His research interests are in the areas of continuum mechanics, mathematical materials science, and applied mathematics and looks at how structural imperfections, or defects, in crystalline materials interact and evolve. Currently, his work focuses on theoretical and computational defect mechanics in crystalline, liquid crystalline, and metallic glass systems, coarse-graining of nonlinear time-dependent systems, and the interplay of differential geometry and structural mechanics in the design and actuation of thin sheets.