In-plane dynamic mechanical properties of partially liquid filled multicell structure
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摘要: 为探究部分充液多胞元结构的抗冲击防护性能，结合充液内凹胞元的落锤冲击试验，建立了充液内凹胞元、部分充液内凹多胞元结构的冲击动态特性二维FEM数值分析，计算得到了部分充液内凹多胞元结构的变形破坏模式，讨论了不同冲击速度下部分充液内凹多胞元结构的动力学响应特性。结果表明：在充液胞元破损后，水介质会流入相邻未充液胞元，形成二次鼓胀吸能效应，从而有效提高结构壁面的变形吸能水平；结构中的充液区域和未充液区域的变形破坏模式分别为鼓胀拉伸和屈曲弯折；随着冲击速度的提高，结构的单位体积应变能以及对初始冲击载荷的削弱作用均得到增强。横向充液方式可以等效为变刚度弹簧的串联布置，该方式仅影响结构的局部刚度，纵向充液方式可以等效为多层变刚度弹簧的并联布置，该方式会影响结构的整体刚度；充液区域与未充液区域的等效刚度呈动态变化，结构变形模式由各区域实时的等效刚度决定。当载荷冲击速度较高时，横向和纵向部分充液内凹多胞元结构对初始冲击载荷的削弱能力均优于未充液内凹多胞元结构。Abstract: In order to investigate the impact protection performance of partially liquid filled multicell structure, the two-dimensional FEM numerical analysis of the impact dynamic characteristics of liquid filled inner concave cell structure, unfilled inner concave cell structure, partially liquid filled inner concave multicell structure and unfilled inner concave multicell structure was established by combining the drop hammer impact test of liquid filled and unfilled inner concave cell structure. The deformation/failure mode of partially liquid filled inner concave multicell structure was obtained, and the dynamic response characteristics and energy absorption characteristics of partially liquid filled inner concave multicell structures at different impact velocities were discussed by using the initial load weakening factor and the strain energy per unit volume, respectively. The results show that after the breakage of the liquid filled cell, the water medium will flow into the adjacent unfilled cell, developing a secondary bulging energy absorption effect, thus effectively increasing the deformation energy absorption level of the structure wall; the deformation damage modes of the liquid filled and unfilled regions of the structure are bulging tension and flexural bending, respectively; the strain energy per unit volume of the structure and the weakening effect on the initial impact load are enhanced with the increase of the impact velocity. The transverse filling method can be equated with tandem arrangement of variable stiffness springs, which only affects the local stiffness of the structure. And the longitudinal filling method can be equated with a parallel arrangement of multiple layers of variable stiffness springs, which affects the overall stiffness of the structure; the equivalent stiffness of the filled and unfilled regions changes dynamically, and the deformation mode of the structure is determined by the equivalent stiffness of each region in real time. When the load impact velocity is high, both transverse and longitudinal partially liquid filled inner concave multicell structures are superior to the unfilled inner concave multicell structure in weakening the initial impact load.
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图 2 部分充液内凹多胞元结构的二维有限元模型
Figure 2. Two-dimensional FEM model of partially liquid filled concave multicell structure
图 3 内凹多胞元结构二维有限元模型的有效性验证
Figure 3. Validity verification of two-dimensional FEM model of concave multicell structure
图 4 未充液多胞元结构的典型变形破坏模式
Figure 4. Typical deformation/failure modes of unfilled multicell structures
图 5 横向充液多胞元结构的典型变形破坏模式
Figure 5. Typical deformation/failure modes of transversely liquid filled multicell structures
图 6 横向充液多胞元结构的典型应力-应变曲线
Figure 6. Stress-strain curve of transversely liquid filled multicell structures
