COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โข...
Transcript of COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โข...
Topology Optimization of Lithium-Ion Battery Electrode Microstructure Morphology for Reduction of Damage
Accumulation and Longevity of Battery Life
Philip L. Clarke a, Reza Abedi a
a Dept. of Mechanical, Aerospace & Biomedical Engineering, University of Tennessee Space Institute, 411 B. H. Goethert Parkway, MS 21, Tullahoma, TN, 37388, USA,
{pclarke, rabedi}@utsi.edu
Motivations
โข Ubiquitous use in portal devices โข Cellular Phones โข Notebook
โข Energy storage device for renewable power sources
โข Solar, Hydro-, Geothermal power sources
โข LIB are top contenders to compensate intermittent nature of renewable sources.
โข Hybrid Electrical Vehicles (HEV) and Fully Electric Automotive Vehicles (EAV)
โข Higher gravimetric energy density of 150 Wh/kg [1]
โข Higher volumetric energy density of 150 Wh/kg [1]
โข Longer life of >1000 cycles [1] โข Relatively low cost [1] โข Global sales projection of approx.
3.5 trillion cells by 2015 (600% increase over 15 years)[2]
Challenges in Specific Applications
โข Commercial Demands: โข 150 km driving range โข 10-15 year lifespan โข 1000 cycles at 80% depth-of-
discharge
โข LIB Issues: โข Limited capacity โข Limited lifespan due to aging
mechanisms โข High cost for sustainability
New materials experience greater
volumetric expansion, stresses
and fracture
Fracture reduces cycle life and increases cost of system maintenance
New electrode materials for
capacity increase
Attempts to mitigate LIB Issues:
๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ฆ๐ฆ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ = 372๐๐๐๐๐ ๐๐โ ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ฆ๐ฆ๐๐๐บ๐บ๐๐๐บ๐บ๐๐๐๐๐๐ = 4000๐๐๐๐๐ ๐๐ โ ~300% ๐๐๐๐๐ถ๐ถ๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐๐โ
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
COMSOL Physics Implementation
โข Governing Equations โข Solid Mechanics: (General Form PDE)
๐ป๐ป โ ๐ช๐ช = ๐ป๐ป โ ๐๐ = ๐ป๐ป โ ๐ช๐ช ๐๐๐๐ โฮฉ3๐ถ๐ถ โ ๐ถ๐ถ๐บ๐บ๐บ๐บ๐๐ = 0
โข Electrochemical Diffusion: (General Form PDE)
๏ฟฝฬ๏ฟฝ๐ถ + ๐ป๐ป โ ๐ช๐ช = ๏ฟฝฬ๏ฟฝ๐ถ + ๐ป๐ป โ โ๐๐ ๐ป๐ป๐ถ๐ถ โฮฉ๐ ๐ ๐ ๐
๐ป๐ป๐๐๐บ = 0
๐๐ = ๐๐
๐๐ = ๐๐
COMSOL Physics Implementation
โข Governing Equations โข Electrochemical Diffusion: (General Form PDE)
๏ฟฝฬ๏ฟฝ๐ถ + ๐ป๐ป โ ๐ช๐ช = ๏ฟฝฬ๏ฟฝ๐ถ + ๐ป๐ป โ โ๐๐ ๐ป๐ป๐ถ๐ถ โฮฉ๐ ๐ ๐ ๐
๐ป๐ป๐๐๐บ = 0
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
Importance of Understanding Fracture
Fracture causes: โข Capacity Fade from structural
disorder โข Dislocation from Current collector โข Dislocation of conductive matrix
โข Increase growth of Passivated
Layers โข E.g. Solid Electrolyte Interphase (SEI) โข Increase impedance
THE MORE WE KNOW THE BETTER!
