Auxetic mechanical metamaterials for strain amplification

Abstract

Mechanical metamaterials can amplify deformation through geometry-driven mechanisms, transforming small global strains into localized regions of enhanced strain without altering the constituent material. This capability is attractive for applications requiring controlled deformation and mechanical responsiveness, including sensing, actuation, energy harvesting, and adaptive structures. Although numerous auxetic lattice architectures have been proposed, their reported mechanical performances are difficult to compare because previous studies have employed different material models, geometric definitions, loading conditions, and evaluation methodologies. Consequently, quantitative design guidelines for selecting the most appropriate architecture remain limited. This study addresses this gap through a unified finite element framework that systematically compares four representative auxetic lattice architectures (re-entrant, star-shaped, arrowheaded, and chiral) under identical material properties, geometric scaling, boundary conditions, loading conditions, and performance metrics. A hyperelastic poly(butylene adipate-co-terephthalate) constitutive model was used to investigate 36 geometric configurations by varying cell angle and structural thickness. Mechanical performance was evaluated in terms of strain amplification factor (SAF), effective Poisson's ratio, effective stiffness, stress distribution, and relative density. The results reveal pronounced architecture-dependent trade-offs, with lattice topology producing nearly a six-fold variation in strain amplification (SAF ≈ 1.4–8). The star-shaped and re-entrant lattices achieved the highest strain amplification, whereas the arrowheaded lattice consistently exhibited the lowest strain amplification but the highest stiffness and most negative effective Poisson's ratio. The resulting Ashby-style performance maps are reported to establish a quantitative design framework for balancing strain amplification, auxeticity, stiffness, and lightweighting, providing practical guidance for selecting auxetic lattice architectures according to application-specific mechanical requirements.