Developments of the arbitrary lagrangian-eulerian method in non-linear solid mechanics applications to forming processes

The numerical simulation of forming processes can be performed using the updated Lagrangian method. However, in general in the case of large deformations distortion of the mesh occurs. As a result the calculation becomes inaccurate or it may even crash. Hence a complete remeshing for an element mesh with a new mesh topology is necessary. The Arbitrary Lagrangian{ Eulerian (ALE) method can be used to reduce mesh distortion in order to prevent complete remeshings. In this thesis we investigate the applicability of the ALE method and try to improve several of its aspects.