Calculus of Variations and Geometric Measure Theory

A. Braides - N. A. Nodargi

Homogenization of cohesive fracture in masonry structures

created by braidesa on 20 May 2019
modified on 28 Mar 2020


Published Paper

Inserted: 20 may 2019
Last Updated: 28 mar 2020

Journal: Math. Mech. Solids
Volume: 28
Pages: 181-200
Year: 2020
Doi: 10.1177/1081286519870222

ArXiv: 1905.07171 PDF


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.

Keywords: Homogenization, Gamma-convergence, Functions of Bounded Deformation, fracture, Masonry