Issue 29

A. Bacigalupo et alii, Frattura ed Integrità Strutturale, 29 (2014) 1-8; DOI: 10.3221/IGF-ESIS.29.01 5            2 2 2 2 2 2 2 2 2 2 2 2 3 1 4 3 1 cos sin 4 3 sin cos 2 3 3sin 4 cos 12 3 1 sin cos 2 s s s s s E E k E S E a A E                                 (4) depend on the Young’s modulus, the slenderness ratio t l   and the angle  of inclination of the ligaments. The constitutive Eq. (3) show the coupling between the extensional strains 11  and 22  and the asymmetric strains 12  and 21  through the elastic constant A . The elastic moduli, with the exception of parameter  , depend on the parameter of chirality  , but only the constant A is an odd function of this parameter, i.e. it reverses its sign when the handedness of the material pattern is flipped over. In case of symmetric macro-strain fields, the fourth order elastic tensor for the hexagonal system corresponds to that of the transversely isotropic system whose elastic moduli in the plane of the lattice are:          2 4 2 2 3 2 hom 2 2 2 2 hom 2 4 2 2 2 hom 3 cos sin 2 3 1 cos sin 1 3 cos sin 3= 1 4 s s E E E                            G (5) For the tetrachiral lattice, the constitutive equation is written [15]: 11 11 22 22 12 12 21 21 1 1 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B B B B m S m S                                                                             (6) where four elastic moduli are related to the lattice parameters as follows         2 2 2 2 2 2 2 2 2 2 2 cos sin 2 sin cos 1 sin cos 1 3sin 4 cos 12 s s s s E k E B E S E a                           (7) Similarly to the hexachiral honeycomb, a coupling is obtained between the extensional strains and the asymmetric strains through the elastic modulus B which is an odd function of the parameter of chirality  , while the other elastic moduli are even functions. In case of symmetric macro-strain fields, the resulting classical fourth order elasticity tensor has the elastic