Harnessing topology and nonlinearity for advanced elastic wave control

In this talk we will investigate structures for advanced control of elastic waves using concepts and tools from topological materials and nonlinear dynamics. This line of research has practical applications in the design of robust elastic wave devices. In addition, it has potential for reconfiguring flexible elastic materials and proposing wave-driven mechanisms for soft robotics.

The first part of the talk will focus on topological mechanics. The recent discovery of topological materials in condensed matter physics has led to the emergence of a new notion of topology associated with the intrinsic wave dispersion of a structure. As a result, numerous mechanical designs have been developed that exhibit non-trivial and robust energy localisation. This talk will give a brief overview of the different classes of topological mechanical metamaterials, and then present a new family of finite-frequency mechanical metamaterials that we have recently introduced. Here, robust topological properties appear in deformation coordinates, while topological edge waves appear for free boundaries.

The second part of the talk will focus on the nonlinear dynamics of flexible elastic metamaterials. Flexible elastic metamaterials (flexEMs) are defined as engineered structures that can deform substantially, repeatedly and reversibly. Although recent advances have improved our understanding of the quasi-static mechanical properties of flexEMs, there are not many studies on their nonlinear dynamic response. In this talk, two types of flexEMs will be presented. One consisting of (i) rotating rigid units (particles of different shapes) coupled with soft elastic elements and (ii) a lattice of coupled buckled beams, a bistable mechanical metamaterial. Using various analytical and numerical techniques, we were able to find a variety of nonlinear wave solutions, including solitons, breathers and wave extreme events, that can be supported by these types of flexEMs.