Meshless meso-modeling of masonry in the computational homogenization framework

In the present study a multi-scale computational strategy for the analysis of structures made-up of masonry material is presented. The structural macroscopic behavior 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 mesoscale and representative of the heterogeneous material. The attention is focused on those materials that can be regarded as an assembly of units interfaced by adhesive/cohesive joints. Therefore, the smallest UC is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter show an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of Finite Element Method (FEM) while the Meshless Method (MM) is adopted to solve the BVP at the mesoscopic level. The material tangent stiffness matrix is evaluated at both the mesoscale and macroscale levels for any quadrature point. Macroscopic localization of plastic bands is obtained performing a spectral analysis of the tangent stiffness matrix. Localized plastic bands are embedded into the quadrature points area of the macroscopic finite elements. In order to validate the proposed CH strategy, numerical examples relative to running bond masonry specimens are developed.