Department of Orthopaedics and Sports Medicine, BB 1065D, 1959 NE Pacific Street, Box 356500, Seattle, WA 98195-6500, USA.
J Biomech. 2011 Aug 11;44(12):2337-43. doi: 10.1016/j.jbiomech.2011.05.006. Epub 2011 Jul 13.
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.
有限元分析在足与鞋生物力学领域得到了广泛应用，用于确定足底压力以及软组织和鞋材内部的应力和应变。在处理足部等解剖结构时，由于分支和嵌入式结构带来的几何复杂性，六面体网格生成占据了模型开发时间的大部分。迄今为止，四面体网格在足与鞋生物力学中一直是首选方法，因为它可以更容易地自动化。在这里，我们使用非线性有限元程序 Abaqus（Simulia，Providence，RI）来研究在压缩和剪切载荷、材料不可压缩性和摩擦接触条件下，四面体和六面体单元的优缺点，这些条件在足与鞋生物力学中很常见。这项研究表明，在一系列模拟条件下，混合六面体单元（Abaqus C3D8H）表现良好，而混合线性四面体单元（Abaqus C3D4H）表现不佳。另一方面，具有改进的应力可视化功能的增强二次四面体单元（Abaqus C3D10I）在接触压力和接触剪切应力预测方面与混合六面体单元表现相当。虽然与裸足和穿鞋条件下的六面体单元模拟相比，增强二次四面体单元模拟的计算成本更高，但由于减少了劳动力和加快了模型开发，增强二次四面体单元的公式似乎非常有前途，这一切都与更方便的网格生成有关。
