Graphical Abstract Figure
Abstract
Models that can accurately describe deformation and stress in lithium-ion batteries are required to inform new device designs that can better withstand mechanical fatigue. Developing such models is particularly challenging because (i) there is a need to capture several different materials including active materials, binders, current collectors, and separators, and (ii) the length scales of interest are highly disparate (ranging from a few microns, relevant to active material particles, up to centimeters, relevant to whole devices). In this study, we present a continuum mechanical model that resolves individual active material particles of a nickel-manganese-cobalt-oxide cathode, and predicts the mechanical response of the cathode coating as a whole. The model is validated by comparison with experimental tests which mimic industrial-scale electrode calendaring, and then a parametric study is conducted to provide insight into the roles of the material and geometric properties of the electrode's constituents on the cathode's overall behavior.
References
1.
Kang
, K.
, Meng
, Y. S.
, Bréger
, J.
, Grey
, C. P.
, and Ceder
, G.
, 2006
, “Electrodes With High Power and High Capacity for Rechargeable Lithium Batteries
,” Science
, 311
(5763
), pp. 977
–980
. 2.
Zhao
, Y.
, Stein
, P.
, Bai
, Y.
, Al-Siraj
, M.
, Yang
, Y.
, and Xu
, B.-X.
, 2019
, “A Review on Modeling of Electro-chemo-mechanics in Lithium-Ion Batteries
,” J. Power Sources
, 413
, pp. 259
–283
. 3.
Owen
, J. R.
, 1997
, “Rechargeable Lithium Batteries
,” Chem. Soc. Rev.
, 26
(4
), pp. 259
–267
. 4.
Vetter
, J.
, Novák
, P.
, Wagner
, M. R.
, Veit
, C.
, Möller
, K.-C.
, Besenhard
, J.
, Winter
, M.
, Wohlfahrt-Mehrens
, M.
, Vogler
, C.
, and Hammouche
, A.
, 2005
, “Ageing Mechanisms in Lithium-Ion Batteries
,” J. Power Sources
, 147
(1–2
), pp. 269
–281
. 5.
Etacheri
, V.
, Marom
, R.
, Elazari
, R.
, Salitra
, G.
, and Aurbach
, D.
, 2011
, “Challenges in the Development of Advanced Li-Ion Batteries: A Review
,” Energy Environ. Sci.
, 4
(9
), pp. 3243
–3262
. 6.
Safari
, M.
, Morcrette
, M.
, Teyssot
, A.
, and Delacourt
, C.
, 2009
, “Multimodal Physics-Based Aging Model for Life Prediction of Li-Ion Batteries
,” J. Electrochem. Soc.
, 156
(3
), pp. A145
–A153
. 7.
Sahu
, S.
, and Foster
, J. M.
, 2023
, “A Continuum Model for Lithium Plating and Dendrite Formation in Lithium-Ion Batteries: Formulation and Validation Against Experiment
,” J. Energy Storage
, 60
, p. 106516
. 8.
Birkl
, C. R.
, Roberts
, M. R.
, McTurk
, E.
, Bruce
, P. G.
, and Howey
, D. A.
, 2017
, “Degradation Diagnostics for Lithium Ion Cells
,” J. Power Sources
, 341
, pp. 373
–386
. 9.
McDowell
, M. T.
, Xia
, S.
, and Zhu
, T.
, 2016
, “The Mechanics of Large-Volume-Change Transformations in High-Capacity Battery Materials
,” Extreme Mech. Lett.
, 9
, pp. 480
–494
. 10.
Lenze
, G.
, Röder
, F.
, Bockholt
, H.
, Haselrieder
, W.
, Kwade
, A.
, and Krewer
, U.
, 2017
, “Simulation-Supported Analysis of Calendering Impacts on the Performance of Lithium-Ion-Batteries
,” J. Electrochem. Soc.
, 164
(6
), pp. A1223
–A1233
. 11.
