# Department of Mechanics: Seminar: Abstract LaMalfaRibolla 2019

### Multi-scale computational homogenization for the analysis of masonry structures

#### Emma La Malfa Ribolla, Czech Technical University in Prague, formerly University of Palermo, Italy

**Room B-366, Faculty of Civil Engineering, CTU in Prague**

**Monday, 22 July 2019, 11am**

Masonry material, generally constituted by regular or random assemblage of blocks and mortar joints, is characterized by a strong nonlinear constitutive response. Similarly to other heterogeneous materials, the macroscopic or structural behavior depends on the kinematic and static phenomena occurring at the mesoscopic level, i.e. at the constituents’ observation level. In particular, anisotropy, stiffness degradation and irreversible displacement observed at the macro- scale are the results of the opening-closing, sliding and dilatancy occurring at the joints. It follows that the development of reliable stress analyses still represents a demanded challenge task. In the last few decades, the development of multi-scale computational homogenization (CH) techniques has been increasing. These techniques are characterized by the fact that the macroscopic medium is considered homogeneous and its response is obtained from the solution of a mesoscopic Boundary Value Problem (BVP) formulated for a representative volume element or unit cell (UC). For masonry material characterized by a regular texture, a first-order homogenization scheme based on a discontinuous-continuous approach is presented. At the mesoscopic level the formation and propagation of fracture is modeled employing a UC consisting of an elastic unit surrounded by elasto-plastic zero-thickness interfaces [1], characterized by a discontinuous displacement field. The choice of adopting an elasto-plastic response of mortar represents a good compromise between ease of applicability and effective representation of the decohesion process occurring at the joint level. At the macroscopic level, instead, the model maintains the continuity of the displacement field. The inelastic effects are enclosed in a smeared way, introducing a strain localization band established on the basis of a spectral analysis of the UC acoustic tensor. Another key-point is the numerical solution of the UC BVP, which is obtained by means of a more cost-effectiveness mesh-free model, for this reason the strategy has been named FE·Meshless. Both linear and periodic boundary conditions have been applied to the UC. It will be show that the meshless UC response strongly reduce the number of degrees of freedom with respect to a standard FE discretization under uniform displacements, in addition to the this aspect, meshless UC periodic response allows to obtain the anti-periodicity of tractions using a considerably reduced number of degrees of freedom with respect to the FE response. The FE·Meshless strategy has been validated through numerical applications presented in [2-3] .

**References**

[1] Giambanco, G., Rizzo, S. and Spallino R. (2001). Numerical analysis of masonry structures via
interface models. Computer Methods in Applied Mechanics and Engineering, 190(49-50),
6493-6511.

[2] Giambanco, G., La Malfa Ribolla, E. and Spada, A. (2018). Meshless meso-modeling of masonry
in the computational homogenization framework. Meccanica, (53)7, 1673-1697.

[3] Spada, A., Giambanco, G. and La Malfa Ribolla, E. A FE-Meshless multiscale approach for
masonry materials. Procedia Engineering, 109, 364-371, Favignana, June 22-24, 2015.