This paper presents a multi-scale model for the analysis of the in-plane structural response of regular masonry. It is based on a computational periodic homogenization technique and is characterized by the adoption of the Cosserat continuum model at the macroscopic structural level, taking into account the influence of the microstructure on the global response and correctly describing the localization phenomena; at the microscopic representative volume element (RVE) level, where the nonlinear constitutive behavior, geometry, and arrangement of the masonry constituents are modeled in detail, a standard Cauchy model is employed. An isotropic nonsymmetric damage model is adopted for the bricks and mortar joints. The solution algorithm is based on a parallelization strategy and on the finite-element method. Some numerical applications on typical masonry structures are reported, showing both the global response curves and the stress and damage distributions on the RVEs

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SUMMARYA new beam finite element is presented, with a generalized section constitutive law based on damage mechanics and plasticity, to analyse the cyclic structural response of plane frames. Both displacement-based and force-based (FB) approaches are used and compared, to demonstrate the significant advantages of the FB formulation in the presence of material non-linearity. In order to overcome the analytical problems and the pathological mesh dependency of the numerical response in the presence of strain-softening post-peak behaviour, a classical non-local regularization procedure is adopted first, based on the integral definition of the associated variable governing the damaging evolution process. Subsequently, for the FB element a new simple regularization technique is proposed based on a selected integration procedure along the element length, which predefines the location of the Gauss points in the beam region, where the localization phenomena take place. As for the other computational aspects, an iterative element state determination is adopted for the FB formulation and a local predictor-corrector algorithm is used to solve the incremental evolution problems of the damage and plastic internal variables. Finally, some examples are shown on simple beams and frames, subjected to monotonically increasing and cyclic loading conditions.

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