The Finite Cell Method for Nonlinear Problems of Solid Mechanics

The conventional finite element method requires the discretization of the domain of interest into a finite element mesh, whose boundaries have to coincide with the physical boundaries of the problem. While this constraint can be easily achieved for most applications in solid mechanics, difficulties arise for structures with very complex boundaries. Corresponding geometry descriptions, which are usually available in the form of CAD data or spatial voxel models, have to be transferred into finite element meshes by mesh generation algorithms that are error prone, often yield largely distorted elements and are computationally very expensive. The recently introduced Finite Cell Method (FCM) [1,2] circumvents the difficult generation of complex, finely graded finite element meshes. Its main feature is the combination of high-order finite elements by a fictitious domain approach, which allows for an extension of the physical domain beyond its potentially complex boundaries. The resulting embedding domain, consisting of both fictitious and physical part, is chosen such that it can be meshed easily by a rectangular grid of high-order elements. The complex information of physical geometry is conveniently incorporated during the numerical integration