In the present study a multi-scale computational strategy for the analysis of masonry structures is presented. The structural macroscopic behaviour is obtained making use of the Computational Homogenization (CH) technique based on the solution of the boundary value problem (BVP) of a detailed Unit Cell (UC) chosen at the meso-scale and representative of the heterogeneous material. The smallest UC is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of finite element method while the Meshless Method (MM) is adopted to solve the BVP at the mesoscopic level. The work focuses on the BVP solution. The consistent tangent stiffness matrix at a macroscopic quadrature point is evaluated on the base of BVP results for the UC together with a localisation procedure. Validation of the MM procedure at the meso-scale level is demonstrated by numerical examples that show the results of the BVP for the simple cases of normal and shear loading of the UC.

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