A high-continuity multi-scale static and dynamic modelling of periodic materials

The equations of motion of a second-order continuum representative of a classical heterogeneous periodic material are derived through a variational-asymptotic homogeniza- tion technique and the overall elastic moduli and the inertial properties are evaluated. The proposed approach is an extension of a dynamic homogenization method developed by the Authors [9] and [10] which has the aim to improve the accuracy of description of the overall inertial terms and of the dispersive functions. This procedure is applied to the case of elastic layered materials with two orthotropic phases having an orthotropy axis parallel to the layers. To evaluate the reliability of the model the dispersion functions here obtained are compared with those from the analytical model applied to heterogeneous material [1, 2], and with those obtained by the Authors in the previous approach [9].