COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข...

24
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 โ€ข...

Page 1: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

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

Page 2: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Motivations

โ€ข Ubiquitous use in portal devices โ€ข Cellular Phones โ€ข Notebook

โ€ข Energy storage device for renewable power sources

โ€ข Solar, Hydro-, Geothermal power sources

โ€ข LIB are top contenders to compensate intermittent nature of renewable sources.

โ€ข Hybrid Electrical Vehicles (HEV) and Fully Electric Automotive Vehicles (EAV)

โ€ข Higher gravimetric energy density of 150 Wh/kg [1]

โ€ข Higher volumetric energy density of 150 Wh/kg [1]

โ€ข Longer life of >1000 cycles [1] โ€ข Relatively low cost [1] โ€ข Global sales projection of approx.

3.5 trillion cells by 2015 (600% increase over 15 years)[2]

Page 3: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Challenges in Specific Applications

โ€ข Commercial Demands: โ€ข 150 km driving range โ€ข 10-15 year lifespan โ€ข 1000 cycles at 80% depth-of-

discharge

โ€ข LIB Issues: โ€ข Limited capacity โ€ข Limited lifespan due to aging

mechanisms โ€ข 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:

๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘ฆ๐‘ฆ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ๐บ = 372๐‘š๐‘š๐‘š๐‘š๐‘š ๐‘”๐‘”โ„ ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘ฆ๐‘ฆ๐‘†๐‘†๐บ๐บ๐‘†๐‘†๐บ๐บ๐‘†๐‘†๐‘†๐‘†๐‘†๐‘† = 4000๐‘š๐‘š๐‘š๐‘š๐‘š ๐‘”๐‘” โ†’ ~300% ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’โ„

Page 4: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Electrochemistry + Solid Mechanics Coupling

Elasto-Diffusion Induced Fracture/Damage

Theory of Anisotropy

Optimization

Conclusion

Page 5: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

COMSOL Physics Implementation

โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE)

๐›ป๐›ป โ‹… ๐šช๐šช = ๐›ป๐›ป โ‹… ๐ˆ๐ˆ = ๐›ป๐›ป โ‹… ๐‘ช๐‘ช ๐œ–๐œ–๐‘‡๐‘‡ โˆ’ฮฉ3๐ถ๐ถ โˆ’ ๐ถ๐ถ๐บ๐บ๐บ๐บ๐‘Ÿ๐‘Ÿ = 0

โ€ข Electrochemical Diffusion: (General Form PDE)

๏ฟฝฬ‡๏ฟฝ๐ถ + ๐›ป๐›ป โ‹… ๐šช๐šช = ๏ฟฝฬ‡๏ฟฝ๐ถ + ๐›ป๐›ป โ‹… โˆ’๐’Ÿ๐’Ÿ ๐›ป๐›ป๐ถ๐ถ โˆ’ฮฉ๐‘…๐‘…๐‘…๐‘…

๐›ป๐›ป๐œŽ๐œŽ๐บ = 0

๐’„๐’„ = ๐Ÿ๐Ÿ

๐’„๐’„ = ๐ŸŽ๐ŸŽ

Page 6: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

COMSOL Physics Implementation

โ€ข Governing Equations โ€ข Electrochemical Diffusion: (General Form PDE)

๏ฟฝฬ‡๏ฟฝ๐ถ + ๐›ป๐›ป โ‹… ๐šช๐šช = ๏ฟฝฬ‡๏ฟฝ๐ถ + ๐›ป๐›ป โ‹… โˆ’๐’Ÿ๐’Ÿ ๐›ป๐›ป๐ถ๐ถ โˆ’ฮฉ๐‘…๐‘…๐‘…๐‘…

๐›ป๐›ป๐œŽ๐œŽ๐บ = 0

Page 7: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Electrochemistry + Solid Mechanics Coupling

