A non-linear discrete homogenized strategy is used to reproduce out-of-plane two-way bending shake table tests on full-scale unreinforced masonry walls. The numerical strategy represents unreinforced masonry walls as an assemblage of rigid quadrilateral plates connected through non-linear interfaces represented. The material response laws for these non-linear interfaces are derived from a homogenization procedure performed at the meso-scale by a finite-element plate model. This discrete model can simulate masonry orthotropy, full softening behaviour and failure. Bending and torsional deformation modes are represented. The performance of the numerical models in describing the response of the experimentally tested full-scale specimens is presented. The numerical strategy is then used to study the behaviour of unreinforced masonry walls in configurations hitherto untested. Such numerical results are then compared to state-of-the-art analytical approaches. Potential avenues of improvement for the implemented analytical methods are also highlighted.@en

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

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

The paper deals with the analysis of FRCM (Fiber Reinforced Cementitious Matrix) reinforced masonry panels in simple bending by means of a two-step homogenization approach. In the first step, homogenization is performed on unreinforced masonry through a straightforward procedure already validated for in-plane loaded FRCM reinforced panels, where the elementary cell is discretized by means of 24 CST elastic elements (bricks) and joints are reduced to interfaces with holonomic softening behavior. Out-of-plane homogenized quantities (moment-curvature relationships) are then obtained by simple on-thickness integration. At a structural level (step two), masonry is modeled with rigid elements and homogenized torsional and bending springs, whereas FRCM by two noded trusses with equivalent mechanical properties evaluated on the base of experimental data available. The implementation is handled within the commercial FE software Abaqus. As a matter of fact, the Concrete Damage Plasticity Model (CDP) already implemented into the code allows taking into account the progressive change of stiffness of brittle supports when subjected to alternate cracking-crushing mechanisms, as well as to properly deal with the cyclic behavior. The validation of the procedure is conducted against a series of full scale masonry walls tested by Nanni and co-workers at the University of Miami. A tri-dimensional heterogeneous micro-modeling technique is also used for both unreinforced and FRCM strengthened panels to further validate the homogenization model proposed. The discretization adopted is adjusted in order to allow the presence of two eight-noded FEs along the mortar joint thickness. FRCM is modeled by means of truss elements whose mechanical properties are calibrated to reproduce the behavior of the textile net embedded into the cementitious matrix. The elastic and inelastic mechanical parameters of all the materials involved into the numerical analyses have been calibrated in agreement with laboratory tests, when available. Pros and cons of the two numerical strategies are discussed mostly with respect to the accuracy of the outcomes in terms of global behavior of the panels and damage mechanisms, as well as with respect to the computational effort required by the two approaches to complete the analyses.

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