Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Getreidemarkt 9, A-1060, Vienna, Austria.
ARTORG Center for Biomedical Engineering Research, University of Bern, Stauffacherstr. 78, CH-3014, Bern, Switzerland.
Int J Numer Method Biomed Eng. 2019 May;35(5):e3188. doi: 10.1002/cnm.3188. Epub 2019 Mar 13.
Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.
均匀化有限元（FE）分析能够预测与骨质疏松症相关的骨折，并在临床应用中变得有用。FE 分析的预测取决于表观、非均匀、各向异性、弹性和屈服材料特性，这些特性通常是通过对小梁骨进行隐式微有限元（μFE）分析来确定的。本研究的目的是探索一种显式 μFE 方法来确定小梁骨的表观屈服后行为，超越弹性和屈服特性。骨组织的材料行为通过弹塑性描述，采用 von Mises 屈服准则，并通过平面帽关闭，以区分拉伸和压缩中的屈服后行为。为了触发元素删除并再现小梁骨的损伤，对拉伸和压缩的两个极限应变进行了校准。进行了收敛性分析以评估网格的作用。使用周期性兼容的混合均匀边界条件应用了十三个载荷情况，以对三个体积分数不断增加的人小梁骨样本进行分析。研究了大应变中致密化的影响。收敛性研究表明，表观极限应力和应变强烈依赖于单元尺寸。成功地在归一化应力空间中拟合了小梁骨的表观二次强度表面。再现了致密化的影响，并与以前的实验结果很好地相关。本研究表明，显式 FE 公式和单元删除技术具有通过 μFE 分析再现小梁骨损伤的潜力。对于实际计算时间，适当考虑网格敏感性仍然具有挑战性。
