Special finite element formulations based on asymptotic thin layer models

This paper proposes a new modeling technique for thin layers of constant thickness. Very thin layers with material properties that significantly differ from those of the surrounding medium appear in a variety of applications, such as the coating of fibers in composite materials or the crust of the earth in global geophysical calculations. The traditional full FE modeling of such thin layers is generally associated with difficult meshing and high computational cost. While theoretical asymptotic models in which thin layers are modeled as interfaces with no thickness, on which appropriate boundary conditions are implemented have been known from some time, no computational models have been established for such layers. The purpose of this paper is to present a framework for the implementation of such a technique using the finite element method, with particular focus on a traditional lateral membrane deflection problem, within the framework of two-dimensional elasticity.