Data transfer within a finite cell remeshing approach applied to large deformation problems

The present work is a comparative study of different data transfer techniques in the context of the finite cell method (FCM) in combination with remeshing for hyperelastic problems undergoing large deformations. The FCM is an immersed-boundary method that uses Cartesian grids for the discretization so as to avoid the generation of boundary conforming meshes. To overcome problems with heavily distorted meshes at large deformation states, we apply a remeshing procedure. During the remeshing, the data containing the deformation history has to be transferred between the meshes. In the present study, different methods are considered and compared: radial basis functions without and with polynomial extension, inverse distance weighting, and \(\textit{L}_\text {2}\) ${\mathit{L}}_{\text{2}}$ -projection applying the shape functions used in the FCM for the trial and test functions.