Phenomenological force and swelling models for rechargeable lithium-ion battery cells

Three phenomenological force and swelling models are developed to predict mechanical phenomena caused by Li-ion intercalation: a 1-D force model, a 1st order relaxation model, and a 3-D swelling model. The 1-D force model can estimate the Li-ion intercalation induced force for actual pack conditions with preloads. The model incorporates a nonlinear elastic stiffness to capture the mechanical consequences of Li-ion intercalation swelling. The model also separates the entire state of charge range into three regions considering phase transitions. The 1st order relaxation model predicts dynamic swelling during relaxation periods. A coefficient of relaxation is estimated from dynamic and quasi-static swelling at operational conditions. The 3-D swelling model predicts the swelling shape on the battery surface for all states of charge. This model introduces an equivalent modulus of elasticity, which is dependent on the state of charge, to capture material transformations of the electrodes, and the orthotropic expansion of the jellyroll in a direction perpendicular to the electrode surfaces. Considering the simplicity of the measurements and direct physical correlations between stress and strain, the proposed models can enhance battery management systems and power management strategies.