An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: Classification and applications Original Research Article

In the second paper of this two-part contribution, a specialisation towards Neo–Hookean material will be made of the generic hyperelastic arbitrary Lagrangian–Eulerian (ALE) formulation derived in Part 1. First, for the sake of comparison and classification, several existing ALE solution schemes are discussed, including total and updated approaches, as well as monolithic and staggered algorithms. Then, implementational details are provided for the newly proposed ALE strategy. The versality and the limitations of the present formulation are shown by means of a set of one-dimensional and multi-dimensional numerical examples. In particular, it is shown that with the proposed ALE formulation, potential energies can be obtained that are minimum for the considered topology.