A parametric class of composites with a large achievable range of effective elastic properties

In this paper, we study an instance of the G-closure problem for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two isotropic materials. We focus on the case when one material has zero stiffness, i.e., single-material structures with voids. This problem is important, in particular, in the context of designing small-scale structures for metamaterials that can be manufactured using additive fabrication. A range of effective metamaterial properties can be obtained this way using a single base material.