A unified Planar Poisson’s Ratio Design Method (PPRDM) for meiotic metamaterials that exhibit negative compressibility based on a minimal chiral meiotic structure

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Meiotic metamaterials are intricately designed structures characterized by a positive Poisson’s ratio, surpassing the conventional limit of 0.5 observed in natural materials. This exceptional attribute allows them to contract or expand perpendicularly to the applied stretch or compression, respectively. Structures featuring a high positive Poisson’s ratio exhibit a counter-intuitive negative compressibility behavior, holding significant promise for diverse applications spanning various domains. Despite the potential of Poisson’s ratio metamaterials, including auxetic, anepirretic, and meiotic structures, their recent development has been hindered by the lack of efficient design methods. This paper aims to address this limitation, concentrating on the meiotic variant of a minimal 2D auxetic structure recently proposed. We employ a design method incorporating two topological transformations, not only enabling the creation of known meiotic structures but also facilitating the generation of new ones while understanding the impact of chirality. Additionally, the proposed method enables the categorization of these structures into three achiral families that present meiotic behavior and can exhibit negative linear compressibility and three chiral families that possess an auxetic behavior. Only the base chiral structure was found to exhibit a meiotic behavior while being chiral. In an effort to enhance comprehension and standardization, we introduce a naming protocol and define the associated unit cell for these structures. We also delve into the potential of tessellations within this framework. Finally, our study examines meiotic structures from the perspective of surface strain, a more general metrics, linked to the compressibility, providing further insights into their unique mechanical properties. • A chiral meiotic structure is proposed as a base for all planar meiotic metamaterials. • A three step design method is proposed combining two topological transformations. • All known and novel meiotic structures are classified in six groups. • A naming protocol encodes the geometry and chirality of planar meiotic metamaterials. • The surface strain, linked to the compressibility, is proposed as a general metric.

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