Development of a nonlinear mesh distortion resistant simulation methodology for the friction welding process

• Applicant: Professor Dr.-Ing. Elmar Woschke
• Subject Area: Mechanics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 554937854

Friction welding (FW) is an industrially well-established joining process because it is economical, robust, precise and reproducible. Various simulation approaches are available for the efficient optimization of process parameters or for the development of new FW variants. Due to the characteristics of the FW process, the simulation must be treated as a nonlinear deformation process, both materially and geometrically. A weak point of the simulation is the necessary remeshing of the geometries during the time integration. Besides the obvious additional time and computational effort due to the process of re-discretization itself, also the tangent matix necessary for the Newton-Raphson method, which has to be set up and inverted again as well, implies a significant additional effort. To overcome these disadvantages, an alternative approach to the usual isoparametric finite elements can be used, which provides two different types of shape functions to approximate the virtual and the non-virtual field quantities. The result is an un-symmetric element stiffness matrix, which is why the method is also referred to as un-symmetric finite element method (UFEM). It can be shown that this alternative formulation is mesh distortion resistant, i.e., accurate results w.r.t the discretization are generated even in the presence of large deformations and highly distorted elements. Thus, it is possible to avoid the problem of repeated remeshing in the simulation of the FW process, which promises significant advantages both in terms of computational time and the inevitable discretization and interpolation errors as well as post-processing. Despite the development of the UFEM approach since the 2000s, the transfer to geometrically as well as materially nonlinear problems with geometrically distorted elements has been insufficient so far. Within the scope of the project, the application of UFEM for FW simulations is therefore to be developed and analyzed in detail with regard to the advantages and potential disadvantages, taking into account the process-specific conditions.

• DFG Programme: Research Grants