A limit analysis approach based on Cosserat continuum for the evaluation of the in-plane strength of discrete media: Application to masonry

Abstract

In the frame of Cosserat continuum theory, an upscaling procedure for the assessment of the in-plane strength domain of discrete media is developed. The procedure is the extension to the Cosserat continuum of a procedure initially formulated for the Cauchy continuum, based on the kinematic approach of limit analysis and the classical homogenisation theory. The extension to the Cosserat continuum is made in order to take into account the effect of particles' rotation on the strength of the discrete medium. The procedure is illustrated with regard to periodic assemblies of blocks in contact and is then generalised to the whole class of discrete periodic media with particles of the same type. The case of masonry is considered as an application. Strength criteria of columns and walls are formulated in terms of non-symmetric stresses and in-plane couples. The procedure allows to show how the in-plane strength of the medium is reduced as a result of particles' rotation.

Scale dependent continuum approaches for discontinuous assemblies: ‘Explicit’ and ‘implicit’ non-local models

“…[16,17,18]. It has been shown, moreover, that, due to the presence of the 45 relative rotation between macro (local rigid) and micro rotation, that corresponds to the skew-symmetric part of strain, the micropolar continuum is particularly suitable to investigate the behaviour of anisotropic (specifically orthotropic) media [18,19,20,21,22]. If micro rotations are 50 constraint to follow the local rigid (macro) rotations, the theory becomes of Couple Stress, and by further adding statical constraint on couples the classical continuum is recovered (See for instance Appendix in [16]).…”

Mechanical Behavior of Anisotropic Composite Materials as Micropolar Continua

“…As well-known, in the description of complex materials, such as composites, the discrete, and heterogeneous nature of matter must be taken into account, because interfaces and material internal phases dominate the gross behavior. The presence of material internal structure can be accounted by direct discrete modeling, with generally high computational cost (Suzuki et al, 1991;Baggio and Trovalusci, 2000;Rapaport and Rapaport, 2004;Yang et al, 2010;Godio et al, 2017;Baraldi et al, 2018;Reccia et al, 2018) or by adopting multiscale or coarse-graining techniques for deriving homogenized continua (Budiansky, 1965;Sanchez-Palencia, 1987;Nemat-Nasser et al, 1996;Blanc et al, 2002;Curtin and Miller, 2003;Jain and Ghosh, 2009;Trovalusci and Ostoja-Starzewski, 2011;Nguyen et al, 2012;Sadowski et al, 2014;Altenbach and Sadowski, 2015;Greco et al, 2016. However, the classical Cauchy model (Grade 1) is not reliable in the presence of problems dominated by the microstructure size, both in the non-linear, such as in the case of strain localization phenomena, and linear regimes (de Borst, 1991;Sluys et al, 1993;Masiani and Trovalusci, 1996;Trovalusci andMasiani, 1999, 2003).…”

‘Explicit’ and ‘implicit’ non-local continuous descriptions for a plate with circular inclusion in tension

“…time and/or length scales become comparable, the discrete nature of structure starts to play a key role on properly describing the overall mechanical behaviour. Since classical (local) theory of elasticity is incapable of capturing the size effects [1][2][3][4][5], and direct discrete modelling techniques are not practical due to their computational expense [6][7][8][9][10], enriched non-classical continuum theories [11][12][13][14][15][16] have been often proposed in the literature. Among them, the micropolar (Cosserat) theory [17][18][19] and Eringen's nonlocal theory [16,20,21], both of which incorporate size effects associated with the material's internal structure by different principles [1][2][3][4][5][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], will be the main object of this study.…”