Out of plane model for heterogeneous periodic materials: the case of masonry

The aim of this paper is to propose a 3D model to study masonry walls subject to in plane and out of plane actions through a rigorous homogenization procedure. 2D rigorous models in several perturbative parameters have been already developed – by Cecchi–Di Marco (European J. Mech. A Solids 19 (2000) 535–546), Cecchi–Rizzi (Internat. J. Solids Structures 38/1 (2001) 29–36) and Cecchi–Sab (European J. Mech. A Solids 21 (2002) 249–268) – so as to study the behaviour of masonry walls subject to actions parallel to the middle plane. By comparison with previous models, in this paper the study of masonry takes into account the formulation of a 3D model where masonry is assumed periodic in the middle plane, i.e. in the orthogonal directions to the thickness. The size of the thickness is comparable with the one of the period. The asymptotic model that has been developed allows the identification of the 3D solid with a 2D Love–Kirchoff plate, in which the anisotropy is connected with the arrangement of blocks. The obtained results give the values of homogenized elastic plate constants (Caillerie, Math. Meth. Appl. Sci. 6 (1984) 159–191).