Homogenization methods for interface modeling in damaged masonry

Amna Rekik 1, * Frédéric Lebon 2
* Corresponding author
1 MMP - Mécanique des Matériaux et Procédés
LaMé - Laboratoire de Mécanique Gabriel Lamé
2 M&S - Matériaux et Structures
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
Abstract : The aim of the present study was to reproduce damage in masonry by combining structural analysis and homogenization methods. In the case of a masonry structure composed of bricks and mortar, a third material is assumed to exist, which is a mixture of the two materials sandwiched between the other two. This new layer has a small thickness, a low stiffness and a given damage ratio. The mechanical problem set by this masonry, which was initially a 3-D problem, is solved numerically in 2-D terms using finite element methods and modeling the three materials: brick, mortar and the interface material defined above. The properties of the third material are obtained by performing the following three steps: (i) Firstly an exact homogenization of a brick/mortar laminate defining a first homogeneous equivalent medium (HEM-1) is performed. (ii) Secondly, we assume the HEM-1 to be damaged and apply the Kachanov model to assess the global behavior of the damaged HEM-1, thus defining a second equivalent homogeneous medium denoted HEM-2. (iii) Thirdly, an asymptotic analysis is performed to model HEM-2 as an interface or a joint. The properties of this joint are deduced from those of the HEM-2 material. This interface is modeled numerically with connector finite elements. This method is applied to two cases: a triplet of full bricks and a triplet of hollow bricks both subjected to shear loading. The numerical results obtained are compared with experimental data available in the literature.
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Amna Rekik, Frédéric Lebon. Homogenization methods for interface modeling in damaged masonry. Advances in Engineering Software, Elsevier, 2012, 46 (1), pp.35-42. ⟨10.1016/j.advengsoft.2010.09.009⟩. ⟨hal-00652805⟩

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