Design of Auxetic Metamaterials via Adaptive Body-Fitted Mesh-Based Bi-Directional Evolutionary Structural Optimization

Fixed-grid topology optimization is widely used for auxetic metamaterial design, but its discretization-dependent boundaries may require substantial refinement or post-processing, potentially altering slender ligaments and the resulting deformation mechanisms. This study develops an adaptive body-fitted bi-directional evolutionary structural optimization (BESO) framework for two-dimensional periodic auxetic metamaterials. The topology is persistently represented by an implicit field on a fixed background grid, while a geometry-conforming T6 finite-element mesh is regenerated for periodic homogenization at each iteration. Mutual-energy sensitivities are normalized by element area and transferred from the nonuniform analysis mesh back to the background design field, enabling stable evolutionary updates under repeated remeshing. The adaptive workflow reconstructs the boundary within the optimization loop, avoiding a separate post-optimization B-spline smoothing step; in the fixed-grid Q4 comparison, this smoothing reduces the magnitude of the Poisson’s ratio. The mesh-parameter study shows how the adaptive mesh-size ratio affects computational time and the optimized auxetic response. In the tested comparison, the adaptive workflow shows closer agreement between the optimized and independently verified Poisson’s ratios.