Remeshing and data transfer in the finite cell method for problems with large deformations

Abstract

AbstractThe simulation of complex structures using standard finite element discretization techniques can be challenging because the creation of the boundary conforming meshes for such structures can be time‐consuming. Therefore, fictitious domain methods are attractive alternatives because the underlying mesh does not have to conform to the boundary. One fictitious domain method is the finite cell method where a structured non‐geometry conforming Cartesian grid is created and the geometry is then described by a simple indicator function. When solving non‐linear problems, for example, if large deformations are taken into account, broken cells are typically heavily distorted and may lead to failure of the overall solution procedure. To tackle this issue remeshing is applied to proceed with the simulation. In previous publications, radial basis functions (RBFs) were applied to map the deformation gradient between the different meshes. However, it is not clear whether this is the best way to transfer data during the remeshing procedure. Therefore, we investigate whether there are alternative methods that can be used instead. This is then compared to the RBF interpolation and applied to different numerical examples with hyperelastic materials.