Contact Modelling of Shells for Roll Forming Simulations

Abstract

Roll forming is a bending-dominant process in which a metal sheet is fed through a number of roll stands. These consist of rollers that impose elasto-plastic deformations on the sheet to generate a desired profile. Conventional approaches to model this process utilize Lagrangian continuum finite elements, where nodal points coincide with material particles. This is problematic for the axially moving sheet due to the movement of the mesh at the contact zone, which may cause numerical oscillations. Furthermore, the refinement of the mesh in the vicinity of the rollers becomes difficult.

We take advantage of the low thickness of the sheet and use the nonlinear Kirchhoff-Love shell theory with three translational and two rotational degrees of freedom per particle of the material surface. A Mixed-Eulerian-Lagrangian (MEL) framework is employed, which uses a Eulerian coordinate in axial direction and a conventional Lagrangian coordinate in transverse direction to parametrize the material surface. The nodal point deflection is thereby decoupled from the axial motion of the material particles. This allows for a mesh, which is fixed axially, but follows the deformation of the material in the transverse directions. As a result, an advection problem arises for the plastic variables in account for their downstream transport. A stress resultant plasticity model for shell bending with isotropic hardening is used. It is solved with a variant of the well established return-mapping scheme and features the usual alternation of elastic predictor and plastic corrector. Additionally, a finite difference scheme is applied to carry the plastic variables downstream.