An accurate time integration scheme for arbitrary rotation motion: application to metal forming simulation

Within the frame of implicit velocity based formulations with solid elements, usual time integration schemes often turn out unsatisfactory when the movement has large rotations, especially in metal forming applications such as ring rolling or cross-wedge rolling. These rotations generally require using a much higher order integration scheme with inherent difficulties in implementing such schemes. For pure rotation motions, it is possible to use a low order integration scheme by rewriting the motion equations in the cylindrical frame that is supported by the rotation axis. Accordingly, a first order scheme is sufficient to accurately integrate the movement but it is restricted to specific problems. In the more general case, it is possible to derive parts of the domain where rotations are predominant along with the governing rotation axis from the velocity field gradient. The motion equations are then rewritten in the resulting local cylindrical frame. Performances of this first order scheme are first evaluated and highlighted over simple analytical problems, before being applied to the finite element simulation of the torsion test, and then to more complex metal forming problems involving large rotations. The accuracy and efficiency of this scheme is so numerically demonstrated.