Closed-form expressions for the macroscopic in-plane elastic and creep coefficients of brick masonry

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 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.