Elastic waves in complex media

Extreme wave phenomena in flexible elastic metamaterials

A flexible elastic meta-lattice allowing the observation of solitary waves

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. We are working with two types of flexEMs. 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 several nonlinear wave solutions, including solitons, breathers and wave extreme events, that can be supported by these types of flexEMs.

Related publications:

• https://www.sciencedirect.com/science/article/pii/S2352431624000798
• https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.054212

Dynamical mechanical instabilities

Slender structures can undergo different forms of mechanical instabilities, leading to potentially large and rapid deformation of the object. For a long time, they have been regarded as detrimental-one would rather not use a bridge that buckles!-, but over the last 20 years this opinion have shifted. Mechanical instabilities can be indeed be used to pattern a surface, achieve large or rapid motion, as illustrated in different natural processes, from the shape of living tissues to the fast motion of carnivorous plants. Now, these nonlinear phenomena are more and more used in manufactured objects, at low scales in MEMS, or in flexible metamaterials to achieve exotic properties. It is therefore important to understand instabilities and find ways to control their characteristics. To do so we investigate how dynamics affect the instabilities. We have shown how rapid actuation allows to lower the instability threshold and generates complex dynamics in the structure. More generally, we are interested in dynamically triggered instabilities as well as dynamics of the instability itself.

Chronophotography of a snap-through instability in a beam

Space & time-dependent soft structures

Parametric instability in a soft stripAnother spectacular mechanical instability occurs when a string undergoes a temporal modulation of its tension. As evidenced in the XIXth century by Franz Melde, such a string exhibits large transverse deformations together with a marked sub-harmonic response. We have recently evidenced an atypical response emerging in the case of a very soft string. These results highlight the rich physics of systems for which the modulation becomes spatio-temporal. Our group investigates the nonlinear dynamics of soft structures (string, strips, plates and lattices).

Topology & nonlinearity

We investigate structures for advanced control of elastic waves using concepts and tools from topological materials and nonlinear dynamics. 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 localization. However, the great majority of these works is limited in the linear regime. Using analytical, continuation and bifurcation techniques, we have studied the interplay of nonlinearity and topology, revealing new nonlinear topological solutions and self-induced topological transitions. In addition, recently we have introduced a new family of finite-frequency mechanical metamaterials. Here, robust topological properties appear in deformation coordinates, while topological edge waves appear for free boundaries. 

Robust wave guiding process powered by topological insulationRelated publications:

• https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.21.024049
• https://www.nature.com/articles/s41467-023-42321-3
• https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054224