Out of Plane Models for Composite Brickwork-Like Materials

Abstract

A multiscale analysis of out of plane loaded masonry wall is here proposed. This analysis has been developed both in linear elasticity and for the determination of the ultimate strength domain. The term masonry wall has been used with reference to a periodic composite brickwork-like panel. Two textures (stack bond and running bond) are taken into account. In the case of elastic blocks connected by elastic interfaces (i.e. mortar thin joints), an asymptotic model has been performed to obtain an identification of the 3D solid with a 2D Love-Kirchhoff plate model. Furthermore in the case of infinitely rigid blocks connected by elastic interfaces, also the shear effects have been taken into account leading to the identification of a Reissner-Mindlin homogenized plate model. The bending constants of both Love-Kirchhoff and Reissner-Mindlin models are the same, while the shear constants of the Reissner-Mindlin model are identified using a simple procedure of compatible identification between a 3D discrete model and a 2D one.The multiscale approach is also used for the determination of the ultimate strength domain of a periodic brickwork made of 3D rigid and infinitely resistant blocks and mortar joints modeled as no tension Mohr-Coulomb interfaces. The panel is modeled as a homogeneous Love-Kirchhoff plate. A kinematic approach has been performed in the case of stack bond masonry. Hence, both a projection of the homogenized strength domain, when the moment M 12 is zero, and the bounds on the extreme values of M 12 have been analytically obtained.