Two mechanical metamaterials based on fragmentation-reconstitution (FR) deformation mechanism are designed herein not only to establish the condition of Poisson's ratio discontinuity but also to offer a simpler, and hence a technically more feasible, FR metamaterial. Each metamaterial consists of interconnected rigid rhombi with slits within every rhombus such that prescription of on-axis strain would fragment each rhombus unit into six sub-units, while a reversal of the strain would reconstitute every six sub-units into a single rhombus. By geometrical construction, the Poisson's ratio expressions of both metamaterials were developed for infinitesimal and finite deformations. Results show that each metamaterial has no unique Poisson's ratio at the original state, but instead has two distinct Poisson's ratio, with a consolidated value of −1 under compression but abruptly jumps to other values under tension. The observations made for these metamaterials suggest that each of them can behave as two different materials under tension and compression, thereby enabling them to function in ways that cannot be achieved by other materials and metamaterials.
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