Strength domain of non-periodic masonry by homogenization in generalized plane state

This paper deals with the evaluation of the strength domain for non-periodic masonry using a random media micromechanical approach. The generalized plane state formulation is used in order to more accurately describe the masonry behavior and failure criteria proposed in literature. Considering the masonry as a heterogeneous material with random microstructure, the elastic characteristics of the homogenized continuum and the strength domain are evaluated by using the hierarchy theory related to partitions with increasing dimensions through the application of natural and essential boundary conditions with proportionally growing values. An overall failure criterion based on the mean stress state of each phase is introduced. The proposed procedure is validated by comparison with the experimental results obtained with periodic masonry subjected to biaxial stress states recovering the main failure mechanisms. Then the approach is applied to an actual non-periodic masonry introducing peculiar algorithms in order to evaluate strength surfaces and to verify the convergence of the domains obtained through the application of natural and essential boundary conditions with the increasing size of portion dimensions at the mesoscale level.