AMaSiS 2021 - Abstract

Schoof, Raphael

Efficient parallel simulation of contact problems for chemo-mechanically modeled battery active particles

Coauthors: G.F. Castelli, and W. Dörfler
Karlsruher Institut für Technologie, Germany

Lithium ion batteries (LIBs) are one of the key technologies in terms of future energy storage to meet the challenges posed by climate change. During battery operation, mechanical degradation is a crucial aging mechanism of LIBs. An inhomogeneous lithium concentration profile during charging and discharging can lead to large mechanical stresses, which can finally induce particle fracture. This behavior is particularly crucial for phase separating electrode materials, where large concentration gradients evolve. However, the increase in mechanical stress must not be neglected if the swelling of the particle is restricted to a limited surrounding area, e.g., due to the material structure or the current collector.
The used particle model couples lithium diffusion, large deformations and phase separation based on a thermodynamically consistent transport theory, see [2]. A solid solution model describes the diffusion and a finite strain theory models the deformations. A phase-field model is used to deal with the phase separation. In the end, a common free energy density connects all different phenomena. To incorporate the restricted swelling, the model is extended by an obstacle contact, compare [4].
The resulting Cahn--Hilliard-type phase-field model approach is computationally expensive to solve. To overcome the current limited applications, the highly efficient adaptive numerical solution algorithm in space and time from [1,3] is used. The particle contact is treated with the concept of the primal-dual active set algorithm. Additionally, a parallel distributed memory implementation leads to a larger range of electrode particle shapes examined. Finally, physical and numerical aspects of the model and the solver for an electrode particle of lithium iron phosphate are investigated and discussed. The influence and interrelation of phase separation and mechanics as well as different shaped obstacles are pointed out. The efficiency and the large computational savings due to the adaptive solution algorithm as well as the parallel distributed memory implementation allow the further analysis of computationally demanding parameter regimes and also three-dimensional particle geometries.

Keywords: Lithium ion battery, Phase-field model, Mechanics, Contact problem, Numerical simulation, Finite element method.

References [1] G.F. Castelli: Numerical Investigation of Cahn--Hilliard-Type Phase-Field Models for Battery Active Particles. Ph.D. thesis, Karlsruhe Institute of Technology (KIT), 2021. To be published.
[2] G.F. Castelli, L. von Kolzenberg, B. Horstmann, A. Latz, and W. Dörfler: Efficient Simulation of Chemical-Mechanical Coupling in Battery Active Particles. Energy Technol., 9(6):2000835, (2021).
[3] G.F. Castelli, and W. Döer: Study on an Adaptive Finite Element Solver for the Cahn--Hilliard Equation. Numerical Mathematics and Advanced Applications ENUMATH 2019, Ed.: F.J. Vermole and C. Vuik, 245253, (2021).
[4] J. Frohne, T. Heister, and W. Bangerth: Efficient Numerical Methods for Large-Scale, Parallel Solution of Elastoplastic Contact Problems. Int. J. Numer. Meth. Engng, 105(6):416439, (2016).