ALE formulation and its application in solid mechanics

In this paper an incremental approach is used to derive an arbitrarily-Lagr angian-Eulerian (ALE) finite element formulation including a complete expre ssion of the external virtual work. The characteristics of this formulation and its differences from similar ones in literatures are discussed. A deta iled discussion on the loading correction analysis is given based on the de generated updated Lagrangian description from ALE, and a modified expressio n for the surface loading correction contribution to the system stiffness m atrix is presented. Some of the numerical difficulties with the ALE formula tion, namely the mesh motion and the stress integration scheme, are discuss ed 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 wedg e-shaped dies are given and compared to various other formulations and solu tions in the literature. (C) 1998 Elsevier Science S.A. All rights reserved .