Eulerian Finite Cover Method for Solid Dynamics

In order to deal with the kinematic and dynamic boundary conditions in the Eulerian framework, we develop an Eulerian finite cover method (FCM) for large deformation solid dynamics by incorporating the approximation strategy of the FCM into the existing Eulerian explicit finite element method. The operator split method is employed to solve Eulerian solid dynamics problems, and the resulting numerical algorithm consists of two steps. One is the nonadvective step, in which the standard Lagrangian FC analysis is carried out with the explicit time integration scheme, and the other is the advective step, in which the CIVA method is applied to project the solution obtained in the nonadvective step to the Eulerian mesh. Two representative numerical examples are presented to validate the proposed Eulerian FCM and demonstrate its capability especially in appropriately treating the kinematic and dynamic boundary conditions.