Elastic measurements on macroscopic three-dimensional pentamode metamaterials

Pentamode metamaterials approximate tailorable artificial liquids. Recently, microscopic versions of these intricate three-dimensional structures have been fabricated, but direct experimental characterization has not been possible yet. Here, using three-dimensional printing, we fabricate macroscopic polymer-based samples with many different combinations of the small connection diameter $d$ and the lattice constant $a$. Direct measurements of the static shear modulus and the Young's modulus reveal that both scale approximately according to $(d/a)^3$, in good agreement with continuum-mechanics calculations. For the smallest accessible values of $d/a \approx 1.5\%$, we find derived ratios of bulk modulus $B$ to shear modulus $G$ of $B/G \approx 1000$.