Transient analysis of diffusion-induced deformation in a viscoelastic electrode

In this study, we analyze the transient diffuse-induced-deformation of an electrode consisting of the conducting polymer polypyrrole (PPY) by using the theories of linear viscoelasticity and diffusion-induced stress. We consider two constitutive relationships with dependence of viscosity on strain rate: Kelvin-Voigt model and three-parameter solid model. A numerical method is used to solve the problem of one-dimensional, transient diffusion-induced-deformation under potentiostatic operation. The numerical results reveal that the maximum displacement occurs at the free surface and the maximum stress occurs at the fixed end. The inertia term causes the stress to increase at the onset of lithiation. The stress decreases with increasing lithiation time and approaches zero for prolonged lithiation. Compared with the two different constitutive relationships between the Kelvin-Viogt model and three-parameter solid model, it can be found that the spatiotemporal distribution of lithium ion concentrations in the Kelvin-Viogt model is larger than that in the three-parameter solid model at the same moment, whereas the stress of the Kelvin-Viogt model is smaller owing to more than one spring in the three-parameter solid model.