3D Isogeometric Analysis of intercalation-induced stresses in Li-ion battery electrode particles

Abstract

This paper is concerned with a three-dimensional coupled chemo-mechanical model for intercalation-induced stresses. Thereby, a diffusion model is enhanced by a drifting term involving the gradient of the hydrostatic stress state. A straightforward Finite Element discretization of the coupled diffusion would require C1-continuous shape functions. The implementation is thus based on the concept of Isogeometric Analysis, permitting a discretization purely in terms of the displacements and the concentration field. Furthermore, it allows to set up an operator matrix for the computation of the hydrostatic stress gradient in terms of the primal variables.The model is verified, in a simplified form, using analytical results from literature. It is subsequently employed for the study of the mechanical behavior of spherical and ellipsoidal particles under galvanostatic boundary conditions. The simulation data show a stress relaxation effect that becomes significant both in stiff electrode materials and for high charge rates. During charging, a characteristic tensile core-compressive shell structure develops. Once the stresses have reached a material-dependent threshold, they enhance the diffusion and drive ions away from regions of high compressive hydrostatic stress, that is, towards a particle’s core. Over time, this leads to reduced concentration gradients which, in turn, reduces the stresses in the particle already during the charging process. Models that neglect the stress effect consequently predict stress levels that are not only of higher magnitude, but that also do not decay.A comprehensive study on the influence of geometry, material constants, and charge rate has been performed. It sheds light on the distributions of stresses in ellipsoidal electrode particles. These have been reported to exhibit lower stress levels than spherical particles. Using a transformation of Cartesian stresses into a prolate spheroidal coordinate system, it can be shown that these particles equilibrate stresses by deformations along the semi-major axis. At the same time, a region of high stresses develops as a “belt” around the particles’ equator. Their intensity depends on the shape of the particle but is below that observed in spherical and oblate spheroidal particles. This offers an explanation for the longevity of these particles under cyclic charging processes.