A Multi-Level Interface Model for Damaged Masonry

The aim of this paper is to propose a new micro-mechanical model in the context of the deductive approach used to derive interface models. This model, based on a previous study introduced previously by A. Rekik and F. Lebon [31, 32], is used to reproduce the damage in masonry by combining structural analysis and homogenization methods. The focal point of this method is to assume the existence of a third material, called interphase, which is a mixture of the two principal constituents of masonry, brick and mortar, and that is the interface between them. This new element presents a low thickness, a low stiffness and a given damage ratio. The mechanical problem of masonry, initially a 3D problem, is solved numerically as a 2D problem using finite element methods. The properties of the interface brick-mortar material are obtained using three essentials steps. First of all, an exact homogenization of a laminates is used to define a first homogeneous equivalent medium named HEM-1. After, the assumption of damaged material is taken into account by using the general framework given by M. Kachanov [13, 24, 35, 36] to evaluate the global behaviour of the damaged HEM-1 defining thus a second equivalent homogeneous medium noted HEM-2. The last step consists in using an asymptotic analysis technique which 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 as proposed in former papers [2, 15, 17, 34]. Particularly, through the second homogenization are taken into account the variability of microcracks oriented family and simultaneously the opening-closure effects (unilateral behaviour). Numerically this interface is modelled with connector finite elements. Numerical results are compared to experimental ones available in the literature [7]