A comparison between a 3D discrete model and two homogenised plate models for periodic elastic brickwork

Abstract

A Love–Kirchhoff plate model for in plane and out of plane actions of linear elastic periodic brickwork has been already proposed by Cecchi and Sab [Eur. J. Mech. A.-Solids, 21 (2002a) 249]. In this work, the case of infinitely rigid blocks connected by elastic interfaces (the mortar thin joints) is considered. A numerical discrete 3D model is proposed and compared to the homogenised Love–Kirchhoff plate model. In order to enhance this plate model, shear effects are taken into account leading to the identification of a new Reissner–Mindlin homogenised 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 the 3D discrete model and the 2D one. A numerical evaluation of the scatter between the 3D discrete model and both Love–Kirchhoff and Reissner–Mindlin models is performed on a test case for various values of the ratio between the thickness of the wall and its overall size, and for various values of the parameter that characterises the heterogeneity of the wall. It is shown that both plate models coincide asymptotically with the discrete 3D model, the convergence being better for the Reissner–Mindlin model.