The Periodontal Ligament (PDL) play

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.