Phase contrast mediated switch of auxetic mechanism in composites of infilled re-entrant honeycomb microstructures

Metamaterials are man-made, usually periodically microstructured materials with at least one uncommon property, e.g., auxeticity. Often, their properties are due to their specific microstructural layouts in addition to their constituent materials. In this work, we explore the influence of constituent materials on the effective elasticity of a two-phase composite consisting of a infilled re-entrant honeycomb microstructure. We show that the composite with non-auxetic constituent materials becomes auxetic if the Young's modulus contrast between the two phases exceeds a certain critical value. We reveal the existence of a phase contrast mediated switch of auxetic mechanism — a finding reported for the first time in this paper. If the re-entrant honeycomb phase is stiffer than the filling phase, the auxeticity stems from the conventional re-entrant mechanism, similar to re-entrant honeycomb structures. However, if the re-entrant honeycomb phase is softer than the filling phase, the auxeticity originates from the relative microscopic sliding between adjacent fillings under macroscopic axial loading. Our results provide guidelines on tuning the effective elasticity and the auxeticity of such composites by educated choices of the constituent materials and the underlying microstructural geometry.