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Numerical Simulation of the Size Effects in Nanostructured Li-Ion Batteries Using the Isogeometric Analysis

Materials such as Si, Al and Sn are considered as active sites during the formation of Li-alloys. During the Li insertion, the volume of the active sites expands over 100% at maximum capacity. As a result, large internal stresses are produced. The effect of stresses is widely acknowledged. However, as the size of these particles is small, the gradient effects cannot be ignored. In this paper, we present for the first time the size effects within a purely gradient elasticity framework for a composite model with an inner Sn particle and a C matrix. Each of these constituents has different internal lengths. As the constitutive equation involves higher order gradient terms, the conventional finite element method is not suitable. We employ B-spline functions with the framework of the iso-geometric analysis spatial discretization. The effect of internal characteristic length on the radial and hydrostatic stresses is studied. It is observed that the internal length has significant impact on the stresses amplitudes.