An extended arbitrary Lagrangian–Eulerian finite element method for large deformation of solid mechanics

In this paper, a new computational technique is presented based on the eXtended arbitrary Lagrangian–Eulerian finite element method (X-ALE-FEM) for large deformation of solid mechanic problems. An arbitrary Lagrangian–Eulerian (ALE) technique is employed to capture the advantages of both Lagrangian and Eulerian methods and alleviate the drawbacks of the mesh distortion in Lagrangian formulation. The X-FEM procedure is implemented to capture the discontinuities independently of element boundaries. The process is accomplished by performing a splitting operator to separate the material (Lagrangian) phase from convective (Eulerian) phase, and partitioning the Lagrangian and relocated meshes with some triangular sub-elements whose Gauss points are used for integration of the domain of elements. In order to demonstrate the efficiency of X-ALE-FEM technique in large deformations, several numerical examples including the die pressing with flexible and rigid central cores and coining problem are presented and the results are compared with those of classical FE and X-FEMs.