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Y. Vetyukov, P.G. Gruber, M. Krommer, J. Gerstmayr, I. Gafur, G. WInter:
"Mixed Eulerian-Lagrangian description in materials processing: deformation of a metal sheet in a rolling mill";
International Journal for Numerical Methods in Engineering, 109 (2017), 10; 1371 - 1390.

The paper is concerned with the modeling of the planar motion of a horizontal sheet of metal in a rolling mill. Inhomogeneous velocity profiles, with which the material is generated at one roll stand and enters the next one, lead to the time evolution of the deformation of the metal strip. We propose a novel kinematic description in which the axial coordinate is an Eulerian one, while the transverse motion of the sheet is modeled in a Lagrangian framework. The material volume travels across a finite element mesh, whose boundaries are in contact with the roll stands. The concise mathematical formulation of the method is different from the classical form of the arbitrary Lagrangian-Eulerian approach with a rate form of constitutive relations. The undeformed state of the strip is incompatible owing to the varying time rate of the generation of material. We treat this phenomenon by introducing the notion of intrinsic strains, which are mathematically described using the multiplicative decomposition of the deformation gradient. We currently present the approach for quasistatic simulations of in-plane elastoplastic deformations of the strip. A practically relevant problem with two strip segments and three roll stands is studied in a numerical example.

http://dx.doi.org/10.1002/nme.5314