Research Topic

Three-dimensional isogeometric analysis of mechanically coupled diffusion problem in Li-ion batteries based on Cahn-Hilliard phase-field model

Diffusion-induced stresses(DIS) in Li-ion batteries

Diffusion-induced stresses can occur as a result of compositional inhomogeneities during solid-state diffusion in many technological situations, such as lithium diffusion in battery electrodes. Experiments have shown that both cathode and anode of Li-ion batteries suffer mechanical degradation during cyclic charging and discharging process, which suggests high stresses developed in both electrodes. Silicon's high lithiation capacity makes it an attractive choice for use as negative electrodes in lithium-ion batteries. However, a volumetric strain of as much as 270% in the anode Si has been observed when fully charged. Therefore, an appropriate chemo-mechanical modeling of the electrode particles in lithium-ion batteries with large deformations is needed.

DIS problems have been widely studied during the last several decades. Nevertheless, such theories and simulations with large deformations are still at their infancy. In this work, a great effort is contributed to a continuum-level FEM model which couples species diffusion with large elastic-plastic deformations of the body, taking into account the phase segregation caused by the diffusion species.

Cahn-Hilliard phase-field large elasto-plastic deformation model

In situ TEM observations have revealed the coexistence of lithium-poor and lithium-rich phasesin the electrode particles during charging and discharging, which suggests that the concentration of Li-ion does not change gradually but experiences a gap at a certain interface.

To meet this need, traditionally two different approaches have been used: sharp-interface models and phase-field(diffuse-interface) models, of which the latter provides an alternative description for phase-transition phenomena. The key idea in phase-field models is to replace sharp interfaces by thin transition regions where the interfacial forces are smoothly distributed.

In this work the Cahn-Hilliard phase-field theory is employed, in which the chemical potential is the function of both the concentration and its gradient

Isogeometric concept

The Cahn-Hilliard equation includes the Laplacian of the concentration, making the governing diffusion equation the fourth-order derivative of the concentration. Furthermore, due to a chemo-mechanical coupling, the chemical potential deduced from a microforce balance and thermodynamically consistent constitutive relationship is also a function of deformation gradient, resulting in a coupled term of the third-order. 

Possible finite element solutions include mixed methods and discontinuous Galerkin formulation, of which, however, both are in request of extra degrees of freedom.

To achieve a straightforward numerical treatment of such high-order differential equations, isogeometric concept is applied in the finite element implementation, in which the basis derived from the geometry is used to approximate the solution fields, allowing for the possibility of higher-order, in our case C1 , continuity.

Key Research Area

Mechanics of Continuum, Lithium-ion batteries, Cahn-Hilliard phase-field, isogeometric ananlysis


Ying Zhao


Dolivostraße 15

D-64293 Darmstadt



+49 6151 16 - 24390


+49 6151 16 - 24404


zhao (at) gsc.tu...

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