Cauchy and Cosserat equivalent continua for the multiscale analysis of periodic masonry walls

The present paper deals with the problem of the determination of the inplane behavior of periodic masonry material. Masonry is considered a composite material obtained as a regular distribution of blocks connected by horizontal and vertical mortar joints. The macromechanical equivalent Cauchy and Cosserat models are derived by means of the homogenization procedure, which make use of the Transformation Field Analysis (FTA) in order to account for the nonlinear effects occurring in the components. The micromechanical analysis is developed considering a Cauchy model for the masonry components. In particular, the linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is proposed for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Numerical applications are performed in order to assess the performances of the proposed models in reproducing the mechanical behavior of the masonry material. In particular, two different masonry textures are considered, remarking their different behavior.Moreover, for one masonry texture, the response is derived considering two possible RVEs