Arbitrary Lagrangian Eulerian (ALE) description for large deformation metal forming problems

Arbitrary Lagrangian Eulerian (ALE) description has been used to simulate large-deformation, metal-forming problems. Certain mesh governing algorithms are implemented in ALE formulations to control mesh convection. A punch problem is simulated and advantages of ALE simulations over pure Lagrangian simulations are shown.; Traditionally, Lagrangian and Eulerian kinematic descriptions are used for finite-element analysis of large-deformation problems. In the Lagrangian description, the grid points adhere to the material points throughout the course of deformation. Lagrangian description has certain limitations in large-deformation problems. In the Eulerian description the reference system is kept fixed in space, and every spatial point is identified by an invariable set of three independent co-ordinates. Because of excessive movement of interfaces and boundaries, it is arduous to take material associated boundary conditions into account. This research pursues Arbitrary Lagrangian Eulerian (ALE) description which combines the advantages of both Lagrangian and Eulerian descriptions. ALE introduces an additional (reference) mapping, which brings additional flexibility in the formulation so that mesh neither adheres to the material nor the space; rather the mesh is in relative motion with the material and it rearranges itself during the deformation process.