Convergence behavior of high-resolution finite element models of trabecular bone
Convergence behavior of high-resolution finite element models of trabecular bone
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DOI：
10.1115/1.2800865
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发表时间：
1999-12-01
影响因子：
1.7
通讯作者：
Keaveny, TM
中科院分区：
文献类型：
--
作者：
Niebur, GL;Yuen, JC;Keaveny, TM
有限元模型的收敛行为取决于所用单元的大小、单元多项式阶数以及所施加载荷的复杂性。对于骨小梁的高分辨率模型，结构和密度的变化也可能很重要。本研究的目的是调查这些因素对高分辨率骨小梁模型收敛行为的影响。两个人椎骨和两个牛胫骨骨小梁标本进行建模，在四个分辨率范围从20到80 μ m，并进行压缩和剪切载荷。结果表明，收敛行为取决于两个贷款模式（轴向与剪切）和试样的体积分数。与20 μ m分辨率相比，在40 μ m分辨率下，所有试样的表观杨氏模量差异均小于5%，表观剪切模量差异均小于7%。相比之下，在80 μ m分辨率的表观模量的差异高达41%，这取决于试样测试和加载模式。总的来说，当平均骨小梁厚度与单元尺寸的比值大于4时，表观特性的差异总是小于10%。使用高阶元素并没有改善结果。组织水平参数，如最大主应变没有收敛。组织水平的应变收敛时，认为相对于阈值，但只有当应变在高斯点，而不是元素的质心进行评估。这些研究结果表明，良好的收敛性，可以获得这种建模技术，虽然元素的大小应根据因素，如加载模式，平均小梁厚度，和特定的输出参数的兴趣。
The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 mu m and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both lending mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 mu m resolution, the differences in apparent Young's modulus at 40 mu m resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 mu m resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.