Numerical Treatment of Inelastic Constitutive Behaviour within an ALE-Framework of Rolling
|Bearbeitung:||ext. M. Ziefle|
|Förderung durch:||This work is financed by the German Research Foundation (DFG).|
In this project calculation methods for the numerical contact analysis of rolling rubberlike solids are developed. As main application field here the tire problem is picked out. For the finite element analysis of rolling contact problems Arbitrary Lagrangian Eulerian (ALE) methods are well established. These techniques enable a time independent formulation for elastic bodies under stationary rolling conditions and for local mesh refinement concentrated to the contact region. A drawback is on the computation of history dependent material properties because the path of material points is not traced inherently. This affects inelastic constitutive behavior as well as frictional contact. Following a fractional-step strategy the treatment of inelastic material behavior could be solved in this ALE-formulation. For this, an additional advection equation is used to describe the flux of the material particles through the fixed mesh. For the numerical solution of that equation a time discontinuous Galerkin (TDG) method is implemented and yields good results. The developed scheme can be used for any consistent constitutive model which is based on internal variables. The developed procedure is tested by the computation of a typical FE-Tire-Model.
Figure 1: FE-Mesh of rolling solid rubber disc.
Figure 2: Frequency depending effects: a) normal contact pressure distribution, b) rolling resistance torque
Figure 3: Frequency depending effects: resulting normal contact force
Figure 4: Three different states of damage (max. 10%)
Figure 5: Evolution of internal damage variable
Figure 6: FE-model of a typical car tire.
Figure 7: Contact pressure maximum (in MPa) moves to leading edge
Figure 8: Maximum inelastic (viscoelastic) state moves to trailing edge