Elasto-Diffusion Induced Fracture/Damage

Theory of Anisotropy

Optimization

Conclusion

Page 8: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Importance of Understanding Fracture

Fracture causes: โ€ข Capacity Fade from structural

disorder โ€ข Dislocation from Current collector โ€ข Dislocation of conductive matrix

โ€ข Increase growth of Passivated

Layers โ€ข E.g. Solid Electrolyte Interphase (SEI) โ€ข 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)

Page 9: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Issues with Sharp Crack Modeling Issues arise from FEM discretization

Fixed Mesh Discretization: โ€ข Pro: Relatively simple โ€ข Con: Inaccurate pattern resolution

XFEM โ€“ Enriched Mesh Elements: โ€ข Pro: Relatively more accurate โ€ข Con: Challenging and still in

development stage โ€ข Issues of singularity still arise

Mesh Adaptivity โ€“ Front Tracking: โ€ข Pro: Can exactly capture fracture โ€ข Con: Expensive and Elements can

distort and impose error โ€ข Challenging geometric problem

Page 10: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Bulk Damage โ€ข Statistical averaging of solution field

โ€ข Alleviates issues of singularity

โ€ข Solution is inclusive of damage location

โ€ข Continuum viewpoint

โ€ข Alleviates issues stemming from

discretization

โ€ข Can be represented in terms of: โ€ข Material Properties โ€ข Mechanical Fields

๐ท๐ท๐‘†๐‘† =๐œ•๐œ•๐‘š๐‘š๐ท๐ท๐œ•๐œ•๐‘š๐‘š

= 1 โˆ’๐ธ๐ธ๐ท๐ท๐ธ๐ธ

โ€ข Coupling through damage parameter

definition: โ€ข Continuum Damage coupling to

Mechanical Response: ๐‘€๐‘€๐‘’๐‘’๐ถ๐ถ๐‘š: ๐ˆ๐ˆ๏ฟฝ = 1 โˆ’ ๐ท๐ท โˆ’1๐ˆ๐ˆ

๐ท๐ท๐ถ๐ถ๐‘š๐‘š๐ถ๐ถ๐‘”๐‘”๐‘’๐‘’: ๐ท๐ท = ๐‘“๐‘“(๐ˆ๐ˆ, ๐๐,๐ธ๐ธ, โ€ฆ )

๐‘š๐‘š ๐‘š๐‘šD

๐‘š๐‘šD ๐‘š๐‘šD

RVE

Page 11: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Bulk Damage

Stochastic and Randomness of Solution Probability

โ€ข Appropriate for non-deterministic solution modeling

โ€ข Most electrode active materials are brittle

Courtesy of Barai & Mukherjee 2013

Specific Proposed Implementation: Weibullโ€™s distribution formulation

๐ท๐ท = 1 โˆ’ ๐‘’๐‘’โˆ’๐œŽ๐œŽโˆ—๐œŽ๐œŽ๐‘Š๐‘Š

๐‘š๐‘š๐‘Š๐‘Š

โ€ข Based on โ€˜weakest-linkโ€™ approach

โ€ข Appropriate where initial distribution of flaw is important

Page 12: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

COMSOL Physics Implementation

โ€ข Governing Equations โ€ข Damage Evolution: (Distributed Ordinary Differential Equation)

๏ฟฝฬ‡๏ฟฝ๐ท = ๐ท๐ท๐‘ ๐‘ ฬ‡ ๐ถ๐ถ๐‘“๐‘“ ๐ท๐ท๐‘ ๐‘  > ๐ท๐ท | ๐ท๐ท๏ฟฝฬ‡๏ฟฝ๐‘  > 0 0 ๐‘’๐‘’๐ถ๐ถ๐‘š๐‘’๐‘’๐‘œ๐‘œ๐‘œ๐‘œ๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’

๐ท๐ท๐‘ ๐‘  = 1 โˆ’ ๐‘’๐‘’โˆ’max ๐œŽ๐œŽ1,0

๐œŽ๐œŽ๐‘Š๐‘Š

๐‘š๐‘š๐‘Š๐‘Š

Page 13: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Electrochemistry + Solid Mechanics Coupling

