Several tools for the prediction and the assessment of the structural behavior of masonry buildings have been developed in recent decades. Numerical tools have been favorably developed and preferred over analytical approaches, given the complex mechanical response of masonry and the irregular geometries of historic masonry buildings. In this chapter, a thorough review of numerical strategies for the analysis of masonry structures is presented. Additionally, classification of these strategies is also suggested to logically organize the extensive literature on this topic. Even though a wholly congruent categorization of all the numerical tools is essentially unrealistic given the specific aspects of each solution developed, the existing numerical strategies are subdivided into four classes: block-based models, continuum models, geometry-based models, and macroelement models. Each class is thoroughly reviewed and the open challenges in numerical modeling of masonry structures are critically examined.@en

In this paper, a damaging block-based model is proposed for the numerical analysis of the cyclic behaviour of full-scale masonry structures. Solid 3D finite elements governed by a plastic-damage constitutive law in tension and compression are used to model the blocks, while a cohesive-frictional contact-based formulation is developed to simulate their cyclic interaction. The use of tests on small-scale specimens to calibrate the mechanical properties of the numerical model is presented and discussed. The tests belong to a comprehensive experimental campaign performed on calcium silicate brick masonry. The calibrated models are used to simulate in-plane and out-of-plane cyclic tests on masonry walls made of the same material, as well as a quasi-static cyclic pushover test on a full-scale terraced masonry house. The efficiency, the potentialities and the accuracy of the model here proposed are shown and discussed. The capability of explicitly representing structural details (e.g. running bonds) and any in-plane and through-thickness texture of masonry, which appears essential to study the response of masonry structures, is guaranteed by the block-based modelling approach. A good agreement between the numerical results and the experimental outcomes is observed. This allows to validate the model in the cyclic response as well as the strategy proposed for its mechanical characterization.@en

Masonry structures, although classically suitable to withstand gravitational loads, are sensibly vulnerable if subjected to extraordinary actions such as earthquakes, exhibiting cracks even for events of moderate intensity compared to other structural typologies like as reinforced concrete or steel buildings. In the last half-century, the scientific community devoted a consistent effort to the computational analysis of masonry structures in order to develop tools for the prediction (and the assessment) of their structural behavior. Given the complexity of the mechanics of masonry, different approaches and scales of representation of the mechanical behavior of masonry, as well as different strategies of analysis, have been proposed. In this paper, a comprehensive review of the existing modeling strategies for masonry structures, as well as a novel classification of these strategies are presented. Although a fully coherent collocation of all the modeling approaches is substantially impossible due to the peculiar features of each solution proposed, this classification attempts to make some order on the wide scientific production on this field. The modeling strategies are herein classified into four main categories: block-based models, continuum models, geometry-based models, and macroelement models. Each category is comprehensively reviewed. The future challenges of computational analysis of masonry structures are also discussed.@en