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 symmetry. This provides the opportunity to investigate novel classes of quasicrystal inspired elastic composites whose mechanical static and dynamic properties are largely unexplored. This presentation illustrates the performance of continuous elastic quasicrystals composites, here denoted as quasiperiodic (QP) composites, characterized by different rotational symmetry orders which is directly enforced through a design procedure in reciprocal space. Static 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, lead to equivalent stiffness characteristics that interpolate those of the constituent materials while maintaining high levels of isotropy for all filling fractions. Thus, QP composites exhibit more uniform strain energy distributions when compared to periodic 4-fold and 6-fold symmetric configurations. Similarly, nearly-isotropic wave propagation is observed over a broader range of frequencies. The spectral dynamic properties are also investigated by enforcing rotational symmetry constraints in a wedge-type unit cell, which allows for the estimation of bandgaps, whose presence is confirmed in frequency response computations. Wave directionality and bandgaps are also estimated through parallel studies conducted on plate structures characterized by QP patterns of surface stubs. These experiments show clear bandgaps, illustrate how wave fronts reflect the rotational symmetry of the domains, and demonstrate that higher order geometries lead to isotropic propagation over a broader range of frequencies. 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.