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).
The Effect of Micro-Polar Rotation in 2D Cosserat Solids
Nicholas Fantuzzi;Francesco Tornabene
2018
Abstract
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
