On a new finite element technology for electromagnetic metal forming processes

The increasing need for lightweight building components has led to the development of new methods to manufacture such components. A promising concept is the systematic application of high-speed metal forming methods. Electromagnetic forming is one such method. Here, the deformation of the workpiece is driven by the Lorentz force which results from the interaction of a current generated in the workpiece with a magnetic field generated by a coil adjacent to the workpiece. This force represents an additional volume- or body-force density contribution in the balance of linear momentum. The numerical treatment of the coupled set of partial differential equations for the mechanical and electromagnetic fields can be made more efficient from the computational point of view by using the finite element technology suggested here, which is based on reduced integration and hourglass stabilisation. The main idea behind this new technology is to expand the constitutive quantities in a Taylor expansion with respect to a point on the local coordinate axis in the thickness direction. The result is a weak system of equations which decomposes into a part to be evaluated in two Gauss points and in addition the so-called hourglass stabilisation to be computed analytically.