三維負(fù)泊松比超材料拓?fù)鋬?yōu)化設(shè)計(jì)

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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

負(fù)泊松比材料作為一種力學(xué)超材料，因其在單軸載荷下呈現(xiàn)反常的橫向變形行為（拉伸時橫向膨脹，壓縮時橫向收縮），近年來在航空航天、生物醫(yī)學(xué)、防護(hù)裝備及智能傳感器等領(lǐng)域展現(xiàn)出廣闊的應(yīng)用前景[1]。（剩余10139字）