This thesis has been devoted to the study and development of algorithms for Finite Element (FE) simulations of mechanical processes involving large deformations. Aspects of three different formulations have been considered:

(i) The single material Arbitrary Lagrangian-Eulerian (ALE) formulation is a method where the FE mesh is allowed to move independently to the material flow. An FE program, based on this formulation, has been developed. The program handles plane strain and axisymmetrical problems. The main contributions are the development of a mesh smoothing scheme for boundary nodes and a second order accuratead vection algorithm.

(ii) The multi-material Eulerian formulation is a method where the material flows through a fixed mesh and where each element can contain a mixture of two or more different materials at the same time. Contributions are a new mass flux scheme and a new, penalty-based, Lagrangian-Eulerian coupling algorithm. Also a milling model, utilizing a Lagrangian-Eulerian switch technique for the minimizing of advection related dissipation errors, has been introduced. The simulations have been performed with the explicit FE program LS-DYNA.

(iii) The multi-material ALE formulation is a method allowing the FE mesh to move independently to the material flow and where each element in the mesh can contain a mixture of two or more different materials. The contributions are different methods for the definition of the ALE mesh motion, aiming at minimized numerical advection related errors and a minimized mesh size.