Elasto-Diffusion Induced Fracture/Damage

Theory of Anisotropy

Optimization

Conclusion

Page 14: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Anisotropic Theory

Non-Uniform Expansion

โ€ข Non-Uniformity in mechanical responses

โ€ข Non-Uniformity in damage evolution

โ€ข Multiphysics effects in context on LIB

โ€ข Self-Limiting Strain

Courtesy of Liu, et. al. 2011

Courtesy of Lee, et. al. 2012 Courtesy of Goldman, et. al. 2011

Page 15: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Anisotropic Theory COMSOL Implementation

๐œŽ๐œŽ๐บ๐บ๐‘–๐‘– = ๐‘ช๐‘ช๐’Š๐’Š๐’Š๐’Š๐’Š๐’Š๐’Š๐’Š๐œ–๐œ–๐‘˜๐‘˜๐‘†๐‘†๐‘š๐‘š๐บ๐บ๐‘†๐‘†๐บ

Ccubic crystal =

๐ถ๐ถ11 ๐ถ๐ถ12๐ถ๐ถ12 ๐ถ๐ถ11

๐ถ๐ถ12 0๐ถ๐ถ12 0

0 00 0

๐ถ๐ถ12 ๐ถ๐ถ120 0

๐ถ๐ถ11 00 ๐ถ๐ถ44

0 00 0

0 00 0

0 00 0

๐ถ๐ถ44 00 ๐ถ๐ถ44

๐‘š๐‘š =2๐ถ๐ถ44

๐ถ๐ถ11 โˆ’ ๐ถ๐ถ12โˆถ ๐‘€๐‘€๐‘’๐‘’๐ถ๐ถ๐‘’๐‘’๐‘€๐‘€๐‘œ๐‘œ๐‘’๐‘’ ๐‘’๐‘’๐‘“๐‘“ ๐‘š๐‘š๐‘’๐‘’๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐‘œ๐‘œ๐‘’๐‘’๐ถ๐ถ๐‘ฆ๐‘ฆ

Courtesy of Goldman, et. al. 2011

Subsequent Non-Uniform Damage

Page 16: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Electrochemistry + Solid Mechanics Coupling

Elasto-Diffusion Induced Fracture/Damage

Theory of Anisotropy

Optimization

Conclusion

Page 17: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Importance of Optimization

โ€ข Counterintuitive Concepts!

โ€ข Design rules to limit electrode

degradation

โ€ข Also limits usable capacity

โ€ข Optimization finds optimal

design

โ€ข Minimize damage

โ€ข 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

Page 18: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Optimization Framework

โ€ข Multi-Objective Scheme โ€ข Both Mechanical response and capacity optimized simultaneously โ€ข Pareto Optimization

โ€ข Optimization based on: โ€ข Gravimetric energy density โ€ข Volumetric energy density โ€ข Effective (Usable) capacity โ€ข Stress generation โ€ข Damage Criteria

โ€ข Optimization Issue: โ€ข Altering electrode parameters such as particle size

โ€ข limits fracture โ€ข accelerate failure in systems susceptible to side

reactions (SEI formation).

โ€ข Proposed Solution โ€ข Optimization of different aspect of electrode

characteristic โ€ข Optimize electrode surface (Electrode-electrolyte

interface) โ€ข Subject to higher stresses than current collector

interface

Page 19: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Implemented COMSOL Geometries

Courtesy of Goldman, et. al. 2011

Page 20: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

COMSOL Physics Implementation โ€ข Implemented Boundary Conditions

๐šช๐šช โ‹… ๐’๐’ =๐ถ๐ถ๐‘†๐‘†๐น๐น

:๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐‘œ๐‘œ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’ ๐‘“๐‘“๐‘“๐‘“๐‘€๐‘€๐‘’๐‘’

