Keyak J H, Rossi S A
Department of Orthopaedic Surgery, University of California, Irvine Medical Center, Orange 92868-5382, USA.
J Biomech. 2000 Feb;33(2):209-14. doi: 10.1016/s0021-9290(99)00152-9.
Finite element (FE) models are often used to model bone failure. However, no failure theory for bone has been validated at this time. In this study, we examined the performance of nine stress- and strain-based failure theories, six of which could account for differences in tensile and compressive material strengths. The distortion energy, Hoffman and a strain-based Hoffman analog, maximum normal stress, maximum normal strain, maximum shear strain, maximum shear stress (tau(max)), Coulomb-Mohr, and modified Mohr failure theories were evaluated using automatically generated, computed tomographic scan-based FE models of the femur. Eighteen matched pairs of proximal femora were examined in two load configurations, one approximating joint loading during single-limb stance and one simulating impact from a fall. Mechanical testing was performed to assess model and failure theory performance in the context of predicting femoral fracture load. Measured and FE-computed fracture load were significantly correlated for both loading conditions and all failure criteria (p < or = 0.001). The distortion energy and tau(max) failure theories were the most robust of those examined, providing the most consistently strong FE model performance for two very different loading conditions. The more complex failure theories and the strain-based theories examined did not improve performance over the simpler distortion energy and tau(max) theories, and often degraded performance, even when differences between tensile and compressive failure properties were represented. The relatively strong performance of the distortion energy and tau(max) theories supports the hypothesis that shear/distortion is an important failure mode during femoral fracture.
有限元（FE）模型常用于模拟骨破坏。然而，目前尚无针对骨的破坏理论得到验证。在本研究中，我们检验了九种基于应力和应变的破坏理论的性能，其中六种能够解释拉伸和压缩材料强度的差异。使用基于计算机断层扫描自动生成的股骨有限元模型，对畸变能、霍夫曼及其基于应变的类似理论、最大正应力、最大正应变、最大剪应变、最大剪应力（τ(max)）、库仑 - 莫尔和修正莫尔破坏理论进行了评估。在两种载荷配置下检查了18对匹配的近端股骨，一种近似单腿站立期间的关节载荷，另一种模拟跌倒的冲击。进行力学测试以评估模型和破坏理论在预测股骨骨折载荷方面的性能。对于两种载荷条件和所有破坏准则，测量的和有限元计算的骨折载荷均显著相关（p≤0.001）。畸变能和τ(max)破坏理论在所检验的理论中最为稳健，在两种非常不同的载荷条件下提供了最一致的强大有限元模型性能。所检验的更复杂的破坏理论和基于应变的理论，相较于更简单的畸变能和τ(max)理论，并未提高性能，甚至在考虑拉伸和压缩破坏特性差异时，性能常常下降。畸变能和τ(max)理论相对较强的性能支持了剪切/畸变是股骨骨折期间重要破坏模式的假设。
