三维负泊松比超材料拓扑优化设计

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Topology optimization for 3D metamaterials with negative Poisson's ratio

HU Tiannan1， GUO Honghu² （1. DepartmentofechanicalEngneeringandience，Kyoto UnversityKyoto6553o，Jan;2.Facultyofied Engineering， Waseda University， Kyoto l69-8555， Japan）

Abstract： Negative Poisson's ratio metamaterials have significant application potential in aerospace， biomedical engineering， and flexible electronics due to their anomalous mechanical behavior of expanding laterally under tension and contracting laterally under compression. However， existing research predominantly focuses on 2D or 3D isotropic designs， which struggle to meet practical engineering demands for direction-dependent material properties. This paper proposed a density-based topology optimization method for designing 3D orthotropic negative Poisson's ratio metamaterials. By constructing a novel multi-objective optimization function combined with homogenization theory， negative Poisson's ratio characteristics in three orthogonal directions for unit cell structures was achieved. First， based on the SIMP （solid isotropic material with penalization） material interpolation model， geometric constraints were introduced to ensure unit cell symmetry while eectively reducing computational scale. Second， a new objective function and optimization model were established through penalty functions. Finally， the equivalent mechanical properties were calculated using finite element homogenization under periodic boundary conditions， with design variables updated through sensitivity analysis. Numerical examples demonstrate that the optimized unit cells exhibit negative Poisson's ratio behavior in all three principal directions. This study provides a theoretical foundation for the controllable fabrication of 3D orthotropic auxetic metamaterials and expands the design and application scope of mechanical metamaterials.

Keywords： topology optimization; negative Poisson's ratio; metamaterial; homogenization method; density method

负泊松比材料作为一种力学超材料，因其在单轴载荷下呈现反常的横向变形行为（拉伸时横向膨胀，压缩时横向收缩），近年来在航空航天、生物医学、防护装备及智能传感器等领域展现出广阔的应用前景[1]。（剩余10139字）