A Cahn–Hilliard-type phase-field theory for species diffusion coupled with large elastic deformations: Application to phase-separating Li-ion electrode materials

Abstract

We formulate a unifi ed framework of balance laws and thermodynamically consistent constitutive equations which couple Cahn-Hilliard-type species diffusion with large elastic deformations of a body. The traditional Cahn-Hilliard theory, which is based on the species concentration and its spatial gradient leads to a partial differential equation for the concentration which involves fourth-order spatial derivatives in the concentration; this necessitates use of basis functions in fi nite-element solution procedures that are piecewise smooth and globally C 1-continuous. In order to use standard C 0-continuous fi nite-elements to implement our phase-fi eld model, we use a split method to reduce the fourth-order equation into two second-order partial differential equations (PDES). Specifi cally, we introduce an additional variable-as in the micromorphic theories of continua-and formulate a theory which depends on actual concentration, the micromorphic concentration, and the gradient of the micromorphic concentration. These two PDES, when taken together with the PDE representing the balance of forces, represent the three governing pdes for chemomechanically coupled problems. These equations are amenable to fi nite-element solution methods which employ standard C 0-continuous fi nite-element basis functions. We have numerically implemented our theory by writing a user-element subroutine for the widely used fi nite-element program Abaqus/Standard. We use this numerically implemented theory to fi rst study the diffusion-only problem of spinodal decomposition in the absence of any mechanical deformation. Next, we use our fully-coupled theory and numerical-implementation to study the combined effects of diffusion and stress on the lithiation of a representative spheroidal-shaped particle of a phase-separating electrode material.

A phase‐field model for chemo‐mechanical induced fracture in lithium‐ion battery electrode particles

“…A thermodynamically consistent model of chemo‐mechanics at finite strains of Li‐ion electrodes, which accounts for swelling and phase segregation, has recently been proposed by Anand and Di Leo et al. . The subsequently developed finite strain theory for the chemo‐elasticity at fracture accounts for gradient‐extended Cahn–Hilliard‐type diffusion and the possibility of phase segregation.…”

Phase field modeling of electrochemically induced fracture in Li‐ion battery with large deformation and phase segregation

“…In the work of Singh et al [13], a generalized BV kinetics model was proposed, which includes the influence of the phase transition on the surface reaction in a 1D case. In the mechanically coupled modeling, a few efforts have been made to treat the electrochemical reaction on the surface directly through the modified BV equation [17,18]. In the two dimensional case, a reaction model coupled with the Cahn-Hilliard bulk diffusion was presented by Dargaville and Farrell [15].…”

The understanding of solid electrolyte interface (SEI) formation and mechanism as the effect of flouro‐o‐phenylenedimaleimaide (F‐MI) additive on lithium‐ion battery

“…In that case, some experimental and theoretical works are conducted to gain an understanding of the formation and composition process of SEI and the prediction of the thickness of SEI growth . However, the evolutionary process of SEI layer formation has not been fully understood.…”