Mixed Eulerian-Lagrangian modeling of sheet metal roll forming

We propose a nonlinear shell finite element model to simulate sheet metal roll forming, a continuous forming process to produce endless metal profiles. A mixed Eulerian-Lagrangian kinematic description is employed to overcome the drawbacks of the common Lagrangian parametrization. The finite element mesh is detached from the particle motion in axial direction and, thus, facilitates a two-step solution procedure to capture the continuous forming process: First, an equilibrium is sought with the account for contact and plastic flow. Secondly, the material transport is taken into account, which amounts to the integration of an advection problem for the plastic variables. The continuum plasticity model with through-the-thickness integration for the stress resultants guarantees a precise resolution of the forming process in each cross section of the Kirchhoff- Love shell. A series of simulations is carried out to ascertain the convergence of the numerical scheme, to highlight the impact of characteristic parameters and to establish a correspondence to a reference computation with the commercial software Abaqus in a simplified static setting. A physical experiment is devised on an actual roll forming mill to assess the quality of the current computational model.

Automated summary

We propose a nonlinear shell finite element model to simulate the continuous forming process of sheet metal roll forming. A mixed Eulerian-Lagrangian kinematic description is employed, and the finite element mesh is detached from the particle motion to facilitate a two-step solution procedure. The continuum plasticity model guarantees a precise resolution of the forming process in each cross section of the Kirchhoff-Love shell, and the numerical scheme is validated through simulations and a physical experiment.