Kwade
, A.
, Haselrieder
, W.
, Leithoff
, R.
, Modlinger
, A.
, Dietrich
, F.
, and Droeder
, K.
, 2018
, “Current Status and Challenges for Automotive Battery Production Technologies
,” Nat. Energy
, 3
(4
), pp. 290
–300
. 12.
Kespe
, M.
, and Nirschl
, H.
, 2015
, “Numerical Simulation of Lithium-Ion Battery Performance on Sidering Electrode Microstructure
,” Int. J. Energy Res.
, 39
(15
), pp. 2062
–2074
. 13.
Wang
, C.-W.
, Yi
, Y.-B.
, Sastry
, A.
, Shim
, J.
, and Striebel
, K.
, 2004
, “Particle Compression and Conductivity in Li-Ion Anodes With Graphite Additives
,” J. Electrochem. Soc.
, 151
(9
), pp. A1489
–A1498
. 14.
Giménez
, C. S.
, Finke
, B.
, Schilde
, C.
, Froböse
, L.
, and Kwade
, A.
, 2019
, “Numerical Simulation of the Behavior of Lithium-Ion Battery Electrodes During the Calendaring Process Via the Discrete Element Method
,” Powder Technol.
, 349
, pp. 1
–11
. 15.
Giménez
, C. S.
, Helmers
, L.
, Schilde
, C.
, Diener
, A.
, and Kwade
, A.
, 2020
, “Modeling the Electrical Conductive Paths Within All-Solid-State Battery Electrodes
,” Chem. Eng. Technol.
, 43
(5
), pp. 819
–829
. 16.
Antartis
, D.
, Dillon
, S.
, and Chasiotis
, I.
, 2015
, “Effect of Porosity on Electrochemical and Mechanical Properties of Composite Li-Ion Anodes
,” J. Compos. Mater.
, 49
(15
), pp. 1849
–1862
. 17.
Zheng
, H.
, Tan
, L.
, Liu
, G.
, Song
, X.
, and Battaglia
, V. S.
, 2012
, “Calendering Effects on the Physical and Electrochemical Properties of Li [Ni1/3Mn1/3Co1/3] O2 Cathode
,” J. Power Sources
, 208
, pp. 52
–57
. 18.
Haselrieder
, W.
, Ivanov
, S.
, Christen
, D. K.
, Bockholt
, H.
, and Kwade
, A.
, 2013
, “Impact of the Calendering Process on the Interfacial Structure and the Related Electrochemical Performance of Secondary Lithium-Ion Batteries
,” ECS Trans.
, 50
(26
), pp. 59
–70
. 19.
Chen
, L.
, Xie
, X.
, Xie
, J.
, Wang
, K.
, and Yang
, J.
, 2006
, “Binder Effect on Cycling Performance of Silicon/Carbon Composite Anodes for Lithium Ion Batteries
,” J. Appl. Electrochem.
, 36
(10
), pp. 1099
–1104
. 20.
Chou
, S.-L.
, Pan
, Y.
, Wang
, J.-Z.
, Liu
, H.-K.
, and Dou
, S.-X.
, 2014
, “Small Things Make a Big Difference: Binder Effects on the Performance of Li and Na Batteries
,” Phys. Chem. Chem. Phys.
, 16
(38
), pp. 20347
–20359
. 21.
Magasinski
, A.
, Zdyrko
, B.
, Kovalenko
, I.
, Hertzberg
, B.
, Burtovyy
, R.
, Huebner
, C. F.
, Fuller
, T. F.
, Luzinov
, I.
, and Yushin
, G.
, 2010
, “Toward Efficient Binders for Li-Ion Battery Si-Based Anodes: Polyacrylic Acid
,” ACS Appl. Mater. Interfaces
, 2
(11
), pp. 3004
–3010
. 22.
Kim
, I.-S.
, and Kumta
, P. N.
