Derivation of the in-plane elastic characteristics of masonry through homogenization theory

Abstract

The homogenization theory for periodic media allows the global behaviour of masonry to be derived from the behaviour of the constitutive materials (brick and mortar). Such a procedure has been used by many authors but always in an approximate manner. In particular, the homogenization procedure has always been performed in several successive steps, head joints and bed joints being introduced successively. Moreover, masonry was considered either as a two-dimensional media under the plane stress assumption (very thin media), or as a three-dimensional bulk (very thick media), so that its finite thickness was never taken into account.The homogenization theory for periodic media is implemented here in a rigorous way, i.e. in one step and on the real geometry of masonry (finite thickness and actual bond pattern). Numerical applications are carried out and the results are compared with the predictions based on existing simplified approaches. All the above-mentioned approximations turn out to slightly affect the inplane elastic characteristics of masonry, but it is anticipated that, in the non-linear range (plasticity or damage), the same approximations might lead to erroneous results, quantitatively as well as qualitatively (value of the ultimate load and mode of failure).