๐ถ๐ถ๐บ๐บ๐บ๐บ:๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐ถ๐ถ๐‘’๐‘’๐‘€๐‘€๐‘’๐‘’๐‘€๐‘€๐‘’๐‘’ ๐ถ๐ถ๐‘’๐‘’๐‘œ๐‘œ๐ถ๐ถ๐‘’๐‘’๐‘๐‘๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘ฆ๐‘ฆ ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘œ๐‘œ โ€ฒ๐ถ๐ถโ€ฒ ๐ถ๐ถ๐‘’๐‘’ ๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐‘œ๐‘œ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’

๐’–๐’–๐บ๐บ๐บ๐บ:๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ๐ถ๐ถ๐‘’๐‘’๐‘€๐‘€๐‘’๐‘’๐‘€๐‘€๐‘’๐‘’ ๐ถ๐ถ๐‘’๐‘’๐‘œ๐‘œ๐ถ๐ถ๐‘’๐‘’๐‘๐‘๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘ฆ๐‘ฆ๐ถ๐ถ๐ถ๐ถ๐ถ๐ถ๐‘œ๐‘œ ๐ถ๐ถโ€ฒ โ€ฒ๐ถ๐ถ๐‘’๐‘’ ๐‘๐‘๐ถ๐ถ๐‘’๐‘’๐ถ๐ถ๐‘“๐‘“๐ถ๐ถ๐ถ๐ถ๐‘’๐‘’๐‘š๐‘š๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ

๐’–๐’– = 0 โˆถ ๐น๐น๐ถ๐ถ๐‘’๐‘’๐‘’๐‘’๐‘๐‘ ๐‘๐‘๐ถ๐ถ๐‘’๐‘’๐ถ๐ถ๐‘“๐‘“๐ถ๐ถ๐ถ๐ถ๐‘’๐‘’๐‘š๐‘š๐‘’๐‘’๐‘’๐‘’๐ถ๐ถ

๐’–๐’–1๐บ๐บ , ๐ถ๐ถ1

๐บ๐บ ๐’–๐’–1๐บ๐บ , ๐ถ๐ถ1

๐บ๐บ

๐’–๐’–2๐บ๐บ , ๐ถ๐ถ2

๐บ๐บ ๐’–๐’–2๐บ๐บ , ๐ถ๐ถ2

๐บ๐บ

๐šช๐šช โ‹… ๐’๐’

Page 21: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

COMSOL Preliminary Results

๐น๐น1 ๐ท๐ท : โˆซ ๐ท๐ท ๐‘๐‘๐‘‘๐‘‘ ฮฉโˆซ 1 ๐‘๐‘๐‘‘๐‘‘ ฮฉ

๐‘†๐‘†๐ถ๐ถ๐‘’๐‘’๐ถ๐ถ: โˆซ๐‘†๐‘† ๐‘‘๐‘‘๐‘‘๐‘‘

ฮฉโˆซ 1 ๐‘‘๐‘‘๐‘‘๐‘‘ ฮฉ

= 0.8

Page 22: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Electrochemistry + Solid Mechanics Coupling

Elasto-Diffusion Induced Fracture/Damage

Theory of Anisotropy

Optimization

Conclusion

Page 23: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

Conclusion

Implemented iso-/anisotropic elasto-diffusion coupling

Implemented continuum damage physics

โ€œPartialโ€ anisotropic mechanical responses

Account for multiphase lithiation physics

Implement elasto-plastic damage evolution law

Implement robust topology optimization function (COMSOL Livelink w/ MATLAB)

Page 24: COMSOL - Topology Optimization of Lithium -Ion Battery ......COMSOL Physics Implementation โ€ข Governing Equations โ€ข Solid Mechanics: (General Form PDE) ๐›ป๐›ปโ‹…๐šช๐šช= ๐›ป๐›ปโ‹…๐ˆ๐ˆ=

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