Abstract
This article deals with the effective dynamic behavior of elastic materials periodically reinforced by stiff linear slender elastic inclusions. By assuming a small scale ratio ε between the period section size and the characteristic size of the system global strain, and by weighing the constituents stiffness contrast by powers of ε, the dynamic macroscopic behavior at the leading order is derived through the asymptotic homogenization method of periodic media considering different frequency ranges. A two order stiffness contrast (μm/μp=O(ε2)) is shown to lead to a dynamic macroscopic behavior spatially non-local in the transverse direction, where the system behaves as a generalized inner bending continuum, and temporally non-local in the axial direction, where the system behaves, at higher frequency, as a metamaterial in which internal resonance phenomena take place. The consequences of such non-localities on the reinforced medium modes are examined. The system axial and transverse modes are shown to be significantly different from those of usual composites.
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