A new solid-shell finite element technology incorporating plastic anisotropy in forming simulations

In the recent years shell finite element formulations which include only displacement degrees-of-freedom, the so-called solid-shells, have been successfully applied in sheet metal forming. A very efficient strategy to deal with the problem of locking which occurs in bending-dominated problems and in the limit of incompressibility is the method of reduced integration with hourglass stabilization. Further advantages of these finite element technologies are their robustness with respect to severe mesh distortion and the low computational cost. A disadvantage is, however, the necessity to develop a suitable hourglass stabilization which adapts to both, the changing geometry and the usually highly non-linear material behaviour. Most earlier finite element technologies are based on the assumption that the material behaviour is initially isotropic. In the present contribution we develop an approach to include initial and deformation-induced anisotropy. Prerequisite for that is the development of a suitable material law. In contrast to many other current papers we aim at a purely continuum mechanical modelling to arrive at optimal numerical efficiency