Flavia Guarracino, Ph.D. Candidate 37th cycle, University of Trento, DICAM

The Ph.D. project aims at finding new ways of guiding waves or shielding from different frequencies through mechanical properties of micro-structured, hierarchically organized, and “architectured” materials, namely metamaterials, as well as conceiving ad hoc tools and strategies for predicting the characteristics they must own for this to happen.

In order to achieve the proposed aims some kinds of tunable metamaterials will be developed and investigated, which should react to changes in their environment, through zero-energy mechanisms or by changing their stiffness, and thus the frequency at which they disperse or enhance vibrations. These artificial materials should be able to respond mechanically as opposed to classical technological
methods, which rely on electricity to change their properties.
The application possibilities are multifold, from industrial sectors, such as information and communication technologies, and space, to those involving health, energy and environmental areas.

The present research focus is on discrete structures of masses and springs, first in 1D and 2D lattices, with nonlocal connections and nonlocal effects in dynamics. It is known from the classical Bloch theorem that the sole properties of the unit cell yield information for the dynamical behavior of the whole chain, through its dispersion relation, which relates the wavenumber of a wave to its frequency. The band
diagrams are tailored in order to obtain nontrivial dispersion relations and tune them to be able to respond to changes in its environment by closing or widening band gaps, specifically responding to dynamical perturbations at both the micro- and the macroscale.

Recently, non-local configurations have been proposed by adding beyond nearest neighbor couplings among elements in lattices to obtain roton-like dispersion relations and phase and group velocities with opposite signs. Even though the introduction of non-local elastic links in metamaterials has unlocked unprecedented possibilities, literature models and prototypes seem neither to provide criteria to compare local and non-local lattices nor to discuss any related rules governing the transition between the two configurations. A physically reasonable principle that monoatomic one-dimensional chains must obey to pass from single- to multi-connected systems is here proposed through a mass conservation law for elastic springs thereby introducing a suitable real dimensionless parameter α to tune stiffness distribution. Therefore, the dispersion relations as a function of α and of the degree of non-locality P are derived analytically, demonstrating that the proposed principle can be rather interpreted as a general mechanical consistency condition to preserve proper dynamics, involving the spring-to-bead mass ratio.
The proposed principle will be applied to 2D lattices and nonlinear lattices to explore its further implications.