图 7 纵向充液多胞元结构的典型变形破坏模式
Figure 7. Typical deformation/failure modes of longitudinally liquid filled multicell structures
图 8 纵向充液多胞元结构的典型应力-应变曲线
Figure 8. Stress-strain curves of longitudinally liquid filled multicell structures
图 9 横向充液多胞元结构接触力时程曲线（充液方式A）
Figure 9. Contact force time course curve of transversely liquid filled multicell structure (method A)
图 10 横向充液多胞元结构接触力时程曲线（充液方式C）
Figure 10. Contact force time course curve of transversely liquid filled multicell structure (method C)
图 11 横向充液多胞元结构接触力时程曲线（充液方式B）
Figure 11. Contact force time course curves of transversely liquid filled multicell structure (method B)
图 12 纵向充液多胞元结构接触力时程曲线（充液方式E）
Figure 12. Contact force time course curve of longitudinally liquid filled multicell structure (method E)
图 13 不同输出频率下纵向充液多胞元结构载荷削弱曲线（充液方式F）
Figure 13. Load dissipation curves of liquid filled multicell structures at different output frequency (method F)
图 14 不同冲击速度下多胞元结构的初始载荷削弱因子（d）
Figure 14. Initial load weakening factors (d) of multicell structures at different impact velocities
图 15 不同冲击速度下多胞元结构的初期平台应力
Figure 15. Initial platform stress of liquid filled multicell structures at different impact velocities
图 16 不同冲击速度下充液多胞元结构的单位体积应变能（e）时程曲线
Figure 16. History of strain energy per unit volume (e) for liquid filled multicell structures at different impact velocities
图 17 充液多胞元结构的典型吸能模式
Figure 17. Typical energy absorption modes of liquid filled multicellular element structures
表 1 水介质模型参数
Table 1. Required parameters for water model
c/（m·s−1） S1 S2 S3 γ0 A EW/（kJ·m−3） V0 1 484 1.979 0 0 0.11 3 0 1 
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表 2 空气模型参数
Table 2. Required parameters for air model
C0 C1 C2 C3 C4 C5 C6 Ea/（kJ·m−3） 0 0 0 0 0.4 0.4 0 253
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表 3 结构模型参数
Table 3. Required parameters for structure model
Rs/（kg·m−3） Es/GPa νs σy/MPa η β C7/s−1 Pc Fs us 7 800 210 0.3 235 0.25 0 0.040 5 5 0.28 0 注：Rs、Es、νs、σ0、η分别为结构的质量密度、杨氏模量、泊松比、屈服应力、切线模量；β为硬化参数，C7和Pc为Cowper-Symonds应变率模型的应变率参数，Fs为侵蚀元素的有效塑性应变，us为速率影响参数。
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表 4 充液内凹胞元的侧壁剩余间距及结构剩余高度
Table 4. Rremaining sidewall spacing and remaining structure height of liquid filled concave cell structure
研究方法 侧壁剩余间距/mm 侧壁剩余间距相对误差% 结构剩余高度/mm 结构剩余高度相对误差 落锤试验（3D扫描） 132.5 − 245.7 − 三维FEM模型 142.2 7.32 247.5 0.73% 二维FEM模型 140.6 6.11 244.8 0.37%
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表 5 未充液内凹胞元的侧壁剩余间距及结构剩余高度
Table 5. Remaining sidewall spacing and remaining structure height of unfilled concave cell structure
研究方法 侧壁剩余间距/mm 侧壁剩余间距相对误差% 结构剩余高度/mm 结构剩余高度相对误差 落锤试验（3D扫描） 108.9 − 227.2 − 三维FEM模型 106.5 2.20 228.5 0.57% 二维FEM模型 103.2 5.23 220.6 2.90%
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表 6 数值分析计算工况
Table 6. Working conditions of numerical simulation
工况 充液方法 充液位置 载荷冲击速度/（m·s−1） 载荷作用时程/ms 工况 充液方法 充液位置 载荷冲击速度/（m·s−1） 载荷作用时程/ms 1 未充液 − 5 96 15 未充液 − 20 24 2 方式A 1和2 5 96 16 方式A 1和2 20 24 3 方式B 3和4 5 96 17 方式B 3和4 20 24 4 方式C 5和6 5 96 18 方式C 5和6 20 24 5 方式D A和L 5 96 19 方式D A和L 20 24 6 方式E C和J 5 96 20 方式E C和J 20 24 7 方式F E和G 5 96 21 方式F E和G 20 24 8 未充液 − 10 48 22 未充液 − 30 16 9 方式A 1和2 10 48 23 方式A 1和2 30 16 10 方式B 3和4 10 48 24 方式B 3和4 30 16 11 方式C 5和6 10 48 25 方式C 5和6 30 16 12 方式D A和L 10 48 26 方式D A和L 30 16 13 方式E C和J 10 48 27 方式E C和J 30 16 14 方式F E和G 10 48 28 方式F E和G 30 16
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