A structure-preserving immersed finite element method for the dynamics of multiphase continua with thermomechanical coupling

• Applicant: Professor Dr.-Ing. Michael Groß
• Subject Area: Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 498565485

Concerning finite element simulations of moving continua, there are many examples in which a considered continuum consists of different embedded phases. Here, the phases can be flexible solids, fluids as well as rigid bodies. They include a rotor in a Newtonian fluid and a fiber-reinforced material considered as a biphase material. The formulation of the fluid-structure-interaction (FSI) in the first example by means of well-known finite element methods leads to disadvantages in view of computational efficiency and stability if large rotations of embedded phases arise. Well-known reasons are the difficult approximation of convective terms, insufficient meshings of surface contacts as well as frequent remeshings of the phases. The simulation of the solid-solid-interactions in the second example leads to long computing times, because the mesh of the embedded phase determines the number of elements of the surrounding phase. The reason is also the necessary sufficient approximation of surface contacts. These disadvantages can be avoided by an immersed finite element method (IFEM). Aims of this research project is the development and implementation of a new structure-preserving IFEM for dynamic, non-isothermal multiphase continua. Here, fluids as well as solids are taken into account. In order to consider also solids with rigid sections, a noval non-isothermal rigid body formulation is developed, which is directly based on a finite element method. Thereby, micropolar rotational degrees of freedom guarantee the rigidity of the finite element meshes pertaining to the rigid sections. A special variational approach avoids the introduction of an Euler tensor, and rigid sections of flexible solids can be defined by a simple declaration in the total mesh. In this way, thermomechanical couplings between non-isothermal rigid bodies, flexible solids and fluids can be simulated easily. Well-known IFEM assume a fixed Eulerian mesh for the total continuum, and consider Lagrangian meshes only for embedded phases. This restriction will be abolished in the current project, in order to simulate large deformations of non-isothermal multiphase solids by the IFEM. But, also FSI simulations with an Eulerian mesh for a surrounding fluid will be improved by the structure-preserving IFEM. There emerge new space-time approximations, which lead to an increasing numerical stability without user-defined stability parameters.

• DFG Programme: Research Grants