A Method of Cells-type approach to estimate the macroscopic elastic and creep coefficients of brick masonry

The problem of obtaining reliable analytical expressions for the macroscopic elastic and creep coefficients of brick masonry with a regular pattern according to the mechanical properties of the individual constituents (e.g. mortar and units) is dealt with. Starting from the microscopic displacement field estimated over any Representative Volume Element by a refined finite element model with suitable periodicity boundary conditions, a kinematic solution is proposed that depends on a limited number of degrees of freedom and matches the numerical predictions with fair accuracy. According to this field, the macroscopic constitutive law is derived in closed form at various degrees of approximation. A minimization of the potential energy of the RVE under any macroscopic stress respect to all the model d.o.f.s is shown to give values for the macroscopic elastic constants in excellent agreement with the FE results taken as a benchmark. Eventually, the results are extended to the description of the global creep behaviour of brickwork under service loads, assuming both units and mortar to obey Zener rheological model. Using the concept of effective modulus, the proposed approach is found to accurately predict also the macroscopic delayed moduli of brickwork given by the FE model.