Dynamic response and mechanism of mitigation and energy absorption of sandwich beams with a mechanical metamaterial core of negative Poisson’s ratio subjected to high-velocity impact of granular slug
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摘要: 建立了颗粒流子弹发射有限元模型，利用离散元和有限元的联合模拟方法，研究了高速颗粒流冲击负泊松比内凹蜂窝夹芯梁的动态响应及缓冲吸能机理。分析了加载冲量、冲击角、芯材强度以及颗粒流子弹与面板间的摩擦力等因素对夹芯梁动态响应的影响。研究结果表明：夹芯梁在正向颗粒流子弹冲击载荷作用下表现为局部凹陷和整体弯曲的耦合变形模式，面内设计芯材因胞壁弯曲呈现局部内凹的变形模式，面外设计芯材因胞壁屈曲呈现局部褶皱的变形模式。在等面密度的条件下，采用面外设计的硬芯夹芯梁面板的跨中最大挠度比采用面内设计的软芯夹芯梁小，但初始冲击力峰值和冲击力整体水平较高，冲击力响应时间较短。夹芯梁前后面板的跨中最大挠度与冲击载荷近似呈对数线性递增关系。与正向冲击相比，斜冲击下夹芯梁的变形模式具有非对称性，局部凹陷程度减小；在颗粒流子弹不同冲击角度作用下，夹芯梁前后面板的跨中最大挠度、初始冲击力峰值以及传递到夹芯梁的动能和动量占比随冲击角度的增大而减小，而颗粒流子弹与夹芯梁面板间的摩擦因数对夹芯梁的动态响应无显著影响。Abstract: In this paper, a finite element model of the granular slug launcher was constructed. Using the discrete element-finite element coupling method, the dynamic response and mechanism of mitigation and energy absorption of sandwich beams with reentrant honeycomb core of negative Poisson’s ratio subject to high velocity granular slugs were investigated. Effects of the load impulse, impact angle, core strengths and friction between the granular slug and face sheets on dynamic response of sandwich beams were analyzed. The results demonstrated that the active deformation mode of sandwich beam subject to the normal impact of the granular slug is combined local denting and overall bending. The deformation mode of the sandwich in-plane core is local denting mode due to the bending of cell walls, whilst the sandwich out-plane core is local folding mode due to buckling of the cell walls. Compared to the same areal density of the sandwich beam with the in-plane design of the soft core, the deflections of the sandwich beam with the out-of-plane design of the hard core are smaller but both its initial peak and level of impact force are higher and its response time is shorter. The mid-span maximum deflections of front and rear face sheets of the sandwich beam increase with the impact loading approximately log-linearly. Compared to the normal impact, the deformation mode of the sandwich beam subject to the oblique impact is asymmetrical and the local denting area reduced. The mid-span maximum deflections of the front and rear face sheets, the initial peak of impact force and the proportions of kinetic energy and momentum transferred to the sandwich beams subject to velocity granular slug with different impact angles decrease with the increase of the impact angles, while the friction between the granular slug and the face sheets has little effect on dynamic response of sandwich beams.
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图 9 颗粒流子弹正向冲击下夹芯梁的变形（vp=150 m/s）
Figure 9. Deformation of sandwich beam under normal impact of granular slug (vp=150 m/s)
图 14 颗粒流子弹速度时程曲线（vp =150 m/s）
Figure 14. Velocity of granular slug versus time (vp =150 m/s)
图 15 夹芯梁前后面板跨中最大挠度与不同冲量间的关系
Figure 15. Maximum mid-span deflections of face sheets versus impulse
图 16 冲击角为45 °时夹芯梁的变形（vp=150 m/s）
Figure 16. Deformation of sandwich beam (vp=150 m/s,
$ \theta = $ 45°)
图 20 面板跨中最大挠度与冲击角的关系
Figure 20. Maximum mid-span deflections of face sheets versus impact angle
图 23 颗粒流子弹剩余动能占比与冲击角的关系
Figure 23. Relationship between residual kinetic energy proportion and impact angle
图 25 夹芯梁吸收能量占比与冲击角的关系
Figure 25. Relationship between absorbed energy proportion and impact angle
图 27 颗粒流子弹剩余动量、偏转动量占比与冲击角度的关系
Figure 27. Relationships of proportion of residual momentum and proportion of deflection momentum with impact angle
图 29 夹芯梁动量占比与冲击角的关系
Figure 29. Relationship between proportion of momentum and impact angle
图 30 摩擦因数与面板跨中最大扰度的关系
Figure 30. Maximum mid-span deflections of face sheets versus friction coefficients
图 31 芯材面外布置的夹芯梁的变形（vp=150 m/s）
Figure 31. Deformation of sandwich beam with out-of-plane honeycomb core (vp=150 m/s)
图 34 芯材面内和面外布置夹芯梁的跨中挠度时程曲线
Figure 34. Mid-span deflections of sandwich beams with in-plane and out-of-plane honeycomb cores versus time
图 35 芯材面内和面外布置夹芯梁的冲击力时程曲线
Figure 35. Impact forces of sandwich beams with in-plane and out-of-plane honeycomb cores versus time
表 1 颗粒流子弹不同加载冲量
Table 1. Different impulses of granular slug
vp/(m·s−1) v0/(m·s−1) I0/(kN·s·m−2) 120 133.03 23.70 130 143.09 25.50 140 153.03 27.27 150 162.93 29.03 
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