MURRALI, AGNESE 1; TROVALUSCI, PATRIZIA 1; DE BELLIS, MARIA LAURA 1; OSTOJA-STARZEWSKI, MARTIN 2
1) Department of Structural and Geotechnical Engineering, Sapienza, University of Rome, Italy, email@example.com
2) Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, USA
In this work a scale-dependent homogenization approach for describing the mechanical behavior of composite materials with random microstructures, paying attention to materials employed in historical constructions, like roman concrete, rubble filled masonry or magmatic rocks, is proposed. To this aim, a statistical procedure for estimating the constitutive moduli of an equivalent micropolar continuum is performed. This procedure uses finite-size scaling of Statistical Volume Elements (SVEs) and approaches the so-called Representative Volume Element (RVE) through two hierarchies of constitutive bounds, respectively stemming from the numerical solution of Dirichlet and Neumann non-classical boundary value problems, set up on mesoscale material cells. The results of the performed numerical simulations point out the worthiness of accounting spatial randomness as well as the additional degrees of freedom of the Cosserat continuum.
Keywords: Cosserat continua, homogenization, random materials, ancient masonry.