Homogenization of Periodic Masonry: Plane Stress, Generalized Plane Strain or 3d Modelling?

Through the homogenization theory for periodic media, the macroscopic behaviour of masonry may be derived from the behaviour of its constitutive materials (brick and mortar). Such a procedure has been used by many authors but always in an approximate manner. In particular, masonry has been considered either as infinitely thin (two-dimensional media under plane stress), or as infinitely thick (two-dimensional media under generalized plane strain). In order to determine the range of validity of either assumption, the homogenization theory is here implemented in a rigorous way, i.e. taking into account the finite thickness of masonry. Both brick and mortar being assumed as subjected to isotropic damage, numerical computations show that the above-mentioned assumptions have little influence on the macroscopic elastic behaviour of masonry, but may significantly affect its non-linear response (ultimate load and mode of failure).