Abstract

Lithium-ion batteries, with their high energy densities and light-weight designs, have found broad applications in portable electronics and electric vehicles. However, their mechanisms and operation are not yet fully understood, which has motivated a wide span of multi-physical models from different disciplines. In this talk, a thermodynamically consistent phase-field framework is presented, to investigate the electrochemical and mechanical behavior of lithium-ion battery electrode materials during charge and discharge. Within this framework, a series of coupled models is developed sequentially towards the more realistic modeling. Firstly, a mechanically coupled two-phase model of a single particle is proposed, based on a thorough study of the chemical phase—separation of this particle. Thereby, the effect of large strains and the concentration-dependent elastic properties are considered, which has been proved in this thesis to have a great impact on the phase separation. A more comprehensive model is formulated, which deals additionally with the electrochemical reaction on the particle surface and the orthotropic phase separation. The reaction rate is governed by a modified Butler–Volmer equation, which takes both chemical and mechanical states into account. Based on this model, we further investigate the fracture in the particle by the phase-field approach, where the reaction on the newly cracked surfaces is also taken into consideration. Finally, the model of the particle embedded in a polymer matrix is presented to study the interaction between the particle and the surrounding materials. For the implementation two novel finite element methods are used: isogeometric analysis and the B-Spline based finite cell method. Isogeometric analysis is employed in order to treat the fourth-order Cahn–Hilliard equation and the third-order drifting term in a straightforward fashion. To deal with the additional boundary constraint, which states that the normal gradient of the concentration equals to zero, and which arises from the Cahn–Hilliard equation, we propose two variational formulations based on the Lagrange multiplier method and the Nitsche method, respectively, as the weak imposition. Moreover, we also employ finite cell method with Cartesian B-Spline meshes to simulate the composite electrode with complex geometries. In this thesis, the chemical and mechanical fields are fully resolved in a variety of three dimensional simulations. These simulations demonstrate the influence of the phase separation on the stress field, the fracture and the reaction rate. We find that the phase separation results in, among others, an intensified stress field and enhanced reaction rate near the phase interface, and in severe cases it also leads to crack propagation and branching. Moreover, intensive discussions are carried out to explore the factors that contribute to phase separation and suppression, such as the particle size, charge rate and material stiffness.