Developing a Multiscale Reduced-Order Model for Non-Linear Buckling of Auxetic Sandwich Beams Using Variational Asymptotic Method

The current work presents a novel multiscale reduced-order modelling frame- work for predicting the non-linear buckling behaviour of composite sandwich beams with auxetic cores using the Variational Asymptotic Method (VAM). The methodology integrates Variational Asymptotic Homogenisation (VAH) to compute equivalent mechanical properties of auxetic microstructures with dimensional reduction techniques for efficient macro-scale analysis. A sys- tematic parametric study investigates the influence of auxetic core geometries such as Anti-tetrachiral, Cross-chiral (Missing-rib), and Re-entrant configura- tions with varying unit cell dimensions (5.00 mm to 12.50 mm) on buckling performance. Results demonstrate that Re-entrant cores exhibit superior buckling resistance, achieving critical loads of 14,020 N for sandwich beams, approximately 1.95 to 2.75 times higher than the other auxetic configura- tions considered in the present study. The proposed model shows excellent agreement with 3D finite element analysis, with only 1.09% deviation, while reducing computational time by 73.4%. The study provides an validated high fedility multiscale reduced order model for carrying out extensive optimisation studies to optimise the buckling behaviour of sandwich beams with auxetic cores.