Linear elements for metal-forming problems within the flow approach Original Research Article

Simulation of transient and stationary metal-forming processes is presented in the context of a mixed velocity–pressure formulation with a rigid-viscoplastic material model. A fractional step technique is used to obtain in a natural way a discrete Laplacian in the pressure–pressure entries of the system matrix which, as is known, introduces the stabilizing effect and allows for the use of equal order interpolating functions for both discretized variables, in spite of the Babuska–Brezzi condition. The method is suitable for both implicit and explicit time integration schemes. In particular, the explicit version (forward Euler with mass lumping) is developed. The discretization is carried out for linear triangles and tetrahedra which most easily can make use of automatic mesh generators and result in a simple code. Attention is focused on the stabilizing effect as a function of material and numerical parameters. The technique is illustrated with extrusion and upsetting simulation and compared with a known pressure stabilization method.