Mechanical properties of arc concave honeycomb structure with negative Poisson’s ratio
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摘要: 提出一种可变弧边内凹多胞蜂窝负泊松比结构。利用能量法得到了二维结构的等效泊松比和等效弹性模量的解析公式，讨论了弧角对等效泊松比和等效弹性模量的影响，解析解与有限元结果吻合较好，说明了该方法的有效性。利用ABAQUS研究了三维结构的冲击动力学特性，分析了蜂窝结构受冲击时的变形失效模式，讨论了冲击速度、结构应变和曲边弧角对动应力-应变曲线、能量吸收率和平台应力的影响规律。所得结果为该类机械超材料的冲击变形失效和吸能效果研究提供了力学依据。Abstract: In this paper, a variable arc concave honeycomb structure with negative Poisson’s ratio was proposed. The analytical formulas of the equivalent Poisson’s ratio and the equivalent elastic modulus of the two-dimensional structures were given by energy method. The influences of the arc angle on the equivalent Poisson’s ratio and the equivalent elastic modulus were discussed. The present analytical solution is in agreement with the finite element results, which shows validity of the present method. The three-dimensional structures’ characteristics of the dynamic were studied by ABAQUS, and the deformation failure mode of the whole honeycomb structures under impact was analyzed. The influences of the impact velocity, structural strain and arc angle on the dynamic stress-strain curve, the energy absorption rate and the platform stress were discussed. The results provide a mechanical basis for the analysis of impact deformation failure and energy absorption effect of such mechanical metamaterials.
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图 1 可变弧角弧形内凹负泊松比蜂窝材料胞元
Figure 1. Variable arc angle arc concave negative Poisson's ratio cellular material
θ—Internal angle of arc edge; r—Arc radius; h—Half chord length; m—Length of connecting rod
图 2 弧边内凹蜂窝负泊松比二维结构静力分析图
Figure 2. Static analysis diagram of concave honeycomb 2D structure with negative Poisson's ratio
A-L—Structure of the node; F—Axial force; M0—Bending moment; 1—Unit load
图 3 弧边内凹蜂窝负泊松比二维结构模型结构图
Figure 3. Model structure diagram of arc concave honeycomb 2D structure with negative Poisson's ratio
图 4 弧边内凹蜂窝负泊松比二维结构等效泊松比与弧角的关系
Figure 4. Relationship between equivalent Poisson's ratio and arc angle of arc concave honeycomb 2D structure with negative Poisson's ratio
FEA—Finite element analysis
图 5 弧边内凹蜂窝负泊松比二维结构等效弹性模量与弧角的关系
Figure 5. Relationship between equivalent elastic modulus and arc angle of arc concave honeycomb 2D structure with negative Poisson's ratio
图 6 弧边内凹蜂窝负泊松比三维结构模型
Figure 6. Model diagram of arc concave honeycomb 3D structure with negative Poisson's ratio
图 7 不同冲击速度时弧边内凹蜂窝负泊松比三维结构的变形模式(应变为0.4)
Figure 7. Deformation modes of arc concave honeycomb 3D structure with negative Poisson's ratio at different impact velocities (Strain=0.4)
图 8 胞元弧角30°应变为0.4时弧边内凹蜂窝负泊松比三维结构变形图
Figure 8. Deformation diagram of cell with 30° arc angle and 0.4 strain for arc concave honeycomb 3D structure with negative Poisson's ratio
图 9 弧边内凹蜂窝负泊松比三维胞元变形模式
Figure 9. Three-dimensional cell deformation model of arc concave honeycomb 3D structure with negative Poisson's ratio
图 10 不同冲击速度时弧边内凹蜂窝负泊松比三维结构应力-应变曲线
Figure 10. Stress-strain curves of arc concave honeycomb 3D structure with negative Poisson's ratio at different impact velocities
图 11 不同冲击速度下的弧边内凹蜂窝负泊松比三维结构能量吸收曲线
Figure 11. Energy absorption curves of arc concave honeycomb 3D structure with negative Poisson's ratio at different impact velocities
图 12 弧边内凹蜂窝负泊松比三维结构平台应力随冲击速度的变化
Figure 12. Variation of platform stress with impact velocities of arc concave honeycomb 3D structure with negative Poisson's ratio
图 13 弧边内凹蜂窝负泊松比三维结构平台应力随弧角的变化
Figure 13. Variation of platform stress with arc angles of arc concave honeycomb 3D structure with negative Poisson's ratio
Young's modulus E/GPa Density ρ/(kg·m−3) Poisson's ratio ν 71 2770 0.33 
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