A finite element framework for continnua with boundary potentials

Abstract

AbstractThis contribution deals with the implications of the anisotropic boundary potential energies on deformational mechanics in the framework of the two‐dimensional finite element method at finite strains. In the first part of this work ([6])) only the isotropic boundary potentials were considered, however, in this contribution we allow for the anisotropic contributions from the boundary energies, too. The 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 curve‐tangent, as well. For the finite element implementation, a suitable curvilinear coordinate system attached to the boundary is defined and corresponding derivations are carried out. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)