Efficient numerical simulation of in-elastic materialproperties in the framework of the ALE-descripton of rolling bodies

• Applicant: Professor Dr.-Ing. Udo Nackenhorst
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 548358851

The arbitrary Lagangian-Eulerian (ALE) description of stationary rolling contact has been established as golden standard for the Finite Element simulation. The advantages are the time-independent formulation of stationary rolling and the possibility of local mesh-refinement for a high resolution near the contact area. However, in comparison to the pure Lagrangian description there is a restriction to axis-symmetric structures and difficulties to address history dependent behavior have to be addressed. In particular for the treatment of inelastic material behavior special measures have to be taken. While more or less “engineering approaches” on integration along concentric rings of integration points in the reference configuration do not allow for mathematical error control, in particular on irregular meshes, consistent approaches for the solution of the underlying advection-diffusion equations to this date appear numerically costly. In this project we what to transfer an idea, which has been introduced earlier for the robust and efficient solution of the tangential rolling contact problem, namely a mixed finite element formulation which implicitly solves the advection problem within an operator-split approach. For the efficient treatment of rolling contact problems all ALE-code parts will be implemented as UEL-subroutines into the commercial code Abaqus first. Next the advection will be treated by a mixed finite element approximation, where we will investigate if that could be treated by dealing with a single scalar variable, i.e. the equivalent viscoelastic strains, while the three-dimensionality will be tackled locally at element level. This will be cross-checked with the advection of the full 3-D tensor of viscoelastic strains, which will be implemented in a staggered scheme. Besides a couple of benchmark-problems, the efficiency of the algorithm will be demonstrated on a detailed 3D-tyre model. As an outlook the transferability of the approach to alternative applications, e.g. the treatment of highly viscous media in Eulerian as well as ALE description will be investigated in the framework of students’ thesis. All research data will be published in the research data management system of Leibniz University Hannover.

• DFG Programme: Research Grants