A new model of porous electrodes based on the Gibbs free energy is developed, in which lithium-ion (Li-ion) diffusion, diffusion-induced stress (DIS), Butler–Volmer (BV) reaction kinetics, and size polydispersity of electrode particles are considered. The influence of BV reaction kinetics and concentration-dependent exchange current density (ECD) on concentration profile and DIS evolution are numerically investigated. BV reaction kinetics leads to a decrease in Li-ion concentration and DIS. In addition, concentration-dependent ECD results in a decrease in Li-ion concentration and an increase in DIS. Size polydispersity of electrode particles significantly affects the concentration profile and DIS. Optimal macroscopic state of charge (SOC) should consider the influence of the microscopic SOC values and mass fractions of differently sized particles.