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It has widely shown that the Cosserat model is able to describe homogenized continua in which particles and heterogeneity in general are described by an inner rotation termed microrotation [1-3]. Since the beginning, this additional degree of freedom has been properly introduced in reduced-dimensional structural models [4]. Many explicit solutions for Cosserat materials have been produced over years but the case, rather frequent, of orthotropic materials calls for the need of numerical investigations [1-3]. A peculiar feature of generalized continua is the presence of a material internal length [5]. The Cosserat continuum in particular, tends to behave as a Cauchy model when the internal characteristic length is close to the structural dimensions (macro-scale) but only if the material is isotropic or at least orthotetragonal [1]. Moreover, in the orthotropic case the relative rotation, which implies non-symmetries of the angular strain components, plays an important role that cannot be represented by generalized continua of other kinds (second gradient, couple stress, etc.) [2,3]. In the present work, the mechanical behaviour of Cosserat orthotropic two-dimensional block assemblies modeled as Cosserat is investigated paying attention to the material discontinuities and the scale effects. Different numerical approaches, using strong and weak form formulations, are adopted [6]. The results provided by two numerical techniques, the so-called Strong Formulation Finite Element Method (SFEM) [7] and the Finite Element Method, are compared. Convergence, stability and reliability of both numerical techniques will be discussed and advantages and disadvantages in terms of displacement/stress fields will be shown. References [1] Masiani, R. and Trovalusci P., “Cosserat and Cauchy materials as continuum models of brick masonry”, Meccanica, 31, 421-432 1996. [2] Pau, A. and Trovalusci, P., Block masonry as equivalent micropolar continua: the role of relative rotations, Acta Mech, 223 (7), 1455-1471, 2012. [3] Trovalusci, P. and Pau, A., “Derivation of microstructured continua from lattice systems via principle of virtual works: The case of masonry-like materials as micropolar, second gradient and classical continua”, Acta Mech, 225, pp.157-177 (2014). [4] Altenbach, J., Altenbach H. and Eremeyev, V.A., “On generalized Cosserat-type theories of plates and shells: a short review and bibliography”, Arch Appl Mech, 80, pp.73-92 (2010). [5] Sluys, L.J., de Borst, R. and Mühlhaus, H.-B., “Wave propagation, localization and dispersion in a gradient-dependent medium”, Int J Sol Struc, 30, pp.1153-1171 (1993). [6] Fantuzzi, N., Leonetti, L., Trovalusci, P. and Tornabene, F., “Some Novel Numerical Applications of Cosserat Continua”, Intl J Comput Meth, 15, pp.1-38 (2018). [7] Tornabene, F., Fantuzzi, N., Ubertini, F. and Viola, E., “Strong formulation finite element method based on differential quadrature: a survey”, Appl Mech Rev, 67, pp.1-55 (2015). |
