COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation β’...
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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
Transcript of COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation β’...
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
β’ Ubiquitous use in portal devices β’ Cellular Phones β’ Notebook
β’ Energy storage device for renewable power sources
β’ Solar, Hydro-, Geothermal power sources
β’ LIB are top contenders to compensate intermittent nature of renewable sources.
β’ Hybrid Electrical Vehicles (HEV) and Fully Electric Automotive Vehicles (EAV)
β’ Higher gravimetric energy density of 150 Wh/kg [1]
β’ Higher volumetric energy density of 150 Wh/kg [1]
β’ Longer life of >1000 cycles [1] β’ Relatively low cost [1] β’ Global sales projection of approx.
3.5 trillion cells by 2015 (600% increase over 15 years)[2]
Challenges in Specific Applications
β’ Commercial Demands: β’ 150 km driving range β’ 10-15 year lifespan β’ 1000 cycles at 80% depth-of-
discharge
β’ LIB Issues: β’ Limited capacity β’ Limited lifespan due to aging
mechanisms β’ 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:
πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπ¦π¦πΊπΊπΊπΊπΊπΊπΊπΊπΊπΊπΊπΊπΊπΊπΊ = 372πππππ ππβ πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπ¦π¦πππΊπΊπππΊπΊππππππ = 4000πππππ ππ β ~300% πππππΆπΆπΆπΆπππππΆπΆππππβ
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
COMSOL Physics Implementation
β’ Governing Equations β’ Solid Mechanics: (General Form PDE)
π»π» β πͺπͺ = π»π» β ππ = π»π» β πͺπͺ ππππ βΞ©3πΆπΆ β πΆπΆπΊπΊπΊπΊππ = 0
β’ Electrochemical Diffusion: (General Form PDE)
οΏ½ΜοΏ½πΆ + π»π» β πͺπͺ = οΏ½ΜοΏ½πΆ + π»π» β βππ π»π»πΆπΆ βΞ©π π π π
π»π»πππΊ = 0
ππ = ππ
ππ = ππ
COMSOL Physics Implementation
β’ Governing Equations β’ Electrochemical Diffusion: (General Form PDE)
οΏ½ΜοΏ½πΆ + π»π» β πͺπͺ = οΏ½ΜοΏ½πΆ + π»π» β βππ π»π»πΆπΆ βΞ©π π π π
π»π»πππΊ = 0
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
Importance of Understanding Fracture
Fracture causes: β’ Capacity Fade from structural
disorder β’ Dislocation from Current collector β’ Dislocation of conductive matrix
β’ Increase growth of Passivated
Layers β’ E.g. Solid Electrolyte Interphase (SEI) β’ 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: β’ Pro: Relatively simple β’ Con: Inaccurate pattern resolution
XFEM β Enriched Mesh Elements: β’ Pro: Relatively more accurate β’ Con: Challenging and still in
development stage β’ Issues of singularity still arise
Mesh Adaptivity β Front Tracking: β’ Pro: Can exactly capture fracture β’ Con: Expensive and Elements can
distort and impose error β’ Challenging geometric problem
Bulk Damage β’ Statistical averaging of solution field
β’ Alleviates issues of singularity
β’ Solution is inclusive of damage location
β’ Continuum viewpoint
β’ Alleviates issues stemming from
discretization
β’ Can be represented in terms of: β’ Material Properties β’ Mechanical Fields
π·π·ππ =πππππ·π·ππππ
= 1 βπΈπΈπ·π·πΈπΈ
β’ Coupling through damage parameter
definition: β’ Continuum Damage coupling to
