both by comparing the homogenized constitutive functions, while varying the ratios of the elastic coefficients of the mortar and the block, with the rigid solution, and by analysing the structural behaviour that derives from the application, or not, of the rigid model, this being done for two sample problems. It should be underlined that the rigid-block model furnishes qualitatively sound structural answers even for very low ratios between the elastic moduli of the two phases composing the wall, and furnishes answers that are quantitatively sound as well for ratios of the order of 30:1, a realistic ratio in the case of ancient walls. The results obtained can be extended to heterogeneous materials in general, that is, to many of the innovatory materials, the composites, where the constituent phases have stiffness characteristics that are rather different and the condition of regularity of alternation of the phases is adequately plausible.
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