A multiscale force-based curved beam element for masonry arches

Abstract

This paper presents a Timoshenko beam finite element for nonlinear analysis of planar masonry arches. Considering small displacement and strain assumption, the element governing equations are defined according to a force-based formulation that adopts three different parametrizations of the axis planar curve, permitting the exact description of the element geometry for arbitrarily curved arches. Specific quadrature techniques are illustrated to perform numerical integration over the curved axis. A two-scale arch-to-beam homogenization procedure reproduces the nonlinear response of periodic masonry materials, where an equivalent Timoshenko straight beam describes the behavior of the reference Unit Cell made of a single linear elastic brick and a nonlinear mortar layer. Formation of the hinges characterizing the collapse mechanism of the arch is detected taking advantage of the quadrature rule along the axis and a fracture energy based regularization technique is employed to avoid damage localization.

Limit analysis approach for the in-plane collapse of masonry arches

“…In the last decades, among masonry structures, many authors have been focused the attention in particular on the study of masonry arches (Boothby, 1994;Barsotti et al, 2017;Aita et al, 2020;Eroglu et al, 2020) adopting different approaches such as dynamic approach (Oppenheim, 1992;De Lorenzis et al, 2007a,b;Peña et al, 2007); Isogeometric approach (Chiozzi et al, 2016); Discrete Element Method (DEM) (Baraldi et al, 2019); homogenization technique (Reccia et al, 2013) or multiscale approach (Di Re et al, 2018). A recent work of Bruggi (2020) adopt the optimization process for study the optimal shape for arches and vaults.…”

Micromechanical Analysis of Unreinforced and Reinforced Masonry Arches

“…The last, IM, adopts a similar discretization for the resized units, but 5 × 1 zero-thickness interface elements for each joint. As for the mechanical parameters of the constituent materials, these are set according to the available experimental data [5] and the numerical analyses performed by Di Re et al [11]. Tables 1 and 2 contain the mortar mechanical parameters assumed for CM and IM, respectively.…”

“…The main limit is that no information is given on the pre-and post-peak response as well as the evolution process of the nonlinear mechanisms. To overcome these restrictions, accurate nonlinear finite element (FE) models have been developed [10,11,12]. Most of these are typically based on micromechanical, multiscale and macromechanical approaches [13,14] and introduce nonlinear constitutive laws to describe the onset and evolution of degrading mechanisms.…”

Multiscale Model Calibration by Inverse Analysis for Nonlinear Simulation of Masonry Structures Under Earthquake Loading

“…Computational homogenisation, as the FE 2 method (Feyel & Chaboche, 2000), is based on online exchange of information between a microscale Representative Volume Element (RVE) and the macroscale domain (Luciano & Sacco, 1997;Massart, et al, 2007;Addessi & Sacco, 2016;Di Re, et al, 2018;Leonetti, et al, 2018). In general, a macroscale model is used for the analysis and its constitutive behaviour is obtained by the solution of a Boundary Value Problem (BVP) for the corresponding RVE.…”