Lithium Ion Batteries

My work involves the development of a model to determine the contribution of stress to aging of lithium-ion batteries. Lithium-ion batteries work due to the repeated insertion and de-insertion of lithium ions from storage particles at different electrodes. This process causes strains to develop within the storage particle materials – which over time leads to cracks and fracture of the particle. This ultimately contributes to the loss in capacity of the battery and degradation of its properties. Hence it is important to develop a model to predict stresses that arise in the battery in order to develop strategies to minimize these stresses.

Schematic of LI Battery

Schematic of Lithium Ion battery

During my research, we developed a coupled diffusion-stress model to predict stresses as a result of diffusion of lithium into spherical particles. This model was non-dimensionalized and three important non-dimensional parameters that govern the stress response were identified. We then calculated the stress that develops in a spherical storage particle for various values of these parameters and developed stress maps. These maps can be used to predict stress as a function of the non-dimensional parameters and can be used for spherical particles of any material. The results show the inter-dependence of stress and diffusion, with high values of stress modifying the diffusion gradients and vice versa . The details can be found here and here. The results showed that it is a combination of parameters that influence the maximal stresses rather than a single component. More importantly these maps will help identify which combination of material properties are useful for mitigating stresses, and can help focus experimental work on selected materials alone.

Compare All Morphs

This image shows that increasing the number of particles leads to higher stresses.

Our ongoing research is a two pronged effort into further development of this model. The first approach is to extend the model into three-dimensions and analyze irregularly shaped particles. This will start to approach a real battery system and help in verifying experimental results more accurately. The second approach is to study newer high capacity materials such as silicon and tin. These materials promise to improve existing battery capacities significantly. However due to high volume expansion these particles experience high stresses which leads them to rupture very quickly. Experimental work has shown that the presence of coatings can help mitigate these stresses – we aim to develop a model which would explain this behavior. This model would further serve to develop strategies to utilize these materials within electrodes.

Research internships

This project was done in collaboration with Robert Bosch GmbH and I had the opportunity to visit their research headquarters in Schillerhohe, Germany. In my first internship from November to December 2010, we modeled the stress in each of the components, including the binder matrix, in order to determine the expansion of the complete battery. The model was used to analyse the effect of particle shape and morphology on the transport properties as well as the stress within the different components. These stresses were used to model the volume change of the battery. In my second trip from July-August 2012 the model for the entire battery was extended to three-dimensions.

3D Simulation of Cathode

Initial 3D simulations of the cathode. The particles nearer the separator intercalate quicker, and therefore have a higher concentration.

Papers Associated with this work

  • 1. R. Purkayastha and R.M. McMeeking, A Linearized Model for Lithium-Ion Batteries and Maps for their Performance and Failure, Journal of Applied Mechanics, 2011 DOI : 10.1115/1.4005962
  • 2. R. Purkayastha and R.M. McMeeking, An Integrated Two-Dimensional Model of a Lithium- Ion Battery: The effect of material parameters and particle morphology on storage particle stress, Computational Mechanics, 2012, 50(2), 209-227
  • 3. R. Purkayastha and R.M. McMeeking, A Parameter Study of Intercalation of Lithium into Storage Particles in a Lithium Ion Battery, Computational Materials Science, 2013 (Accepted)
  • 4. R. Purkayastha and R.M. McMeeking, Meccanica, Stress due to intercalation of lithium in cubic shaped particles: a parameter study, 51(12) ,3081-3096, 2016

Conference presentations

  • 1. R. Purkayastha and R.M. McMeeking, Effect of Particle Morphology on Stress in a Lithium-Ion Battery Using an Integrated Model in 2-D, Meeting of the Electrochemical Society, Fall 2012
  • 2. R. Purkayastha and R.M. McMeeking, The Use of Non-Dimensional Parameters to Study Stress in Lithium-Ion Battery Electrode Storage Particles, ASME 2012 International Mechanical Engineering Congress & Exposition, 2012

Seminars and Talks

  • 1. R. Purkayastha and R.M. McMeeking, A parameter study of stress in lithium ion battery storage particles, Department Seminar, Metallurgical Engineering and Materials Science, Indian Institute of Technology, Bombay, August 2012
  • 2. R. Purkayastha and R.M. McMeeking, A parameter study of stress in lithium ion battery storage particles, Institute for Applied Materials, (IAM-WBM), Karlsruhe Institute of Technology, 13th July 2012
  • 3. R. Purkayastha and R.M. McMeeking, Stress and aging in lithium ion batteries, Structural Seminar, Materials Department, University of California Santa Barbara


  • 1. R. Purkayastha and R.M. McMeeking, Integrated Model for Storage Particles, Interface Kinetics and Electrolyte in Lithium-Ion batteries, Gordon Conference on Thin Films and Small-Scale Mechanical Behavior, Colby College, Waterville, Maine, 2010
  • 2. R. Purkayastha and R.M. McMeeking, Single Particle Model for Lithium Storage Particles, Tony Evans Memorial Conference, University of California, July 2010