A finite element framework for the numerical implementation of boundary potentials

This contribution deals with the implications of boundary potential energies on deformational mechanics in the framework of the finite element method at finite strains. The common material models in continuum mechanics are taking the bulk into account, nevertheless, neglecting the boundary. However, boundary effects sometimes play a dominant role in the material behavior, e.g. surface tension in fluids. The boundary potentials, in general, are allowed to depend not only on the boundary deformation gradient but also on the spatial surface–normal / curve–tangent, as well. For the finite element implementation, a suitable curvilinear coordinate system attached to the boundary is defined and corresponding geometrical and kinematical derivations are carried out. Afterwards, the discretization of the generalized weak formulation, including boundary potentials, is carried out and finally numerical examples are presented to demonstrate the boundary effects due to the different proposed material behavior. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)