Mesh management methods in finite element simulations of orthodontic tooth movement

• Assessment of ALE and remeshing methods for simulations of orthodontic tooth movement.
• Development of an ALE model for long term tooth movement.
• Large displacement of the tooth is achieved without any remeshing operations.
• Very large deformations of soft tissues is achieved combining ALE and remeshing.

In finite element simulations of orthodontic tooth movement, one of the challenges is to represent long term tooth movement. Large deformation of the periodontal ligament and large tooth displacement due to bone remodelling lead to large distortions of the finite element mesh when a Lagrangian formalism is used. We propose in this work to use an Arbitrary Lagrangian Eulerian (ALE) formalism to delay remeshing operations. A large tooth displacement is obtained including effect of remodelling without the need of remeshing steps but keeping a good-quality mesh. Very large deformations in soft tissues such as the periodontal ligament is obtained using a combination of the ALE formalism used continuously and a remeshing algorithm used when needed. This work demonstrates that the ALE formalism is a very efficient way to delay remeshing operations.