Keywords: masonry, mortar-brick interface, damage modelling, asymptotical method, numerical simulation.

The aim of this work relates to the damage modelling of the mortar-brick interface for masonry walls. In this goal, we are especially interested to define the behaviour of masonry at local and global scales by studying two models:

• The first one, developed by Raous (RCCM) [1], takes into account the damage and the viscosity of the interface. This model defines the damage evolution on the interface between two deformable bodies initially bonded. It deals with the transition problem from the adhesive state to a friction state (in the tangential plane of the interface) and to a unilateral contact state (in the normal direction to the interface).
• The second derives from a bulk model introduced by Gambarotta [2] which takes into account the damage of the mortar joint. We introduce a quasi-fragile damage interface model by an asymptotical technique [3]. This modelling of the damage occurrs in the mortar-brick interface [4] and takes into account the mechanical phenomena which govern their rupture, such as the sliding and the friction at the microscopic scale and the normal and tangential damage. When the thickness of the interface tends to zero, the bulk behaviour moves to the surface behaviour. So we obtain the formulation of the GL-PL asymptotical model [4]. In this case, the damage variable (internal variable) is governed by a limit condition.

These two models are afterwards validated by comparisons with experimental results [5] which are detailed in the first section. These experimental studies are performed on materials and on masonry specimen (two different assemblies composed of two and three full-hollow bricks respectively) in order to identify the mechanical characteristics of the bricks-mortar joint and the mechanical behaviour of masonry submitted to shear test. These studies allowed us to identify phenomena that govern the rupture of the masonry at a local scale and to characterize the mechanical properties and the behaviour law to take into account in finite element computations.

To describe the response of the masonry subjected to shear test, the numerical simulations are performed by two finite element software packages: LMGC90 with the RCCM model and GYPTIS with our asymptotical model. These models are validated by considering different assemblies of masonry, composed by several full or hollow bricks (couplet, triplet, wall) bonded by the mortar joints.

1

M. Raous, L. Cangémi and M. Cocu, "A consistent model coupling adhesion friction and unilateral contact", Comput. Meth. Appl. Mechanics and Eng., 177, 383-399, 1997 . doi:10.1016/S0045-7825(98)00389-2

2

L. Gambarotta and S. Lagomarsino, "Damage models for the seismic response of brick masonry walls. Part I : The continuum model and its application", Eartquake Eng.Struct.Dyn., 26, 441-462, 1997. doi:10.1002/(SICI)1096-9845(199704)26:4<423::AID-EQE650>3.0.CO;2-#

3

E. Sanchez-Palencia and J. Sanchez-Hubert, "Introduction aux méthodes asymptotiques et à l'homogénéisation", Editions Masson, Paris, 1992.

4

C. Pelissou and F. Lebon, "Modélisation asymptotique de l'endommagement dans les interfaces quasi-fragiles", 8th Colloque National en Calcul des Structures, Giens, 21-25 May 2007, to appear.

5

F. Fouchal, "Contribution à la modélisation numérique des interfaces dans les structures maçonnées", PhD, Université de Reims, 2006.

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