Stress analysis of lithium-ion batteries during charging and discharging based on a fractional-order thermal–electrochemical–mechanical model

The non-integer dimension and self-similarity characteristics of the electrodes of lithium-ion batteries (LIBs) in the microscopic form are the crucial characteristics of fractional-order theory. The non-classical energy dissipation mechanism of heat transfer mechanism in porous electrodes is the coupling of diffusion effect and heat wave effect. The inability of integer-order thermal models to precisely describe the transient thermal behavior of porous electrodes places constraints on the accuracy of electrochemical and structural models of the LIB. A fractional-order thermal–electrochemical–structural model (FOTESM) is established to analyze the stress evolution of the LIB under dynamic operating conditions. After introducing the historical weighting term, the fractional-order thermal model is applied to calculate the temperature state and adjust the temperature influencing factors of the electrochemical model. The correlation between the derivative order and the state of charge is studied. The results demonstrate that the stress simulation accuracy of FOTESM is improved by 14.05% at 0 °C and 10.92% at 40 °C versus the integer-order model. Due to the intervention of the derivative order, FOTESM can quickly track the true stress. FOTESM, as a high-order physical field form, is more suitable for analyzing the thermal and mechanical properties on porous electrodes.