The use of finite element models has gained popularity in the field of foot and footwear biomechanics to predict the stress–strain distribution and the treatment effectiveness of therapeutic insoles for pathological foot conditions. However, a comprehensive evaluation of mesh quality is often ignored, meanwhile no golden standard exists for the mesh density and selection of element size at an acceptable accuracy. Here, we make a convergence test and established anatomically-realistic foot models at different mesh densities. The study compared the discrepancy in output variables to the changes of element type and mesh density under barefoot and footwear conditions with compressive and shear loads, which are commonly encountered in foot and footwear biomechanics simulations. For a range of loading conditions simulated in 125 finite element models, the peak plantar pressure consistently converged with optimal mesh size determined at 2.5mm. The convergence variable of principal strains and stress tensors, however, varies significantly. The max von-Mises stress showed strong sensitive behavior to the changes of the mesh density. The pattern for contact pressure distribution became less accurate when the element sizes increase to 6.0mm; in particular, the locations of the pressure peak do not show remarkable changes, but the size of the area of contact still changes. The current study could offer a general guideline when generating a reasonable accurate finite element models for the analysis of plantar pressure distributions and stress/strain states employed for foot and footwear biomechanics evaluations.

中文翻译：

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人足有限元建模中的最优网格准则：多模型输出对网格密度和载荷边界条件的依赖

有限元模型的使用在足部和鞋类生物力学领域得到普及，以预测治疗鞋垫对病理性足部疾病的应力-应变分布和治疗效果。然而，网格质量的综合评价往往被忽略，同时网格密度和单元尺寸选择的可接受精度没有黄金标准。在这里，我们进行了收敛测试，并在不同的网格密度下建立了解剖学上逼真的足部模型。该研究将输出变量的差异与赤足和鞋类条件下的单元类型和网格密度的变化与压缩和剪切载荷进行了比较，这在足部和鞋类生物力学模拟中很常见。对于在 125 个有限元模型中模拟的一系列载荷条件，毫米。然而，主应变和应力张量的收敛变量变化很大。最大 von-Mises 应力对网格密度的变化表现出强烈的敏感行为。当单元尺寸增加到 6.0 时，接触压力分布的模式变得不太准确毫米; 尤其是压力峰值的位置变化不大，但接触面积的大小仍然发生变化。当前的研究可以在生成合理准确的有限元模型以分析用于足部和鞋类生物力学评估的足底压力分布和应力/应变状态时提供一般指导。