The in-plane mechanics of a family of curved 2D lattices

We propose an analytical framework to understand the mechanics and quantify essential elastic properties of two-dimensional hexagonal lattices with curved elements. Generalised closed-form expressions for in-plane Young’s moduli Poisson’s ratios are obtained. It is utmost importance develop physics-based efficient computational models design analysis cellular metamaterials. This paper develops fundamental approaches obtaining generalised capture a large class geometry. The obtained utilising stiffness coefficients constituent structural members unit cell beams. new equivalent then explored investigate seven other unique geometries including two auxetic configurations. Curved beam element as member has significant effect in increasing flexibility lattice it also expands space materials. vary controlled way this favourable feature can be exploited designer values both regular cases. proposed approach provide computationally physically intuitive parametric utilised per requirements considered benchmark results future numerical experimental investigations.