Mechanics and dynamics of two-dimensional quasiperiodic composites

Abstract: Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterial structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry but are unrestricted in rotational symmetries, which leads to largely unexplored mechanical and dynamic properties. We investigate a family of continuous elastic quasicrystals with different rotational symmetry orders that are directly enforced through a design procedure in reciprocal space. Their mechanical properties are investigated as a function of symmetry order and filling fraction. Results indicate that higher order symmetries, such as 8-, 10- and 14-fold, allow for high equivalent stiffness characteristics that interpolate those of the constituent material while maintaining high levels of isotropy for all filling fractions. Thus, quasiperiodic composites exhibit more uniform strain energy distributions when compared to periodic hexagonal configurations. Similarly, nearly-isotropic wave propagation is observed over a broader range of frequencies. Spectral contents are also investigated by enforcing rotational symmetry constraints in a wedge-type unit cell, which allows for the estimation of band gaps that are confirmed in frequency response computations. The investigations presented herein open avenues for the general exploration of the properties of quasiperiodic media, with potentials for novel architectured material designs that expand the opportunities provided by periodic media.