, 2004
, “High Capacity si/c Nanocomposite Anodes for Li-Ion Batteries
,” J. Power Sources
, 136
(1
), pp. 145
–149
. 23.
Xiao
, X.
, Liu
, P.
, Verbrugge
, M.
, Haftbaradaran
, H.
, and Gao
, H.
, 2011
, “Improved Cycling Stability of Silicon Thin Film Electrodes Through Patterning for High Energy Density Lithium Batteries
,” J. Power Sources
, 196
(3
), pp. 1409
–1416
. 24.
Ebner
, M.
, Marone
, F.
, Stampanoni
, M.
, and Wood
, V.
, 2013
, “Visualization and Quantification of Electrochemical and Mechanical Degradation in Li Ion Batteries
,” Science
, 342
(6159
), pp. 716
–720
. 25.
Liu
, G.
, Zheng
, H.
, Song
, X.
, and Battaglia
, V. S.
, 2012
, “Particles and Polymer Binder Interaction: A Controlling Factor in Lithium-Ion Electrode Performance
,” J. Electrochem. Soc.
, 159
(3
), pp. A214
–A221
. 26.
Kovalenko
, I.
, Zdyrko
, B.
, Magasinski
, A.
, Hertzberg
, B.
, Milicev
, Z.
, Burtovyy
, R.
, Luzinov
, I.
, and Yushin
, G.
, 2011
, “A Major Constituent of Brown Algae for Use in High-Capacity Li-Ion Batteries
,” Science
, 334
(6052
), pp. 75
–79
. 27.
Shim
, J.
, Kostecki
, R.
, Richardson
, T.
, Song
, X.
, and Striebel
, K. A.
, 2002
, “Electrochemical Analysis for Cycle Performance and Capacity Fading of a Lithium-Ion Battery Cycled at Elevated Temperature
,” J. Power Sources
, 112
(1
), pp. 222
–230
. 28.
Chen
, J.
, Liu
, J.
, Qi
, Y.
, Sun
, T.
, and Li
, X.
, 2013
, “Unveiling the Roles of Binder in the Mechanical Integrity of Electrodes for Lithium-Ion Batteries
,” J. Electrochem. Soc.
, 160
(9
), pp. A1502
–A1509
. 29.
Santhanagopalan
, S.
, Ramadass
, P.
, and Zhang
, J. Z.
, 2009
, “Analysis of Internal Short-Circuit in a Lithium Ion Cell
,” J. Power Sources
, 194
(1
), pp. 550
–557
. 30.
Cai
, W.
, Wang
, H.
, Maleki
, H.
, Howard
, J.
, and Lara-Curzio
, E.
, 2011
, “Experimental Simulation of Internal Short Circuit in Li-Ion and Li-Ion-Polymer Cells
,” J. Power Sources
, 196
(18
), pp. 7779
–7783
. 31.
Christensen
, J.
, and Newman
, J.
, 2006
, “A Mathematical Model of Stress Generation and Fracture in Lithium Manganese Oxide
,” J. Electrochem. Soc.
, 153
(6
), pp. A1019
–A1030
. 32.
Christensen
, J.
, and Newman
, J.
, 2006
, “Stress Generation and Fracture in Lithium Insertion Materials
,” J. Solid State Electrochem.
, 10
(5
), pp. 293
–319
. 33.
Zhang
, X.
, Shyy
, W.
, and Sastry
, A. M.
, 2007
, “Numerical Simulation of Intercalation-Induced Stress in Li-Ion Battery Electrode Particles
,” J. Electrochem. Soc.
, 154
(10
), pp. A910
–A916
. 34.
Klinsmann
, M.
, Rosato
, D.
, Kamlah
, M.
, and McMeeking
, R. M.
, 2016
, “Modeling Crack Growth During Li Insertion in Storage Particles Using a Fracture Phase Field Approach
,” J. Mech. Phys. Solids
, 92
, pp. 313
–344
. 35.
