Electrochemical–mechanical multi-scale model and validation with thickness change measurements in prismatic lithium-ion batteries

A multi-scale model able to evaluate volume changes from atomic level of active material up to battery level of prismatic lithium iron phosphate–graphite batteries is presented in this work. The model goes through the scales according to the following steps: changes of lattice parameters as a function of lithium intercalation and consequent lattice volume deformation; active material particles deformation; electrode volume changes and porosity reduction; evaluation of the effects of the hard case on the overall battery thickness change through finite element modelling. From the experimental side, the thickness change of prismatic LFP–graphite batteries is measured during operation at different current rates with high-precision optical sensors and the statistical analysis of the results is carried out. Scanning electron microscope analyses are carried out on electrode samples for measuring model parameters and to give a visual proof of the existence of different scales in lithium ion batteries. Finally, the results of the multi-scale model are validated with the experiments.