Complex Fracture (Courtesy of Grantab & Shenoy 2011)
Separation from current collector (Courtesy of Christensen 2010) SEI formation on nanoparticles (Wu, et. al. 2012)
Issues with Sharp Crack Modeling Issues arise from FEM discretization
Fixed Mesh Discretization: โข Pro: Relatively simple โข Con: Inaccurate pattern resolution
XFEM โ Enriched Mesh Elements: โข Pro: Relatively more accurate โข Con: Challenging and still in
development stage โข Issues of singularity still arise
Mesh Adaptivity โ Front Tracking: โข Pro: Can exactly capture fracture โข Con: Expensive and Elements can
distort and impose error โข Challenging geometric problem
Bulk Damage โข Statistical averaging of solution field
โข Alleviates issues of singularity
โข Solution is inclusive of damage location
โข Continuum viewpoint
โข Alleviates issues stemming from
discretization
โข Can be represented in terms of: โข Material Properties โข Mechanical Fields
๐ท๐ท๐๐ =๐๐๐๐๐ท๐ท๐๐๐๐
= 1 โ๐ธ๐ธ๐ท๐ท๐ธ๐ธ
โข Coupling through damage parameter
definition: โข Continuum Damage coupling to
Mechanical Response: ๐๐๐๐๐ถ๐ถ๐: ๐๐๏ฟฝ = 1 โ ๐ท๐ท โ1๐๐
๐ท๐ท๐ถ๐ถ๐๐๐ถ๐ถ๐๐๐๐: ๐ท๐ท = ๐๐(๐๐, ๐๐,๐ธ๐ธ, โฆ )
๐๐ ๐๐D
๐๐D ๐๐D
RVE
Bulk Damage
Stochastic and Randomness of Solution Probability
โข Appropriate for non-deterministic solution modeling
โข Most electrode active materials are brittle
Courtesy of Barai & Mukherjee 2013
Specific Proposed Implementation: Weibullโs distribution formulation
๐ท๐ท = 1 โ ๐๐โ๐๐โ๐๐๐๐
๐๐๐๐
โข Based on โweakest-linkโ approach
โข Appropriate where initial distribution of flaw is important
COMSOL Physics Implementation
โข Governing Equations โข Damage Evolution: (Distributed Ordinary Differential Equation)
๏ฟฝฬ๏ฟฝ๐ท = ๐ท๐ท๐ ๐ ฬ ๐ถ๐ถ๐๐ ๐ท๐ท๐ ๐ > ๐ท๐ท | ๐ท๐ท๏ฟฝฬ๏ฟฝ๐ > 0 0 ๐๐๐ถ๐ถ๐๐๐๐๐๐๐๐ถ๐ถ๐๐๐๐
๐ท๐ท๐ ๐ = 1 โ ๐๐โmax ๐๐1,0
๐๐๐๐
๐๐๐๐
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
Anisotropic Theory
Non-Uniform Expansion
โข Non-Uniformity in mechanical responses
โข Non-Uniformity in damage evolution
โข Multiphysics effects in context on LIB
โข Self-Limiting Strain
Courtesy of Liu, et. al. 2011
Courtesy of Lee, et. al. 2012 Courtesy of Goldman, et. al. 2011
Anisotropic Theory COMSOL Implementation
๐๐๐บ๐บ๐๐ = ๐ช๐ช๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐บ๐บ๐๐๐บ
Ccubic crystal =
๐ถ๐ถ11 ๐ถ๐ถ12๐ถ๐ถ12 ๐ถ๐ถ11
๐ถ๐ถ12 0๐ถ๐ถ12 0
0 00 0
๐ถ๐ถ12 ๐ถ๐ถ120 0
๐ถ๐ถ11 00 ๐ถ๐ถ44
0 00 0
0 00 0
0 00 0
๐ถ๐ถ44 00 ๐ถ๐ถ44
๐๐ =2๐ถ๐ถ44
๐ถ๐ถ11 โ ๐ถ๐ถ12โถ ๐๐๐๐๐ถ๐ถ๐๐๐๐๐๐๐๐ ๐๐๐๐ ๐๐๐๐๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐ฆ๐ฆ
Courtesy of Goldman, et. al. 2011
Subsequent Non-Uniform Damage
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
Importance of Optimization
โข Counterintuitive Concepts!
