Multiscale analysis of masonry structures using homogenization

Abstract

It is common practice when performing seismic vulnerability assessment of masonry buildings to tackle separately out-of-plane and in-plane failure mechanisms developed by load-bearing walls. The former are governed by the dynamics of rigid bodies while the latter is governed by the mechanics of anisotropic continuum media. The present thesis intends to give a contribution to the understanding and modelling of both these failure mechanisms. The behaviour of masonry walls under out-of-plane loads is addressed in the first part of the work (Chapter 3), where the results of a shake-table laboratory campaign on a tuff masonry U-shaped assemblage (façade adjacent to transverse walls) are presented. Scaled natural accelerograms have been adopted in order to analyse the seismic behaviour of the façade. The tests highlight the main factors affecting the dynamic behaviour of the wall, the effects related to the presence of mortar joints and of imperfections, the dependency of the response on the input and the mechanisms of energy dissipation. A modelling strategy based on the Discrete Element Method is then presented, which is shown to reproduce the experimental behaviour of the wall in terms of maximum rotation and time-history response. Finally, test results and numerical time-history simulations are compared to the Italian seismic code assessment procedures. The second part of the thesis (Chapter 4 and 5) deals with modelling in-plane loaded masonry walls by resorting to the homogenization theory for periodic media. First, a Cauchy identification for masonry is developed within the framework of the homogenization theory, which provides analytical expressions for the elastic constants and take into account Poisson effects deriving from the mismatch of brick/joint stiffness and anisotropy deriving from brick interlocking. The results are validated with finite element analyses and experimental data over a wide range of geometrical and mechanical properties of the constituents. Finally, a homogenized limit elastic domain is derived and compared with the experimental tests available in literature, in terms of macroscopic strength and corresponding failure mode. The extension to the non-linear range of homogenization techniques is then addressed within the framework of multi-scale methods. The problem is formulated by referring to a simple micro-mechanical model where masonry is tackled as a system of elastic blocks connected by non-linear interfaces obeying to a Mohr-Coulomb criterion with non associative flow-rule. By introducing affine kinematics within the blocks, the non-linear homogenization problem is expressed in terms of few unknowns and is solved locally by means of an iterative Newton-Raphson scheme. The multi-scale procedure is implemented in the finite element code Abaqus and adopted for studying the in-plane behaviour of masonry panels. Finally, the main limits and the applicability of the proposed methodology to practical engineering problems are discussed by means of an application to real case studie