The Materials Geometry group at Syracuse University studies the structure and properties of soft materials. We apply tools from geometry and topology to uncover the universal features of material behavior with an eye toward learning to design new materials.

Self-folding structures and 4D printing

4D printing is the process of patterning a flat 2D sheet so that it dynamically folds into a complex 3D structure. We work on developing design tools to study self-folding structures with the goal of realizing this process as a useful fabrication tool.

Designing mechanical metamaterials

Changing the geometrical structure of a material can radically change its properties. We take advantage of this to find ways to design new materials with desired effective mechanical properties. Our goal is to uncover the universal features of this kind of design to inform the connections between geometry and mechanics, and enable the rational or computational design of new materials. This includes both static properties, such as designing tunable mechanical metamaterials whose properties change with environmental conditions, and dynamic properties, where geometry and curvature can be used to guide acoustic waves.

Geometric and topological frustration

In many systems, the geometrical constraints of a material’s local structure are not compatible with global order. Think of how, for example, maps always distort the surface of the Earth no matter how they are drawn. This kind of frustration can lead to the formation of defects or control their self-assembly, and features prominently in biology from the sub-cellular scale to the organismal scale. We want to uncover the general principles behind how geometric frustration organizes structures or leads to disorder.

Funding: Our research is funded mostly by the National Science Foundation and in part by the Department of Defense and Syracuse University.