Finite element modeling of thin layers

Very thin layers with material properties I which significantly differ from those of the surrounding medium appear in a variety of applications. Traditionally there are two extreme ways of handling such layers in finite element analysis: either they are fully modelled or they are totally ignored. The former option is often very expensive computationally, while the latter may lead to significant inaccuracies. Here a special technique of modeling thin layers is devised within the framework of the finite element method. This technique constitutes a prudent compromise between the two extremes mentioned above. The layer is replaced by an interface, namely a line or a surface (with zero thickness) in two- or three-dimensional analyses, respectively. Special jump conditions are imposed on this interface to model the effect of the layer. The method is presented in various configurations and variants, and its performance in one representative two-dimensional case is demonstrated via numerical experiments.