Abstract
Negative Poisson's ratio metamaterials, also known as "auxetic" metamaterials, represent a class of mechanical metamaterials with unique mechanical properties: under vertical compressive (tensile) loading, the structure undergoes lateral contraction (expansion). This characteristic is closely related to the topological arrangement of the structure, thus conferring upon negative Poisson's ratio metamaterials broad application prospects across multiple fields. This review will elaborate on the research progress of functional negative Poisson's ratio metamaterials, first presenting recent advances in the static mechanical properties of these metamaterials, including conventional stiffness enhancement, tunable Poisson's ratio, unconventional deformation mechanisms, and the employment of machine learning for tailoring structural properties; second, analyzing the latest developments in functional applications such as impact resistance, blast resistance, vibration control, and others; finally, identifying existing challenges in current research on functional negative Poisson's ratio metamaterials and offering several reference suggestions for future studies.
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Preamble
This paper presents a mathematical framework for machine learning and deep learning methodologies. The theoretical foundation is established through a series of mathematical formulations $ # "%"& $ through $Dvw‘z(cid:255)%tØŒßu˙M(cid:151)£⁄ ~⁄&&(cid:151)’(% ?+?+I@(cid:144)(cid:145)(cid:146)(cid:138)(cid:139) º(cid:236)(cid:237)˙Mt˚¸MO[ØŒßu˙M›(cid:247)$, which describe the core computational models and algorithmic structures.
The proposed approach addresses key challenges in data processing and model optimization. Mathematical expressions $(cid:230)œ(cid:201)(cid:244)Ø(cid:211)(cid:212)bct(cid:201) (cid:148)I(cid:146)‚F% D(cid:147)(cid:148)