Ai
, W.
, Kraft
, L.
, Sturm
, J.
, Jossen
, A.
, and Wu
, B.
, 2020
, “Electrochemical Thermal–Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells
,” J. Electrochem. Soc.
, 167
(1
), p. 013512
. 36.
Rieger
, B.
, Erhard
, S. V.
, Rumpf
, K.
, and Jossen
, A.
, 2016
, “A New Method to Model the Thickness Change of a Commercial Pouch Cell During Discharge
,” J. Electrochem. Soc.
, 163
(8
), pp. A1566
–A1575
. 37.
Oh
, K.-Y.
, Epureanu
, B. I.
, Siegel
, J. B.
, and Stefanopoulou
, A. G.
, 2016
, “Phenomenological Force and Swelling Models for Rechargeable Lithium-Ion Battery Cells
,” J. Power Sources
, 310
, pp. 118
–129
. 38.
Dai
, H.
, Yu
, C.
, Wei
, X.
, and Sun
, Z.
, 2017
, “State of Charge Estimation for Lithium-Ion Pouch Batteries Based on Stress Measurement
,” Energy
, 129
, pp. 16
–27
. 39.
Zhang
, J.
, Huang
, H.
, and Sun
, J.
, 2022
, “Investigation on Mechanical and Microstructural Evolution of Lithium-Ion Battery Electrode During the Calendering Process
,” Powder Technol.
, 409
, p. 117828
. 40.
Lu
, X.
, Daemi
, S. R.
, Bertei
, A.
, Kok
, M. D.
, O’Regan
, K. B.
, Rasha
, L.
, Park
, J.
, et al, 2020
, “Microstructural Evolution of Battery Electrodes During Calendering
,” Joule
, 4
(12
), pp. 2746
–2768
. 41.
Nikpour
, M.
, Barrett
, N.
, Hillman
, Z.
, Thompson
, A. I.
, Mazzeo
, B. A.
, and Wheeler
, D. R.
, 2021
, “A Model for Investigating Sources of Li-Ion Battery Electrode Heterogeneity: Part I. Electrode Drying and Calendering Processes
,” J. Electrochem. Soc.
, 168
(6
), p. 060547
. 42.
Zhu
, J.
, Zhang
, X.
, Luoa
, H.
, and Sahraei
, E.
, 2018
, “Investigation of the Deformation Mechanisms of Lithium-Ion Battery Components Using In-Situ Micro Tests
,” Appl. Energy
, 224
, pp. 251
–266
. 43.
Sahraei
, E.
, Kahn
, M.
, Meier
, J.
, and Wierzbicki
, T.
, 2015
, “Modelling of Cracks Developed in Lithium-Ion Cells Under Mechanical Loading
,” RSC Adv.
, 5
, p. 80369
. 44.
Sahraei
, E.
, Bosco
, E.
, Dixon
, B.
, and Lai
, B.
, 2016
, “Microscale Failure Mechanisms Leading to Internal Short Circuit in Li-Ion Batteries Under Complex Loading Scenarios
,” J. Power Sources
, 319
, pp. 56
–65
. 45.
Finegan
, D. P.
, Squires
, I.
, Dahari
, A.
, Kench
, S.
, Jungjohann
, K. L.
, and Cooper
, S. J.
, 2022
, “Machine-Learning-Driven Advanced Characterization of Battery Electrodes
,” ACS Energy Lett.
, 7
(12
), pp. 4368
–4378
. 46.
Cooper
, S. J.
, Eastwood
, D. S.
, Gelb
, J.
, Damblanc
, G.
, Brett
, D. J.
, Bradley
, R. S.
, Withers
, P. J.
, et al, 2014
, “Image Based Modelling of Microstructural Heterogeneity in LiFePO4 Electrodes for Li-Ion Batteries
,” J. Power Sources
, 247
, pp. 1033
–1039
. 47.
