Research Projects

Metamaterials are engineered material systems with unit-cells generally arranged in periodic arrangement at spatial scales which are smaller than the wavelength of the phenomena that they influence. In fact, their property is governed by the structural arrangement of the individual unit-cells and their shape, geometry, size, orientation, interaction law and arrangement give them the capability to manipulate wave propagation. They exhibit unusual magnitudes of the properties like density, bulk modulus, permittivity etc. which are seldom observed in their individual components. The spatial scale of this artificially incorporated structure is designed such that the wavelength of signals or excitations can interact with these microstructures, and consequently affect its macroscopic properties Of the various kinds of metamaterials, an interesting type of metamaterial is the auxetics which exhibit negative Poisson’s ratio. Another variant of the auxetics incorporates rotational degree of freedom at each microstructural unit in such a way that it introduces chirality in the structure. The classical continuum mechanics is seldom applicable in the study chiral auxetic structures. The auxetics and chiral auxetics are interesting owing to their unique deformation kinematics resulting in negative Poisson’s ratios and tailorable effective properties. Chiral auxetics exhibit coupling between bulk deformation and internal rotations which provide them enhanced resistance to local impacts, in-plane orthotropy, tailorable properties. The first part of this research is a detailed parametric study that generalizes and investigates the frequency band structure of this class of structures. The objective is to study a generalized chiral lattice and the effect of geometric parameters on the effective material properties and their bounds. The second part of the research involves a study of the effect on nonlinearity on the material properties and the propagation characteristics. The inclusion of nonlinearities in the interactions would considerably change the frequency band structures and can exhibit additional wave propagation solutions (soliton/solitary waves, breathers, localized modes etc.) which are hitherto not observable in linear structures. The presence of nonlinearity makes the structure more exotic and thereby increase the applicability in wide ranging applications. Finally, we consider the effect of nonlinear locally resonant units in these materials. It is well-known that bandgaps near the natural frequency of these local resonators. However, a nonlinear oscillator can hardly be characterized by a natural frequency since they generally exhibit amplitude/energy dependent natural frequencies. Thus, the dynamic characteristics of this class of structures are essentially energy dependent. This feature of nonlinear system is seemingly complex, but opens a new horizon for exploring tunable metamaterial structures that can be effectively and predictively designed.