Daniela Addessi¹, Elio Sacco², and Paolo Di Re¹
1) Department of Structural and Geotechnical Engineering, Sapienza University of Rome,
Via Eudossiana 18, 00184 Rome, Italy
{daniela.addessi,paolo.dire}@uniroma1.it
2)  Department of Structures for Engineering and Architecture, University of Naples Federico II,
Via Claudio 21, 80125 Naples, Italy
elio.sacco@unina.it

Keywords: Strengthened masonry, Multi-scale analysis, Damage, Force-based beam.

Abstract. 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 semianalytical 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.