Tan
, C.
, Kok
, M. D.
, Daemi
, S. R.
, Brett
, D. J.
, and Shearing
, P. R.
, 2019
, “Three-Dimensional Image Based Modelling of Transport Parameters in Lithium–Sulfur Batteries
,” Phys. Chem. Chem. Phys.
, 21
(8
), pp. 4145
–4154
. 48.
Liu
, H.
, Foster
, J. M.
, Gully
, A.
, Krachkovskiy
, S.
, Jiang
, M.
, Wu
, Y.
, Yang
, X.
, Protas
, B.
, Goward
, G. R.
, and Botton
, G. A.
, 2016
, “Three-Dimensional Investigation of Cycling-Induced Microstructural Changes in Lithium-Ion Battery Cathodes Using Focused Ion Beam/Scanning Electron Microscopy
,” J. Power Sources
, 306
, pp. 300
–308
. 49.
Usseglio-Viretta
, F. L.
, and Smith
, K.
, 2017
, “Quantitative Microstructure Characterization of a NMC Electrode
,” ECS Trans.
, 77
(11
), pp. 1095
–1118
. 50.
Nara
, H.
, Morita
, K.
, Mukoyama
, D.
, Yokoshima
, T.
, Momma
, T.
, and Osaka
, T.
, 2017
, “Impedance Analysis of LiNi1/3Mn1/3Co1/3O2 Cathodes With Different Secondary-Particle Size Distribution in Lithium-Ion Battery
,” Electrochim. Acta
, 241
, pp. 323
–330
. 51.
Foster
, J. M.
, Chapman
, S. J.
, Richardson
, G.
, and Protas
, B.
, 2017
, “A Mathematical Model for Mechanically-Induced Deterioration of the Binder in Lithium-Ion Electrodes
,” SIAM J. Appl. Math.
, 77
(6
), pp. 2172
–2198
. 52.
Rogak
, S. N.
, and Flagan
, R. C.
, 1990
, “Stokes Drag on Self-Similar Clusters of Spheres
,” J. Colloid Interface Sci.
, 134
(1
), pp. 206
–218
. 53.
Kisters
, T.
, Sahraei
, E.
, and Wierzbicki
, T.
, 2017
, “Dynamic Impact Tests on Lithium-Ion Cells
,” Int. J. Impact Eng.
, 108
, pp. 205
–216
. 54.
Dixon
, B.
, Mason
, A.
, and Sahraei
, E.
, 2018
, “Effects of Electrolyte, Loading Rate and Location of Indentation on Mechanical Integrity of Li-Ion Pouch Cells
,” J. Power Sources
, 396
, pp. 412
–420
. 55.
Kisters
, T.
, Gilaki
, M.
, Nau
, S.
, and Sahraei
, E.
, 2022
, “Modeling of Dynamic Mechanical Response of Li-Ion Cells With Homogenized Electrolyte–Solid Interactions
,” J. Energy Storage
, 49
, p. 104069
. 56.
Kisters
, T.
, Keshavarzi
, M.
, Kuder
, J.
, and Sahraei
, E.
, 2021
, “Effects of Electrolyte, Thickness, and Casing Stiffness on the Dynamic Response of Lithium-Ion Battery Cells
,” Energy Rep.
, 7
, pp. 6451
–6461
. 57.
58.
Schreiner
, D.
, Klinger
, A.
, and Reinhart
, G.
, 2020
, “Modeling of the Calendering Process for Lithium-Ion Batteries With DEM Simulation
,” Procedia CIRP
, 93
, pp. 149
–155
. 59.
Iyer
, A. H.
, Gupta
, P.
, Gudmundson
, P.
, and Kulachenko
, A.
, 2023
, “Measuring Microscale Mechanical Properties of PVdF Binder Phase and the Binder-Particle Interface Using Micromechanical Testing
,” Mater. Sci. Eng. A
, 881
, p. 145352
. 
