An orthotropic damage model for masonry structures

Abstract

An orthotropic damage model specifically developed for the analysis of brittle masonry subjected to in-plane loading is described. Four independent internal damage parameters, one in compression and one in tension for each of the two natural axes of the masonry, are defined allowing the stiffness recovery at crack closure as well as the different inelastic behaviour along each natural axis to be considered. The damage field of the material is defined in terms of four equivalent stresses and results, in the space of the in-plane effective stresses, in a double pyramid with a rectangular base where the slopes of the faces correspond to the internal friction angle of the material. The equivalent stresses also control the growth of the damage parameters. The returning path from the effective to the damaged stresses is given by multiplication by a fourth-rank damage effect tensor, which is a function of the damage parameters and of the effective stress state. Mesh size regularization is achieved by means of an enhanced local method taking into account the finite element size. Good agreement has been found in the comparison between numerical results and experimental data both for masonry shear panels and for a large-scale masonry holed wall

Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches

“…Papa's [107] orthotropic model consists of a unilateral damage model for masonry including a homogenization technique to keep into account the texture of brick and mortar. Berto et al [9] developed a specific damage model for orthotropic brittle materials with different elastic and inelastic properties along the two material directions. The basic assumption of the model is the acceptance of the natural axes of the masonry (i.e.…”

“…More recently, Clemente's et Fig. 22 Analysis of a cyclically-loaded wall with openings (from Berto et al [9]): (a) dx−, (b) dy−, (c) dx+ and (d) dy+ numerical damage contours al. [32] isotropic damage has been modified to account for masonry's orthotropy by Pela' et al ([113], see also Pela' [112]).…”

High-fidelity prediction of crack formation in 2D and 3D pullout tests

“…Instead, in the case of the ASGS method, the last algebraic equation is automatically verified and the Jacobian matrix presents the mathematical structure: (43) Matrices M τ , G τ , D τ , K τ are the same in both the presented methods. Details on the differentiation of the plastic strain tensor ε p with respect to the problem unknown ε h are given in the work by Benedetti et al [23].…”

New Frontiers on Seismic Modeling of Masonry Structures

“…In the scientific literature, there are many significant examples of applications of the non-linear finite element method (FEM) to historical masonry buildings and churches (Mele et al, 2003;Vignoli, 2008, 2011;Araujo et al, 2012;Lourenço et al, 2012;Barbieri et al, 2013;Milani and Valente, 2015), however refined FE approaches (Lofti and Shing, 1994;Anthoine, 1997;Gambarotta and Lagomarsino, 1997;Lourenço and Rots, 1997;Berto et al, 2002;Macorini and Izzuddin, 2011) coupled with sophisticated constitutive laws, require a huge computational cost and advanced abilities in the model implementation and in the interpretations of the results. On the other hand, structural engineers need simple and efficient numerical tools, whose complexity and computational demand should be appropriate for practical engineering purposes.…”