Closed-form expressions for the macroscopic elastic constants of Flemish bond masonry walls

The problem of obtaining reliable closed-form expressions for the macroscopic elastic coefficients of Flemish bond brickwork according to the mechanical properties and the geometry of joints and units is dealt with. Unlike most similar existing works, which are limited to single-wythe walls, here the coexistence of headers and stretchers is taken into account, together with the presence of collar joints. Similarly to the so-called Method of Cells for fiber-reinforced composites, any Representative Volume Element (RVE) of the wall is divided into sub-cells. A piecewise-differentiable 3D strain-periodic displacement field, depending on a limited number of degrees of freedom (d.o.f.s), is formulated over the RVE. Suitable boundary conditions are prescribed at the interfaces between the sub-cells, thus reducing the number of independent d.o.f.s. The remaining d.o.f.s can be related to the macroscopic strains of the RVE. Upon integration of the microscopic stress and strain fields, the homogenized elasticity matrix can be obtained. The accuracy of the theoretical predictions is assessed by comparison with the results of Finite Element analyses of the RVE subjected to elementary macroscopic stresses, and with other benchmarks available in the literature.