Non-local dynamic behavior of linear fiber reinforced materials

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 between the period section size and the characteristic size of the system global strain, and by weighing the constituents stiffness contrast by powers of , 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 () 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. [Copyright &y& Elsevier]