The effect of stress on storage particles within a lithium ion battery, while acknowledged, is not understood very well. In this work three non-dimensional parameters were identified which govern the stress response within a spherical storage particle. These parameters are developed using material properties such as the diffusion coefficient, particle radius, partial molar volume and Young's modulus. Stress maps are then generated for various values of these parameters for fixed rates of insertion, applying boundary conditions similar to those found in a battery. Stress and concentration profiles for various values of these parameters show the coupling between stress and concentration is magnified depending on the values of the parameters. These maps can be used for different materials, depending on the value of the dimensionless parameters. The value of maximum stress generated is calculated for extraction as well as insertion of lithium into the particle.

The model was then used to study to ellipsoidal particles in order to ascertain the effect of geometry on the maximum stress within the particle. By performing a parameter study, we can identify those materials for which particular aspect ratios of ellipsoids are more beneficial, in terms of reducing stress. We find that the stress peaks at certain aspect ratios, mostly at 2 and 1/ 2 . A parameter study was also performed on cubic particle. The values of maximum stresses for both insertion and extraction of lithium were plotted as contour plots. It was seen that the material parameters influenced the location of the maximum stress, with the maximum stress occurring either at the center of the edge between two faces or the point at the center of a face.

Newer materials such as silicon are being touted as new lithium storage materials for batteries due to their higher capacity. Their tendency to rapidly loose capacity in a short period of time has led to a variety designs such are the use of carbon nanotubes or the use of coatings in order to mitigate the large expansion and stresses, which leads to spalling off of the material. We therefore extended the results for spherical storage particles to include the presence of an additional layer of material surrounding the storage particle. We perform a parameter study to see at which material properties are most beneficial in reducing stresses within the particle, and the results were tabulated. It was seen that thicker layers can lead to mitigation in the value of maximum stresses. A simple fracture analysis was carried out and the material parameters which would most likely cause crack growth to occur were identified.

Finally an integrated 2-D model of a lithium ion battery was developed to study the mechanical stress in storage particles as a function of material properties. The effect of morphology on the stress and lithium concentration is studied for the case of extraction of lithium in terms of the previously developed non-dimensional parameters. Both, particles functioning in isolation were studied, as well as in closely-packed systems. The results show that the particle distance from the separator, in combination with the material properties of the particle, is critical in predicting the stress generated within the particle.