Condensed Matter Seminar: Describing non-linear elastic meta-materials with elastic charges

Elastic metamaterials are solids composed of patterned elastic building blocks. The spatial arrangement of the building blocks endows the metamaterial with unusual mechanical properties such as a negative Poisson ratio and strong screening of elastic fields. We describe a novel formalism of understanding these systems, using an analogy with electrostatics and building on recent developments in a nonlinear geometric formulation of elasticity. The formalism maps the elastic problem into that of nonlinear interaction of elastic charges, offering a physically intuitive and quantitatively accurate conceptual framework which explains the linear response, the onset of mechanical instability, some aspects of the post-instability state, and screening of topological defects (disclinations).