Liens transverses ENS de Lyon

Agenda de l'ENS de Lyon

Topological rigidity of mechanical metamaterials

ven 23 sep 2022



Soutenance de thèse de M. GUZMAN JARA Marcelo Andres sous la Direction de M. BARTOLO Denis

Langue(s) des interventions

Description générale

What explains the rigidity of a material? The answer, in most cases, lies in the microscopic stiffness of their components. However, in the 18th century, Maxwell understood that materials made of stiff constituents may exhibit soft modes depending on a macroscopic quantity: the number of degrees of freedom and constraints. Two centuries later we can understand this softness as a topological property. This thesis explores the concept of rigidity from a topological lens. First, I explore the consequences of Maxwell’s realization on networks of beads and springs. These systems enjoy an often overlooked symmetry known as chiral symmetry. I exploit this symmetry to define a new material property, the chiral polarization, encoding both the geometry and topology of the material. It distinguishes between distinct topological phases and also probes their softness by locating zero-energy modes. We confirm these findings by experimentally measuring the chiral polarization on several mechanical metamaterials.

In the second part, I explore the connection between a different topological property, nonorientability, and the location of highly stiff regions in an otherwise homogeneous system. Inspired by the connection between global frustration and non-orientability, we establish a unifying framework describing seemingly distinct mechanical metamaterials. Their common denominator corresponds to the non-orientability of their deformation bundles. Through experiments and simulations, we confirm the existence of highly stiff nodes and lines, and their non-commutative response, paving the way to designing robust and functional mechanical metamaterials.

Mots clés