ORALS

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. As the size of these particles is small, however, the gradient effects cannot be ignored. In this paper, we present, for the first time, the size effects within a purely gradient elasticity framework. A coupled mechanical equilibrium and Li diffusion accounting for the effect of stress on diffusion and the effect of diffusion on stress are considered. We also consider the effect of concentration on the Young's modulus. As the constitutive equation involves higher order gradient terms, the conventional finite element method is not suitable. Moreover, the two-way coupling necessitates the need for higher order shape functions. In this study, we employ B-spline functions with the framework of the iso-geometric analysis for spatial discretization. The effect of internal characteristic length on the concentration evolution and the hydrostatic stresses are studied. It is observed that the internal length has significant impact on the stress amplitudes.