Screening of topological defects in elastic metamaterials

Elastic metamaterials are solids composed of patterned elastic building blocks. The spatial arrangement of the building blocks endows the metamaterial with unusual mechanical properties. For example, elastic sheets with periodically patterned holes have been shown to exhibit negative Poisson ratio as well as other unusual mechanical properties. Here we demonstrate experimentally, and describe analytically, an exotic mechanical response of two dimensional elastic metamaterials - screening of the long-range elastic fields induced by topological defects (disclinations). We find two forms of screening – at low porosities we observe linear screening whose strength depends on the porosity of the sheet. At higher porosities non-linear screening occurs, mediated by a reversible collapse of the holes. We further demonstrate that the recently-suggested theoretical framework of elastic charges in non-Euclidean elasticity well describes the observed linear screening effects. We discuss the limitations of the linearity assumptions, the influence of lattice symmetry of the hole pattern, and provide insights regarding the nonlinear screening behavior which requires going beyond the linear elasticity regime.