We develop an algorithm and computational implementation for simulation of problems that combine Cahn–Hilliard type diffusion with finite strain elasticity. We have in mind applications such as the electro-chemo-mechanics of lithium ion (Li-ion) batteries. We concentrate on basic computational aspects. A staggered algorithm is proposed for the coupled multi-field model. For the diffusion problem, the fourth order differential equation is replaced by a system of second order equations to deal with the issue of the regularity required for the approximation spaces. Low order finite elements are used for discretization in space of the involved fields (displacement, concentration, nonlocal concentration). Three (both 2D and 3D) extensively worked numerical examples show the capabilities of our approach for the representation of (i) phase separation, (ii) the effect of concentration in deformation and stress, (iii) the effect of strain in concentration, and (iv) lithiation. We analyze convergence with respect to spatial and time discretization and found that very good results are achievable using both a staggered scheme and approximated strain interpolation.
Bibliographical noteFunding Information:
We gratefully acknowledge the Financial support by means of ERC-CoG COMBAT (Computational Modeling and Design of Lithium-ion batteries). We also gratefully acknowledge the useful discussions with Dr. Jahed Naghipoor who pointed out the practical importance of swelling during lithiation.
© 2015, Springer-Verlag Berlin Heidelberg.
- Cahn–Hilliard equation
- Coupling with elasticity
- Li-ion batteries
- Screened-Poisson equation
ASJC Scopus subject areas
- Computational Mechanics
- Ocean Engineering
- Mechanical Engineering
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics