Issue 29

M.L. De Bellis et alii, Frattura ed Integrità Strutturale, 29 (2014) 37-48; DOI: 10.3221/IGF-ESIS.29.05 48 Two structural examples are presented. The aim is to discuss the key aspects of the adopted micropolar formulation and to stress the differences obtained using the three presented procedures in terms of the global response. It would appear relevant to carry out further developments, focusing on the formulation of the kinematic map linking the macro- and micro-levels, as well as on the improvement of the identification procedure. The purpose is to better clarify some ongoing issues and to solve inherent limitations of the procedure, as for example the contradictory result consisting in nonvanishing micropolar effects in the presence of homogeneous materials. R EFERENCES [1] Forest, S., Sab, K., Cosserat overall modeling of heterogeneous materials. Mech Res Commun 25 (1998) 449-454. [2] Kouznetsova, V. G., Computational homogenization for the multi-scale analysis of multi-phase materials. Ph.D. thesis, Technische Universiteit Eindhoven, (2002). [3] Bacigalupo, A., Gambarotta, L., Second-order computational homogenization of heterogeneous materials with periodic microstructure. ZAMM-Z Angew Math Me, 90 (11) (2011)796-811. [4] Addessi, D., Sacco, E., A multi-scale enriched model for the analysis of masonry panel. Int. J. Solids Struct. 49 (2012) 865–880. [5] De Bellis, M. L., Addessi, D., A Cosserat based multi-scale model for masonry structures. Int. J. Multiscale Comput. Eng. 9 (2011) 543–563. [6] Addessi, D., Sacco, E., Paolone, A., Cosserat model for periodic masonry deduced by nonlinear homogenization. Eur. J. Mech. A Solid 29 (2010) 724–737. [7] Addessi, D., De Bellis, M. L., Sacco, E., Micromechanical analysis of heterogeneous materials subjected to overall cosserat strains. Mech Res Commun 54, (2013) 27-34. [8] Miehe, C., Schröder, J., Becker, M., Computational Homogenization Analysis in Finite Elasticity: Material and Structural Instabilities on the Micro- and Macro-Scales of Periodic Composites and Their Interaction, Computer Methods in Applied Mechanics and Engineering 191 (2002), pp. 4971-5005. [9] Forest, S., Trinh, D., Generalized continua and non-homogeneous boundary conditions in homogenisation methods. ZAMM-Z Angew Math Me 91 (2) (2011) 90-109. [10] Bouyge, F., Jasiuk, I., Boccara, S., Ostoja-Starzewski, M., A micromechanically based couple-stress model of an elastic orthotropic two-phase composite. Eur J Mech A-Solid, 21 (2002) 465-481. [11] Addessi, D., De Bellis, M. L., Sacco, E., Cosserat modeling of heterogeneous periodic media adopting a micromechanical approach. Int. J. Solids Struct., (2014) Under Review. [12] Yuan, X., Tomita, Y., Andou, T., 2008. A micromechanical approach of nonlocal modelling for media with periodic microstructures. Mech Res Commun, 35 (1-2) (2008) 126 -133. [13] Tran, T. H., Monchiet, V., Bonnet, G., A micromechanics-based approach for the derivation of constitutive elastic coefficients of strain-gradient media, Int J Solids Struct, 49 (2012) 783-792. [14] Bacigalupo, A., Gambarotta, L., Computational two-scale homogenization of periodic masonry: characteristic lengths and dispersive waves, Comput Method Appl M., 213-216 (2012) 16-28. [15] Bacigalupo, A., Gambarotta, L., Second-order computational homogenization of heterogeneous materials with periodic microstructure. ZAMM-Z Angew Math Me, 90 (11) (2011) 796-811.