Modeling the interfaces in masonry structures
This chapter deals with some models for interfaces in the case of masonry structures. Some experimental studies are recalled in the first part. In the second part, four interface models are presented.
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ntroduction
The aim of the chapter is to present some ideas for modeling interfaces in masonry structures. Devising means of modeling interfaces between solids in structural assemblies is obviously now of great importance in the fields of mechanical technology and civil engineering. These interfaces contribute crucially to the strength of many structures, such as optics lenses, airplanes, asphalt pavements and masonry, for example. It is therefore necessary to develop rather fine models. One of the main problems which often arises in this context is that of developing a unified theory: from the tribological point of view, the contact is often unique, in the sense that it depends on the materials, roughness, wear, etc., and especially on the mechanical system involved. The problem of cracking in pavements is obviously quite different from that of the cornering of an airplane tire. Another problem is due to the smallness of the interface in comparison with the size of the structure, as well as the possibly weak mechanical characteristics (in the case of old mortar, for example). A large number of studies have been devoted to the behavior of interfaces. Two main modeling approaches used for this purpose are phenomenological modeling and deductive modeling. In the first approach, the thickness of the interface is taken to be zero and the mechanical properties are obtained from physical considerations and experiments (see for example Fr´emond (1987); Point and Sacco (1996); Freddi and Fr´emond (2006); Raous (2011); Bonetti and Fr´emond (2011) and references therein). The ∗
The author thanks F. Fouchal, C. Pelissou, A. Rekik, R. Rizzoni and I. Titeux for their contribution in this work
M. Angelillo (Ed.), Mechanics of Masonry Structures, CISM International Centre for Mechanical Sciences, DOI 10.1007/ 978-3-7091-1774-3_5, © CISM, Udine 2014
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F. Lebon
second approach consists in focusing on the thin layers of material at the micro-mechanical level, which are usually called the interphase. The mechanical parameters of the interface model, characterized by zero thickness, are identified on the basis of the parameters of the material constituting this interphase. These boundary conditions have been extensively used to model imperfect interface properties. One of the method commonly used to model interface conditions is based on the use of asymptotic techniques (see for example Klarbring (1991); Licht and Michaille (1997); Lebon et al. (1997, 2004); Lebon and Ronel (2007); Lebon and Rizzoni (2008) and references therein), in order to include microscopic considerations in the interface model.
Figure 1. Irregular type of masonry a) b) d) Typical Lozerian structures, France c) Miramas-Le-Vieux, France.
Obviously, one of the problem which arises when modeling interfaces in masonry is due to the the irregularity of the structures (see figure 1). In this chapter, we will deal only with fairly regular structures (see figure 2). Another problem arises with the constitutive equation for the blocks because stones are quite rigid block
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