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Approximate expressions for the macroscopic in-plane elastic and creep coefficients of brick masonry with a regular pattern are derived in closed form, using a homogenization approach for periodic media. A microscopic displacement field fulfilling suitable periodicity boundary conditions, and depending on a\ud limited number of degrees of freedom, is formulated over any masonry Representative Volume Element (RVE). According to this field, closed-form expressions for the macroscopic elastic constants are obtained at various degrees of approximation, either using a Method of Cells-type approach, or minimizing the potential energy of the RVE subjected to any given macroscopic stress. Eventually, the results are extended to the description of the global creep behavior of brickwork under service loads, assuming the creep laws of units and mortar to be expressed by Prony series. Using the FE solution as a benchmark, the proposed approach is found to accurately match both the macroscopic constitutive law in linear elasticity and the time evolution of the macroscopic strains of brickwork under sustained macroscopic stress

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SUMMARYA theoretical model is proposed to describe the evolution of damage in brittle materials, such as concrete and masonry, subjected to increasing or sustained stresses of relatively high intensity. The model is based on the introduction of suitable damage variables in a rheological model. In this way, it is possible to describe the material behaviour under stresses either increasing or constant in time. The capabilities of the model in describing the mechanical response of material elements subjected to different stress histories are illustrated. Some correlations with experimental data from tests performed on masonry and concrete specimens are presented, to assess the reliability of the theoretical predictions. The results of some numerical applications to non-proportional stress paths are also illustrated. Finally, the limitations of the proposal are discussed and possible further improvements are envisaged.

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