Geometric frustration in mechanical metamaterials

Mechanical metamaterials are structures whose geometry imbues them with mechanical properties different than the stuff from which they are made. Guided by machine learning, computational tools, and old-time human ingenuity, the number of metamaterial designs has exploded in recent years. Despite this, basic questions about the relationship between geometry and mechanical response remain unanswered, in part because of it is difficult to organize the broad range of possible mechanical behaviors in even the simplest mechanical systems.

This talk will introduct a few simple classes of irregular (non-periodic) and regular metamaterials, introducing a framework for understanding their mechanical response in the continuum limit in terms a geometric "fiber" bundle. The "curvature" of this geometric structure governs the global mechanical response, and allows allows for more exotic types of global frustration to emerge.