From micro to macromodels for in plane loaded masonry walls: proposition of a multiscale approach

A multiscale model for the structural analysis of the in-plane response of masonry panels, characterized by periodic arrangement of blocks and mortar, is here presented. The model is based on two-scale use: at the microscopic level a classical Cauchy continuous is used, while at the macroscopic level a discrete macroelement model is adopted. Extensive literature exists on micro and macro approaches for masonry, but theories investigating a relationship between the two scales of analysis are still to be developed. With this aim, the authors propose a possible strategy to overcome the critical gap between two approaches. In particular, at the microlevel a homogenization procedure is used to calibrate a strut and tie model at the macrolevel. The purpose is refined modeling of a pier trough micro and macro relationship to analyze, in the perspective, complex masonry structures like historical buildings. Identification between continuous homogenized masonry panels and discrete systems of trusses is based on the equivalence of power spent in the two systems under the same boundary conditions. Hence a strut and tie macromodel in which truss inclination and truss stiffness calibration is obtained from homogenization microanalysis is proposed. In this way it is possible to take into account the sensitivity of some constitutive factors and geometric parameters of masonry, i.e., the arrangement of blocks. To verify the reliability of the procedure, some meaningful cases are analyzed.