Micro, Multiscale and Macro Models for Masonry Structures
The development of adequate stress analyses for masonry structures represents an important task not only for verifying the stability of masonry constructions, as old buildings, historical town and monumental structures, but also to properly design effecti
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Introduction
The development of adequate stress analyses for masonry structures represents an important task not only for verifying the stability of masonry constructions, as old buildings, historical town and monumental structures, but also to properly design effective strengthening and repairing interventions. The analysis of masonry structures is not simple at least for two reasons: the masonry material presents a strong nonlinear behavior, so that linear elastic analyses generally cannot be considered as adequate; the structural schemes, which can be adopted for the masonry structural analyses, are more complex than the ones adopted for concrete or steel framed structures, as masonry elements require often to be modeled by two- or three-dimensional elements. As a consequence, the behavior and the analysis of masonry structures still represents one of the most important research field in civil engineering, receiving great attention from the scientific and professional community. Several numerical techniques have been developed to investigate and to predict the behavior of masonry structures. In fact, in the last decades, the scientific community has demonstrated great interest in the development of sophisticated numerical tools as an opposition to the tradition of rules-of-thumb or empirical and geometrical formulas adopted to evaluate the safety of masonry buildings. In particular, nonlinear models implemented in suitable finite elements formulations currently represent the most common advanced strategy to simulate the structural behavior of masonry structures. The main problem in the development of accurate stress analyses for masonry structures is the definition and the use of suitable material constitutive laws. M. Angelillo (Ed.), Mechanics of Masonry Structures, CISM International Centre for Mechanical Sciences, DOI 10.1007/ 978-3-7091-1774-3_6, © CISM, Udine 2014
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E. Sacco
Taking into account the heterogeneity of the masonry material, which results from the composition of blocks connected together by mortar joints, several modeling approaches have been proposed in literature. Micro-models consider the units and the mortar joints separately, characterized by different constitutive laws; thus, the structural analysis is performed considering each constituent of the masonry material. The mechanical properties that characterize the models adopted for units and mortar joints, are obtained through experimental tests conducted on the single material components (compressive test, tensile test, bending test, etc.). This approach leads to structural analyses characterized by great computational effort; in fact, in a finite element formulation framework, both the unit blocks and the mortar beds have to be discretized, obtaining a problem with a high number of nodal unknowns. Micro-macro, i.e. multiscale, models consider different constitutive laws for the units and the mortar joints; then, a homogenization procedure is performed obtaining a macro-model for masonry which is used to develop the structural analysis. A
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