A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity

P. Areias, E. Samaniego, Timon Rabczuk

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)339-351
Number of pages13
JournalComputational Mechanics
Volume57
Issue number2
DOIs
Publication statusPublished - 2016 Feb 1
Externally publishedYes

Fingerprint

Finite Strain
Elasticity
Lithium-ion Battery
Fourth-order Differential Equation
Phase separation
Approximation Space
Diffusion Problem
Interpolation
Mechanics
Phase Separation
Differential equations
Time Discretization
Second Order Equations
Discretization
Interpolate
Regularity
Finite Element
Numerical Examples
Simulation

Keywords

  • Cahn–Hilliard equation
  • Coupling with elasticity
  • Diffusion
  • Li-ion batteries
  • Screened-Poisson equation

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Mechanical Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Computational Mathematics

Cite this

A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity. / Areias, P.; Samaniego, E.; Rabczuk, Timon.

In: Computational Mechanics, Vol. 57, No. 2, 01.02.2016, p. 339-351.

Research output: Contribution to journalArticle

Areias, P. ; Samaniego, E. ; Rabczuk, Timon. / A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity. In: Computational Mechanics. 2016 ; Vol. 57, No. 2. pp. 339-351.
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