โข Design rules to limit electrode
degradation
โข Also limits usable capacity
โข Optimization finds optimal
design
โข Minimize damage
โข Maximum performance
Previous works optimize based on LIB performance quantities but what about mechanical response (i.e. damage evolution)?
Courtesy of Goldman, et. al. 2011
Optimization Framework
โข Multi-Objective Scheme โข Both Mechanical response and capacity optimized simultaneously โข Pareto Optimization
โข Optimization based on: โข Gravimetric energy density โข Volumetric energy density โข Effective (Usable) capacity โข Stress generation โข Damage Criteria
โข Optimization Issue: โข Altering electrode parameters such as particle size
โข limits fracture โข accelerate failure in systems susceptible to side
reactions (SEI formation).
โข Proposed Solution โข Optimization of different aspect of electrode
characteristic โข Optimize electrode surface (Electrode-electrolyte
interface) โข Subject to higher stresses than current collector
interface
Implemented COMSOL Geometries
Courtesy of Goldman, et. al. 2011
COMSOL Physics Implementation โข Implemented Boundary Conditions
๐ช๐ช โ ๐๐ =๐ถ๐ถ๐๐๐น๐น
:๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐๐๐๐ ๐๐๐๐๐๐๐๐
๐ถ๐ถ๐บ๐บ๐บ๐บ:๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐ถ๐ถ๐๐๐๐๐๐๐๐๐๐ ๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ฆ๐ฆ ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐๐ โฒ๐ถ๐ถโฒ ๐ถ๐ถ๐๐ ๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐๐๐๐
๐๐๐บ๐บ๐บ๐บ:๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐ถ๐ถ๐๐๐๐๐๐๐๐๐๐ ๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐๐๐๐๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ฆ๐ฆ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐๐ ๐ถ๐ถโฒ โฒ๐ถ๐ถ๐๐ ๐๐๐ถ๐ถ๐๐๐ถ๐ถ๐๐๐ถ๐ถ๐ถ๐ถ๐๐๐๐๐๐๐๐๐ถ๐ถ
๐๐ = 0 โถ ๐น๐น๐ถ๐ถ๐๐๐๐๐๐ ๐๐๐ถ๐ถ๐๐๐ถ๐ถ๐๐๐ถ๐ถ๐ถ๐ถ๐๐๐๐๐๐๐๐๐ถ๐ถ
๐๐1๐บ๐บ , ๐ถ๐ถ1
๐บ๐บ ๐๐1๐บ๐บ , ๐ถ๐ถ1
๐บ๐บ
๐๐2๐บ๐บ , ๐ถ๐ถ2
๐บ๐บ ๐๐2๐บ๐บ , ๐ถ๐ถ2
๐บ๐บ
๐ช๐ช โ ๐๐
COMSOL Preliminary Results
๐น๐น1 ๐ท๐ท : โซ ๐ท๐ท ๐๐๐๐ ฮฉโซ 1 ๐๐๐๐ ฮฉ
๐๐๐ถ๐ถ๐๐๐ถ๐ถ: โซ๐๐ ๐๐๐๐
ฮฉโซ 1 ๐๐๐๐ ฮฉ
= 0.8
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
Conclusion
Implemented iso-/anisotropic elasto-diffusion coupling
Implemented continuum damage physics
โPartialโ anisotropic mechanical responses
Account for multiphase lithiation physics
Implement elasto-plastic damage evolution law
Implement robust topology optimization function (COMSOL Livelink w/ MATLAB)
References
1. (Linden, et. al. 2001), Handbook of Batteries. McGraw-Hill, NY
2. (Scrosati, et. al. 2010), Journal of Power Source, 195, 2419-2430
3. (Grantab, et. al. 2011), Journal of Electrochem. Soc., 158, A948-A954
4. (Christensen 2010), Journal of Electrochem. Soc., 157, A366-A380
5. (Barai, et. al. 2013), Journal of Electrochem. Soc., 160, A955-A967
6. (Liu, et. al. 2011), Nano Letters, 11, 3312-3318
7. (Goldman, et. al. 2011), Advanced Func, Mat., 21, 2412-2422