The Geometry of Mechanics

Advances such as 3D printing and self-assembly have revolutionized our ability to build complex structures at small scales. This ability enables us to create artificial structures, called metamaterials, which owe their physical properties not to their chemical composition but to the geometry and interactions among their building blocks. By carefully choosing the shape and layout of building blocks, we can build metamaterials which behave unlike naturally occurring materials. Geometry also plays an important role in the mechanical behavior of thin shells (like ping-pong balls or polymer capsules).

The Paulose group uses the tools of theoretical and computational physics to discover and characterize metamaterials and shell structures with unusual mechanical properties. This REU project will focus on computational explorations of structures with dynamic spring or membrane-like elements, which may stand alone or be coupled together in periodic patterns. The REU student will adapt standard simulation packages in Python, C/C++, or COMSOL to study the response of these structures to external forces and pressures, and use the insights obtained to propose and investigate new structural geometries with potentially interesting response. Investigations may also use 3D printing to build prototypes of promising designs.