Numerically Efficient Simulation of Inelastic Material Properties within the Framework of ALE Formulation for Rolling Bodies

In the framework of ALE-description of rolling contact the treatment of inelastic material requires special attention. The task is to follow the path of the material particles spinning in the spatially fixed mesh. Besides methods based on integration along concentric rings, Streamline-Upwind/Petrov–Galerkin (SUPG) and Time-Discontinuous Galerkin (TDG) approaches have been suggested in literature.

The aim of this project is to develop an efficient and reliable finite-element framework for rolling bodies by combining advanced inelastic material modelling with the ALE formulation. While the ALE setting enables a quasi-steady description of rolling contact by keeping the mesh fixed in the contact region, it also requires a consistent strategy for handling history-dependent internal variables as they are convected through the mesh.

To address this, the project investigates stabilised advection schemes for both scalar internal variables (such as equivalent strain) and tensor-valued quantities (such as viscous right Cauchy–Green–type measures). SUPG-based techniques are employed to ensure accurate transport along streamlines while suppressing spurious oscillations.

On the implementation side, the work involves developing a modular simulation environment in Abaqus. User-defined elements (UEL) are used to realise ALE kinematics and rolling contact, while a UMAT provides the nonlinear viscoelastic–hyperelastic material behaviour. The overall workflow integrates material parameter identification, simulation, and post-processing in a consistent technical framework.