Cosserat and Cauchy materials as continuum models of brick masonry

Abstract

Continuum modeling for masonry-like material accounting for bricks or blocks texture is discussed. The constitutive functions for the contact actions - expressed in terms of size, shape and arrangement of the block assembly - are derived within the framework of the linear elastic Cosserat and Cauchy theories. By varying some important geometrical parameters: the scale factor between the wall and the blocks size, the shape of the bricks and their arrangement, micropolar materials with particular internal constraints are obtained. In a few situations the constrained continuum behaves as a Cauchy continuum. In general, the Cauchy continuum does not provide a proper description of the brick masonry behaviour while the structured continuum model, accounting for the mutual blocks rotation, gives satisfactory results

Continuous and discrete models for masonry like material: A critical comparative study

“…In this case, for modelling a running bond masonry panel, the six constants are determined towards the identification procedure described in section 5 and consequently, two different stiffness matrices are obtained, based, respectively, on REV1 and REV2. The CST element is adopted in order to follow an existent literature dedicated to the analysis of periodic structures modelled as micropolar continua (Masiani et al, 1995;Masiani and Trovalusci, 1996;Providas and Kattis, 2002;Trovalusci and Masiani, 2003;Wheel, 2008). Moreover, the triangular element allows to perform an exact integration for the determination of the stiffness matrix; further details may be found in Appendix A2.2.…”

“…For micropolar continuum see for example Masiani et al (1995), Masiani and Trovalusci (1996), Boutin (1996), Sulem and Mühlhaus (1997), Smyshlyaev and Cherednichenko (2000), Forest et al (2001), Casolo (2009), Salerno and De Felice (2009), Addessi et al (2010), De Bellis and Addessi (2011) and Pau and Trovalusci (2012). For higher order continuum see for example Stefanou et al (2010), Bacigalupo and Gambarotta (2012) and Trovalusci and Pau (2014).…”

On Discrete Structure of Geologic Medium and Continual Approach to Modeling Its Movements

“…Но часто (особенно для систем с большим числом элементов) вопросы глобальной устойчивости кладки и ее макроразрушения имеют больший приоритет, чем точное знание локальных подробностей, поэтому здесь, наряду с дискретным моделированием, стал развиваться континуальный подход. Он реализуется на основе разных способов осреднения [Lourenҫo et al, 2007] с использованием модели Коссера [Masiani, Trovalusci, 1996] или фи-зической теории пластичности [Yuen, Kuang, 2013] и континуального разрушения [Pelà et al, 2011].…”

Multilevel approach for brick masonry walls – Part III: A strategy for free vibration analysis

“…All of these are obtained through an energy equivalence with reference to a general homogeneous deformation state and differ essentially in the identification of the brick rotations. These are taken explicitly as the skew part of the displacement gradient in CAU continuum (see [4]), implicitly defined by the brick rotational equilibrium in RCA (see [5]) or directly identified as the Cosserat micro-rotation in COS (see [4]). Note that all of these do not account for brick deformability, so their results have to be compared with Exact * ones.…”

“…In such cases, coarse modelings based on a finite element discretization of equivalent continua is usually suggested for this purpose (e.g. see [4][5][6][7]). However, equivalent continua, while being tuned to reproduce smooth strain deformations of the masonry, become inaccurate on nonsmooth deformation modes (see [2]).…”