# Homogenization of cohesive fracture in masonry structures

## TL;DR

This paper develops a homogenized mechanical model for masonry structures with blocks and mortar joints, analyzing their asymptotic behavior and deriving a formula for the effective energy considering cohesive and unilateral contact conditions.

## Contribution

It introduces a novel homogenization approach for masonry with cohesive contacts, incorporating unilateral conditions and non-standard growth in the limit energy.

## Key findings

- Derived a homogenization formula for masonry structures.
- Identified macroscopic tensile and compressive stresses.
- Analyzed non-standard growth conditions in the homogenized energy.

## Abstract

We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist in (i) a linear elastic contribution within the blocks, (ii) a Barenblatt's cohesive contribution at contact surfaces between blocks and (iii) a suitable unilateral condition on the strain across contact surfaces, and are governed by a small parameter representing the typical ratio between the length of the blocks and the dimension of the structure. Using the terminology of Gamma-convergence and within the functional setting supplied by the functions of bounded deformation, we analyze the asymptotic behavior of such energy functionals when the parameter tends to zero, and derive a simple homogenization formula for the limit energy. Furthermore, we highlight the main mathematical and mechanical properties of the homogenized energy, including its non-standard growth conditions under tension or compression. The key point in the limit process is the definition of macroscopic tensile and compressive stresses, which are determined by the unilateral conditions on contact surfaces and the geometry of the blocks.