Dynamic impact on the rabbit spine single vertebral body: finite element analysis of the stress distribution of the vertebral body with different impact rates, mesh numbers and material properties

doi:10.3969/j.issn.2095-4344.1417

Abstract

Abstract:

BACKGROUND: Car accidents and falling from high altitudes occur from time to time, most of which cause severe spinal injuries. Therefore, it is important to study the damage characteristics of the spine under impact load. It also provides a biomechanical basis for injury protection and repair of the spine.

OBJECTIVE: The finite element analysis method was used to analyze the damage characteristics and regularity of the single vertebral body of rabbit under impact load, and the effects of different impact velocities, mesh numbers and material properties on the stress distribution of the vertebral body were analyzed. These provided the basis for the dynamic impact test of single vertebral body and the segmental experiment and simulation analysis of the spine.

METHODS: The finite element model of rabbit single vertebral T₁₂was established by Mimics, HyperMesh and Abaqus. First, the sensitivity analysis of the mesh was carried out to select the appropriate number of meshes. Finite element analysis and simulation of vertical impact on vertebral bodies were conducted at different impact velocities. Stress distribution of vertebral body in osteoporotic patients under impact loading was simulated by adjusting the numerical value of material properties. The model was validated by a single vertebral impact test in rabbits.

RESULTS AND CONCLUSION: (1) Through sensitivity analysis, it was found that when the number of grids was 74 224, the results of finite element analysis were much more reasonable than those of other grids. Therefore, the analysis was based on the premise of the number of grids 74 224. Vertebral material like most brittle materials, a 45° angle of failure could occur when subjected to vertical loads. The maximum stress value was mainly concentrated at the two ends of the vertebral body. The direction of stress transmission was consistent with the trend of the trabecular bone. (2) It is concluded that the appropriate number of grids was selected by sensitivity analysis, which makes the results of finite element analysis more reliable. The reliability of the finite element model was verified by experimental verification. The results of finite element analysis can reflect the true situation of the vertebral body under different impact velocities and osteoporotic vertebral body under impact. The finite element analysis method is economical and has strong control and applicability; and the parameters are easy to adjust.

Key words: single vertebra, impact, finite element analysis, damage, speed, drop hammer, impact test, biomechanics

CLC Number:

Han Shibing, Zhang Xushu, Guo Yuan, Du Yiming. Dynamic impact on the rabbit spine single vertebral body: finite element analysis of the stress distribution of the vertebral body with different impact rates, mesh numbers and material properties [J]. Chinese Journal of Tissue Engineering Research, 2019, 23(30): 4828-4835.

Figures/Tables 6

2.2.2 von Mises应力分布以10.0 m/s的von Mises应力云图为例，获得T12在冲击载荷下的应力分布，横截面如图7所示。截面内von Mises应力极值出现在上下两端即A、B处，C处为椎体内部应力最大值，椎体内部其他区域的应力值较小。因此，椎体T12在受到冲击载荷时其应力传递方式是上下两端受到冲击载荷，应力达到极值，然后应力值沿AB轴线向椎体内部逐渐增大，在椎体内部C处达到最大值，最后以C点为中心，再沿DE方向，水平向椎体外侧逐渐增大。 2.2.3 位移云图分布特点以4.4，6.0，7.5，9.0 m/s为例，分析了椎体在0.03 s时椎体的整体位移。通过图8可发现4种冲击速率下整体位移的最大值分别为2.934，4.109，5.972，7.750 mm，且最大值的位置都位于椎体上端。通过位移云图可发现椎体有明显的分界线并与轴线呈45°角，而分界线的位置就是椎体破坏的位置，在前期静态压缩实验中也有类似的结果。 2.2.4 特征点O在竖直方向上的Stress components应力-时间曲线分析特征点O在竖直方向上Stress components应力随时间变化的曲线，如图9所示。通过曲线可以发现特征点O处的单元在椎体受到冲击的瞬间应力达到最大值，在速率较小时最大值与冲击速率成正比，除 4.4 m/s外，其他冲击速率下的极值均在22.5 MPa左右，然后应力随后开始减小，并趋于一个稳定的值。 2.3 不同材料属性对椎体应力的影响 2.3.1 不同材料属性对轴向应力与位移的影响不同材料属性对轴向应力与位移的影响见图10所示，从图中可发现轴向应力与密度、弹性模量呈正相关关系，随着密度、弹性模量的增加其所承受的轴向应力也逐渐增加。而材料属性变化对轴向位移的影响则是随着材料密的减小，轴向位移则是先减小，后逐渐增大，约80%时为最小值。而且当密度、弹性模量较小时的轴向位移更大，当材料密度为原来的60%，70%时的轴向位移远大于100%时的轴向位移。 2.3.2 不同材料属性对特征点O处的影响以冲击速率7.5 m/s为例，不同材料属性下特征点O的应力-时间曲线如图11所示。通过分析曲线可发现不同的材料属性对特征点处的应力影响不明显。 2.3.3 不同材料属性对整体位移云图的影响以t=0.01 s时的受力为例，不同材料属性下的整体位移云图如图12所示，通过位移云图可以发现，不同材料属性下的位移云图变化较为明显，从100%到60%的5种材料属性下的位移最大值分别为4.648，4.927，4.766，4.625，4.859 mm，可见材料属性的不同对位移云图的影响较大。 2.4 实验验证根据有限元不同冲击速率对椎体应力和位移的影响得出：在7 J的冲击能量下椎体已发生完全破坏，因此在Instron CEAST 9350落地式落锤试验机上对单椎体T12进行落锤冲击实验，冲击能量为7 J，实验冲头重400.3 g，冲击设备除冲头外还包括传感器，总质量 5.925 3 kg，根据牛顿第二定律可得出冲击速度为1.5 m/s。冲击效果如图13所示。有限元模拟与实验的载荷-时间曲线的对比图如图14所示，通过对比图可发现从0-0.005 s内实验的载荷曲线和有限元的载荷曲线趋势相同，主要经历了2个阶段，下关节突和椎弓的破坏为第1个阶段，第2个阶段为椎体的破坏。2个曲线图虽然趋势相同但在细节方面存在一点差异，例如载荷的大小和时间节点的对应。造成差异的主要原因是：首先，有限元模拟和分析尽可能还原实验状态但仍存在一些差异，一个是冲击载荷，有限元冲击的冲头为5 kg，冲击速度为1 m/s，相对于实验环境冲击载荷较小；其次，有限元分析设置材料属性与实验时椎体有一定的差异，由于目前国内外现有的研究资料中缺乏新西兰大白兔椎体的材料属性经验公式，而实验有限元模型的材料属性参考人股骨的经验公式，导致材料的杨氏模量变大，因此有限元分析的结果略大于实验的结果；最后，实验中冲击能量过大，导致椎体变形过大，变形程度达到90%以上，因此载荷作用时间较长，而有限元分析为简化模型，作用时间较短，椎体变形程度不足50%，因此载荷作用时间较短。在实际生活中，脊柱的椎骨受到肌肉、韧带、椎间盘等软组织的保护，椎骨变形不会达到实验中的情况，因此分析前2个峰值的变形即可。"

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