Coupled Discrete/Continuous Methodology for in Plane Loaded Elastic Masonry

We study a 2D model which consists of a regular lattice of square rigid grains interacting by their elastic interfaces. Two models have been developed, a discrete one and a continuous one. In the discrete model, the grains which form the lattice are modeled as rigid bodies connected by elastic interfaces (elastic thin joints). In other words, the lattice is seen as a “skeleton” in which the interactions between the rigid grains are represented by forces and moments which depend on their relative displacements and rotations. The continuous model is based on the homogenization of the discrete model (Cecchi and Sab [2]). Considering the case of singularities within the lattice (a crack for example), we will develop a coupling model which uses the discrete model in singular zones (zones where the discrete model cannot be homogenized), and the continuous model elsewhere.