| Summary: | This work investigates the application of homogenization
techniques to the dynamic analysis of periodic solids, with
emphasis on lattice structures. The presented analysis is
conducted both through a Fourier-based technique and through an
alternative approach involving Taylor series expansions directly
performed in the spatial domain in conjunction with a finite
element formulation of the lattice unit cell. The challenge of
increasing the accuracy and the range of applicability of the
existing homogenization methods is addressed with various
techniques. Among them, a multi-cell homogenization is introduced
to extend the region of good approximation of the methods to
include the short wavelength limit. The continuous partial
differential equations resulting from the homogenization process
are also used to estimate equivalent mechanical properties of
lattices with various internal configurations. In particular, a
detailed investigation is conducted on the in-plane behavior of
hexagonal and re-entrant honeycombs, for which both static
properties and wave propagation characteristics are retrieved by
applying the proposed techniques. The analysis of wave propagation
in homogenized media is furthermore investigated by means of the
bridging scales method to address the problem of modelling
travelling waves in homogenized media with localized
discontinuities. This multi-scale approach reduces the
computational cost associated with a detailed finite element
analysis conducted over the entire domain and yields considerable
savings in CPU time. The combined use of homogenization and
bridging method is suggested as a powerful tool for fast and
accurate wave simulation and its potentials for NDE applications
are discussed.
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