Analysis of forming processes with efficient finite element procedures

Forming technologies are widely used in the manufacturing processes of industries. The numerical simulation of such processes makes high demands on the finite element technology. Element formulations which do not show the undesirable effect of locking in the cases of nearly incompressible material behaviour like during the plastification and in large deformations with extreme bending, are required. Unfortunately classical low order isoparametric element formulations show the effect of locking. An underestimation of the deformation associated with an overestimation of the stress state can be observed. To overcome this problem several autors [

1

], [

4

] propose finite element formulations based on the concept of reduced integration with hourglass stabilization by using the enhanced strain method. Especially for the efficient numerical simulation of sheet forming processes so-called solid-shell elements are developed [

2

], [

4

]. The starting point of the present formulation is the same three-field variational functional on which many three-dimensional enhanced strain concepts are based. A new aspect is the Taylor expansion of the first Piola-Kirchhoff stress tensor with respect to the normal through the center of the element. Together with a constant Jacobi matrix due to the computation in the center of the element this concept leads to a powerful element formulation with only two Gauss points over the thickness. Furthermore continuum mechanical laws can be implemented without additional assumptions about the kinematics or the stress state.

A further important aspect is the modelling of the contact behaviour. Advantageous is that the extension of the structure in thickness direction is taken into account by the solid-shell formulation. However working with contact surfaces discretized by low order finite elements leads to discontinuities of the normal vector and to a non-smooth sliding [

3

]. That is why a smoothing of the surface description has to be implemented. For the efficient and user-friendly analysis the solid-shell formulation has been implemented into the commercial code ABAQUS. Examples for comparison of the numerical results with realistic forming processes are given.