Using finite strain 3D‐material models in beam and shell elements

In this paper an interface is derived between arbitrary three‐dimensional material laws and finite elements which include special stress conditions. The mechanical models of beams and shells are usually based upon zero‐stress conditions. This requires a material law respecting the stress condition for each finite element formulation. Complicated materials, e.g. finite strain models are often described in the 3D‐continuum. Considering the zero‐stress condition requires a reformulation of these material laws, which is often complicated. The subject of this paper is to incorporate physically non‐linear 3D‐material laws in beam and shell elements. To this effect a local algorithm will be developed to condense an arbitrary 3D‐material law with respect to the zero‐stress condition. The algorithm satisfies the stress condition at each integration point on the element level.