Issue 29

A. Bacigalupo et alii, Frattura ed Integrità Strutturale, 29 (2014) 1-8; DOI: 10.3221/IGF-ESIS.29.01 3 (a) (b) Figure 2 : Periodic cell of the (a) hexachiral lattice; (b) tetrachiral lattice. (a) (b) (c) Figure 3 : (a) Internal mass with external elastic thick layer; (b) rigid ring and related dofs; (c) internal mass and related dofs. A soft elastic interface connects the internal mass to the rigid ring. To get a simplified formulation, the constitutive equation of the interface is assumed in the form     , c = d k k         f v u (1) f being the force exerted by the rigid ring on the internal mass and c the corresponding couple (see Figure 4). The parameters d k and k  are the isotropic translational stiffness and the rotational stiffness, respectively. Figure 4 : Contact force and couple between the rigid ring and the internal mass. The lattice model is here approximated as a micropolar continuum model resulting from a homogenization process based on the macro-homogeneity criterion, involving both the total potential energy and the kinetic energy through the Hamilton principle (see [13, 16] for reference). The equations of motion for the homogenized beam-lattice are