Multi-scale analysis of masonry structures

Masonry is one of the most famous and widely used heterogeneous composite material, largely employed in historic and architectural buildings. Among the different approaches proposed to study masonry structural behavior, multi-scale procedures are modern and promising tools, representing a fair compromise between detailed description of masonry microstructure and computational burden. This work presents a multi-scale beam-to-beam model for the analysis of unreinforced and strengthened periodic masonry panels under out-of-plane loadings. A two-dimensional Timoshenko force-based beam Finite Element (FE) is used to model the panel at the macroscale. At the microscale, a Unit Cell (UC) made of a brick, a mortar joint and eventually a reinforcing layer is adopted as representative volume element. The UC mechanical behavior is described by a Timoshenko beam model and is linked to the macroscale FE through a semi-analytical homogenization technique. Nonlinear constitutive relationships are considered for mortar and bricks, accounting for the evolution of damage, friction, and unilateral effect. A damage-based bi-linear relationship is assumed for the reinforcing layer, to reproduce the behavior of fabric-reinforced cementitious matrix (FRCM) composite materials. Applications on masonry structural elements of engineering interest are presented, showing also comparisons with experimental evidences.