ALE formulation and its application in solid mechanics Original Research Article

In this paper an incremental approach is used to derive an arbitrarily-Lagrangian-Eulerian (ALE) finite element formulation including a complete expression of the external virtual work. The characteristics of this formulation and its differences from similar ones in literatures are discussed. A detailed discussion on the loading correction analysis is given based on the degenerated updated Lagrangian description from ALE, and a modified expression for the surface loading correction contribution to the system stiffness matrix is presented. Some of the numerical difficulties with the ALE formulation, namely the mesh motion and the stress integration scheme, are discussed and specific applications are given. A general 2D ALE program; ALEFE and its features are introduced. Sample numerical examples as well as a punch indentation, a sheet metal extrusion problem and a compression between wedge-shaped dies are given and compared to various other formulations and solutions in the literature.