Analytical Solution for Coupled Diffusion Induced Stress Model for Lithium-Ion Battery
Abstract
:1. Introduction
2. Problem Formulation
2.1. Mechanical Problem
2.2. Diffusive Problem
2.3. Uncoupled Problem
2.4. Coupled Problem
- The concentration field is calculated according to the physical diffusion coefficient.
- The equivalent diffusion coefficient is calculated for each radial position with the concentration function.
- A new concentration function is computed with the equivalent diffusion coefficient computed in the previous iteration.
3. Results and Discussion
3.1. Compatibility between Model Assumptions and Real Material
3.2. Comparison with the Results of Numerical Models in Literature
3.3. Insertion under Galvanostatic Control
3.4. Extraction under Galvanostatic Control
3.5. Evolution of Von Mises Stress in Time
3.6. Influence of Hydrostatic Stress on Concentration
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
C | Concentration | mol/m |
Initial concentration | mol/m | |
Maximum concentration | mol/m | |
Surface concentration | mol/m | |
D | Diffusion coefficient | m/s |
Equivalent diffusion coefficient | m/s | |
E | Young Modulus | |
F | Faraday constant | 96485.332 As/mol |
I | Current density | A/m |
J | Lithium flux | mol/ms |
M | Mobility | mol· s/Kg |
r | Radius | m |
R | Particle radius | m |
Gas constant | 8.3145 J/mol K | |
State of charge | - | |
T | Temperature 298 | K |
u | Displacement | m |
x | Normalized radial coordinate | - |
Hoop strain | - | |
Chemical strain | - | |
Radial strain | - | |
Chemical potential | J/mol | |
Reference chemical potential | J/mol | |
Poisson ratio | - | |
Hoop stress | MPa | |
Hydrostatic stress | MPa | |
Radial stress | MPa | |
Characteristic time | - | |
Partial molar volume | m/mol |
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Clerici, D.; Mocera, F.; Somà, A. Analytical Solution for Coupled Diffusion Induced Stress Model for Lithium-Ion Battery. Energies 2020, 13, 1717. https://doi.org/10.3390/en13071717
Clerici D, Mocera F, Somà A. Analytical Solution for Coupled Diffusion Induced Stress Model for Lithium-Ion Battery. Energies. 2020; 13(7):1717. https://doi.org/10.3390/en13071717
Chicago/Turabian StyleClerici, Davide, Francesco Mocera, and Aurelio Somà. 2020. "Analytical Solution for Coupled Diffusion Induced Stress Model for Lithium-Ion Battery" Energies 13, no. 7: 1717. https://doi.org/10.3390/en13071717