Mechanical Response: πππππΆπΆπ: πποΏ½ = 1 β π·π· β1ππ
π·π·πΆπΆπππΆπΆππππ: π·π· = ππ(ππ, ππ,πΈπΈ, β¦ )
ππ ππD
ππD ππD
RVE
Bulk Damage
Stochastic and Randomness of Solution Probability
β’ Appropriate for non-deterministic solution modeling
β’ Most electrode active materials are brittle
Courtesy of Barai & Mukherjee 2013
Specific Proposed Implementation: Weibullβs distribution formulation
π·π· = 1 β ππβππβππππ
ππππ
β’ Based on βweakest-linkβ approach
β’ Appropriate where initial distribution of flaw is important
COMSOL Physics Implementation
β’ Governing Equations β’ Damage Evolution: (Distributed Ordinary Differential Equation)
οΏ½ΜοΏ½π· = π·π·π π Μ πΆπΆππ π·π·π π > π·π· | π·π·οΏ½ΜοΏ½π > 0 0 πππΆπΆππππππππΆπΆππππ
π·π·π π = 1 β ππβmax ππ1,0
ππππ
ππππ
Electrochemistry + Solid Mechanics Coupling
Elasto-Diffusion Induced Fracture/Damage
Theory of Anisotropy
Optimization
Conclusion
Anisotropic Theory
Non-Uniform Expansion
β’ Non-Uniformity in mechanical responses
β’ Non-Uniformity in damage evolution
β’ Multiphysics effects in context on LIB
β’ 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
πππΊπΊππ = πͺπͺπππππππππππππππππΊπΊπππΊ
Ccubic crystal =
πΆπΆ11 πΆπΆ12πΆπΆ12 πΆπΆ11
πΆπΆ12 0πΆπΆ12 0
0 00 0
πΆπΆ12 πΆπΆ120 0
πΆπΆ11 00 πΆπΆ44
0 00 0
0 00 0
0 00 0
πΆπΆ44 00 πΆπΆ44
ππ =2πΆπΆ44
πΆπΆ11 β πΆπΆ12βΆ πππππΆπΆππππππππ ππππ πππππΆπΆπππππΆπΆπππππΆπΆπ¦π¦
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
β’ Counterintuitive Concepts!
β’ Design rules to limit electrode
degradation
β’ Also limits usable capacity
β’ Optimization finds optimal
design
β’ Minimize damage
β’ 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
β’ Multi-Objective Scheme β’ Both Mechanical response and capacity optimized simultaneously β’ Pareto Optimization
β’ Optimization based on: β’ Gravimetric energy density β’ Volumetric energy density β’ Effective (Usable) capacity β’ Stress generation β’ Damage Criteria
β’ Optimization Issue: β’ Altering electrode parameters such as particle size
β’ limits fracture β’ accelerate failure in systems susceptible to side
reactions (SEI formation).
β’ Proposed Solution β’ Optimization of different aspect of electrode
characteristic β’ Optimize electrode surface (Electrode-electrolyte
interface) β’ Subject to higher stresses than current collector
interface
Implemented COMSOL Geometries
Courtesy of Goldman, et. al. 2011
COMSOL Physics Implementation β’ Implemented Boundary Conditions
πͺπͺ β ππ =πΆπΆπππΉπΉ
:πΆπΆπππππΆπΆπππππΆπΆπππΆπΆπΆπΆπΆπΆππππ ππππππππ
πΆπΆπΊπΊπΊπΊ:πΆπΆπππππΆπΆπΆπΆππππππππππ πΆπΆπππππΆπΆπππππΆπΆπΆπΆπΆπΆπΆπΆπ¦π¦ πΆπΆπΆπΆπΆπΆππ β²πΆπΆβ² πΆπΆππ πΆπΆπππππΆπΆπππππΆπΆπππΆπΆπΆπΆπΆπΆππππ
πππΊπΊπΊπΊ:πΆπΆπππππΆπΆπΆπΆππππππππππ πΆπΆπππππΆπΆπππππΆπΆπΆπΆπΆπΆπΆπΆπ¦π¦πΆπΆπΆπΆπΆπΆππ πΆπΆβ² β²πΆπΆππ πππΆπΆπππΆπΆπππΆπΆπΆπΆπππππππππΆπΆ
ππ = 0 βΆ πΉπΉπΆπΆππππππ πππΆπΆπππΆπΆπππΆπΆπΆπΆπππππππππΆπΆ
ππ1πΊπΊ , πΆπΆ1
πΊπΊ ππ1πΊπΊ , πΆπΆ1
πΊπΊ
ππ2πΊπΊ , πΆπΆ2
πΊπΊ ππ2πΊπΊ , πΆπΆ2
πΊπΊ
πͺπͺ β ππ
COMSOL Preliminary Results
πΉπΉ1 π·π· : β« π·π· ππππ Ξ©β« 1 ππππ Ξ©
πππΆπΆπππΆπΆ: β«ππ ππππ
Ξ©β« 1 ππππ Ξ©
= 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
βPartialβ 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
