Probing component contributions and internal polarization in silicon-graphite composite anode for lithium-ion batteries with an electrochemical-mechanical model

Silicon–graphite(Si–Gr)composite anodes are attractive alternatives to replace Gr anodes for lithium-ion batteries(LIBs)owing to their relatively high capacity and mild volume change.However,it is difficult to understand electrochemical interactions of Si and Gr in Si–Gr composite anodes and internal polarization of LIBs with regular experiment methods.Herein,we establish an electrochemical-mechanical coupled model to study the effect of rate and Si content on the electrochemical and stress behavior in a Si–Gr composite anode.The results show that the composites of Si and Gr not only improve the lithiation kinetics of Gr but also alleviate the voltage hysteresis of Si and decrease the risk of lithium plating in the negative electrode.What's more,the Si content is a tradeoff between electrode capacity and electrode volume variation.Further,various internal polarization contributions of cells using Si–Gr composite anodes are quantified by the voltage decomposition method.The results indicate that the electrochemical polarization of electrode materials and the electrolyte ohmic over-potential are dominant factors in the rate performance of cells,which provides theoretical guidance for improving the rate performance of LIBs using Si–Gr composite anodes.

HIERARCHICAL STOCHASTIC FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS

In this paper, the hierarchical approach is adopted for series representation of the stochastic nodal displacement vector using the hierarchical basis vectors, while the Karhunen- Loire series expansion technique is employed to discretize the random field into a set of random variables. A set of hierarchical basis vectors are defined to approximate the stochastic response quantities. The stochastic variational principle instead of the projection scheme is adopted to develop a hierarchical stochastic finite element method （HSFEM） for stochastic structures under stochastic loads. Simplified expressions of coefficients of governing equations and the first two statistical moments of the response quantities in the schemes of the HSFEM are developed, so that the time consumed for computation can be greatly reduced. Investigation in this paper suggests that the HSFEM yields a series of stiffness equations with similar dimensionality as the perturbation stochastic finite element method （PSFEM）. Two examples are presented for numerical study on the performance of the HSFEM in elastic structural problems with stochastic Young＇s Modulus and external loads. Results show that the proposed method can achieve higher accuracy than the PSFEM for cases with large coefficients of variation, and yield results agreeing well with those obtained by the Monte Carlo simulation （MCS）.