Mechanical metamaterials are many-body elastic systems that deform in unusual ways, due to the interactions of nearly rigid building blocks. Examples include origami patterns with many folds, or kirigami patterns made by cutting material from an elastic sheet. In either case, the local deformations of the pattern involve internal degrees of freedom which must be matched with the usual global Euclidean invariances — e.g., groups of origami panels move by coordinated rotations and translations, but it is still possible to bend the whole pattern into a curved shape. This talk will introduce the homogenization problem for kirigami and origami metamaterials to a broad audience, and describe our recent results. Our goal is to explain the link between the design of the individual cuts/folds and the bulk deformations they produce. This is joint work with Paul Plucinsky (U. Southern California, Aerospace and Mechanical Engineering) and Paolo Celli (Stony Brook U., Civil Engineering).

This talk will be mathematically self-contained, not assuming a background in elasticity.

Event will be in-person and on Zoom: https://umich.zoom.us/j/98734707290