The Periodontal Ligament (PDL) plays a very important role in load transmission between the teeth and alveolar bone. To capture biomechanical responses of Orthodontics, numerical analysis need to consider multiple types of materials: incompressible visco-hyperelastic for the PDL and compressible elastic for teeth. This article proposes a unified-implementation of smoothed finite element methods (UI-SFEM), which enables the use of different types of smoothing domains for different materials. It has several important properties: (1) A UI-SFEM model can use any types of smoothing domains in a combination as desired for complex systems. (2) The choice of the smoothing domain types can be done in a single model based on the user needs (material properties, incompressible numerical problems). (3) It provides a framework for designing models with different solution properties. Numerical experiments show that the UI-SFEM is efficient and robust against mesh distortion, which is works particularity well for complex biological systems.

中文翻译：

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用于模拟多材料正畸生物力学响应的平滑有限元方法 (UI-SFEM) 的统一实现

牙周韧带 (PDL) 在牙齿和牙槽骨之间的负荷传递中起着非常重要的作用。为了捕捉正畸的生物力学响应，数值分析需要考虑多种类型的材料：PDL 的不可压缩粘超弹性材料和牙齿的可压缩弹性材料。本文提出了平滑有限元方法 (UI-SFEM) 的统一实现，该方法允许对不同材料使用不同类型的平滑域。它有几个重要的特性： (1) UI-SFEM 模型可以根据复杂系统的需要组合使用任何类型的平滑域。(2) 平滑域类型的选择可以根据用户需求（材料属性、不可压缩数值问题）在单个模型中完成。(3) 它为设计具有不同解属性的模型提供了一个框架。数值实验表明，UI-SFEM 对网格畸变有效且鲁棒，特别适用于复杂的生物系统。