Modeling of Intercalation-Induced Stress

Intercalation-induced stress can be modeled by using an analogy to thermal stress. From the constitutive equation presented in Section 26.1.2.2 and the force equilibrium equation, the displacement equation can be written as 

For a one-dimensional spherical particle, this equation can be simplified as d M 2 du 2m 1 + V dc 

Integration of this equation yields a solution for u, from which stresses may be obtained as 

Considering the effect of stress-driven diffusion, the diffusion of Li-ions inside an electrode particle can be described as 

The one-dimensional decoupled diffusion equation without the elimination of stress-dependent terms is easier to solve numerically. With li-ion concentration obtained, intercalation-induced stresses can be calculated using the analytical expressions of Equations 26.4 and 26.5. Governing equations for one-dimensional spherical particles can be solved using the finite difference method. Governing equations for three-dimensional elHpsoidal particles are solved using the finite element analysis package GOMSOL Multiphysics. 

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