Exploiting graded auxeticity for tunable tension-induced out-of-plane buckling in elastic plates for shape morphing

Plates with negative Poisson’s ratios exhibit unconventional mechanical responses; however, the stability behaviour of plates with spatially graded auxeticity remains largely unexplored. This study investigates the linear out-of-plane buckling behaviour of graded auxetic plates subjected to in-plane tensile loading. It is shown that spatial variation in Poisson’s ratio induces internal compressive stress fields under tension, which can trigger out-of-plane buckling despite the absence of externally applied compression. An analytical buckling framework is developed to quantify the critical buckling strain and associated mode shapes as functions of the auxeticity gradient. The analysis reveals that both the onset of buckling and the spatial characteristics of the buckling modes are governed by the internally generated compressive stresses arising from Poisson’s ratio mismatch. Finite element simulations of continuum and lattice-based plate models, together with experiments on additively manufactured graded auxetic sheets, are used to validate the analytical predictions. The results demonstrate that graded auxeticity provides a tunable mechanism for enabling tension-induced out-of-plane buckling, including the localization of compression, the critical strain, and the selected buckling mode. These findings establish a mechanical basis for exploiting spatial auxetic gradients to program instability-driven shape forming in latticed structures. • Tension triggers out-of-plane buckling in plates with graded auxeticity. • Poisson’s ratio mismatch induces internal compressive stress fields. • Analytical model for tension-induced buckling driven by graded auxeticity. • Buckling patterns are programmable via spatial design of auxetic gradients. • Theory is validated by FEA and experiments on 3D printed lattice sheets.