• Corpus ID: 214743269

# On $\Gamma-$Convergence of a Variational Model for Lithium-Ion Batteries

@article{Stinson2020OnO,
title={On \$\Gamma-\$Convergence of a Variational Model for Lithium-Ion Batteries},
author={Kerrek Stinson},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Kerrek Stinson
• Published 31 March 2020
• Mathematics
• arXiv: Analysis of PDEs
A singularly perturbed phase field model used to model lithium-ion batteries including chemical and elastic effects is considered. The underlying energy is given by $$I_\epsilon [u,c ] := \int_\Omega \left( \frac{1}{\epsilon} f(c) + \epsilon\|\nabla c\|^2 + \frac{1}{\epsilon}\mathbb{C} (e(u)-ce_0) : (e(u)-ce_0)\right) dx,$$ where $f$ is a double well potential, $\mathbb{C}$ is a symmetric positive definite fourth order tensor, $c$ is the normalized lithium-ion density, and $u$ is the material…

## References

SHOWING 1-10 OF 47 REFERENCES
Second Order Singular Perturbation Models for Phase Transitions
• Mathematics
SIAM J. Math. Anal.
• 2000
Singular perturbation models involving a penalization of the first order derivatives have provided a new insight into the role played by surface energies in the study of phase transitions problems.
Relaxation of quasiconvex functional in BV(Ω, ℝp) for integrands f(x, u,∇;u)
• Mathematics
• 1993
AbstractIn this paper it is shown that if p(x, u,·) is a quasiconvex function with linear growth, then the relaxed functional in BV(Ω, ℝp) of $$u \to \int\limits_\Omega {f(x, u(x), \nabla u(x)) dx} Computational electro-chemo-mechanics of lithium-ion battery electrodes at finite strains • Engineering • 2015 A finite strain theory for electro-chemo-mechanics of lithium ion battery electrodes along with a monolithic and unconditionally stable finite element algorithm for the solution of the resulting Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance • Mathematics • 2006 The singularly perturbed two‐well problem in the theory of solid‐solid phase transitions takes the form$$I_{\varepsilon}[u] = \int\limits^{}_{\Omega} {1 \over {\varepsilon}} W(\nabla u) +
Gamma Convergence and Applications to Phase Transitions
1. Liquid–Liquid Phase Transitions Consider a fluid confined into a container Ω ⊂ R . Assume that the total mass of the fluid is m, so that admissible density distributions u : Ω→ R satisfy the
A Γ‐convergence result for the two‐gradient theory of phase transitions
• Mathematics
• 2002
The generalization to gradient vector fields of the classical double‐well, singularly perturbed functionals,  I_{\varepsilon} ( u;\Omega ) :=\int_{\Omega}{{1}\over{\varepsilon}} W(\nabla u)
Phase Separation Dynamics in Isotropic Ion-Intercalation Particles
• Physics, Materials Science
SIAM J. Appl. Math.
• 2014
A simple mathematical model of ion intercalation in a spherical solid nanoparticle, which predicts transitions from solid-solution radial diffusion to two-phase shrinking-core dynamics, and a control-volume discretization is developed in spherical coordinates.
Geometric Rigidity Estimates for Incompatible Fields in Dimension $\ge$ 3
• Mathematics
• 2017
We prove geometric rigidity inequalities for incompatible fields in dimension higher than 2. We are able to obtain strong scaling-invariant $L^p$ estimates in the supercritical regime, while for
Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics.
• M. Bazant
• Chemistry
Accounts of chemical research
• 2013
A general theory of chemical kinetics, developed over the past 7 years, is presented, capable of answering questions about how reaction rate is a nonlinear function of the thermodynamic driving force, the free energy of reaction, expressed in terms of variational chemical potentials.