Abstract
This review focuses on energy storage materials modeling, with particular emphasis on Li-ion batteries. Theoretical and computational analyses not only provide a better understanding of the intimate behavior of actual batteries under operational and extreme conditions, but they may tailor new materials and shape new architectures in a complementary way to experimental approaches. Modeling can therefore play a very valuable role in the design and lifetime prediction of energy storage materials and devices. Batteries are inherently multi-scale, in space and time. The macro-structural characteristic lengths (the thickness of a single cell, for instance) are order of magnitudes larger than the particles that form the microstructure of the porous electrodes, which in turn are scale-separated from interface layers at which atomistic intercalations occur. Multi-physics modeling concepts, methodologies, and simulations at different scales, as well as scale transition strategies proposed in the recent literature are here revised. Finally, computational challenges toward the next generation of Li-ion batteries are discussed.
Similar content being viewed by others
References
Scrosati B, Garche J (2010) Lithium batteries: status, prospects and future. J Power Sources 195:2419–2430
Tarascon JM, Armand M (2001) Issues and challenges facing rechargeable Lithium batteries. Nature 414:359–367
Danzer A, Liebau V, Maglia F (2015) Aging of Lithium-ion batteries for electric vehicles. In: Scrosati B, Garche J, Tillmetz W (eds) Advances in battery technologies for electric vehicles. Woodhead Publishing, Cambridge, pp 359–387
Salvadori A, Grazioli D (2015) Computer simulation for battery design and lifetime prediction. In: Scrosati B, Garche J, Tillmetz W (eds) Advances in battery technologies for electric vehicles. Woodhead Publishing, Cambridge, pp 417–442
Lu L, Han X, Li J, Hua J, Ouyang M (2013) A review on the key issues for Lithium-ion battery management in electric vehicles. J Power Sources 226:272–288
Zhang J, Lee J (2011) A review on prognostics and health monitoring of Li-ion battery. J Power Sources 196(15):6007–6014
Barre A, Deguilhem B, Grolleau S, Gerard M, Suard F, Riu D (2013) A review on Lithium-ion battery ageing mechanisms and estimations. J Power Sources 241:680–689
Franco AA (2013) Multiscale modelling and numerical simulation of rechargeable Lithium ion batteries: concepts, methods and challenge. Rsc Adv 3(32):13027–13058
Landstorfer M, Jacob T (2013) Mathematical modeling of intercalation batteries at the cell level and beyond. Chem Soc Rev 42:3234–3252
Doerffel D, Sharkh SA (2006) A critical review of using the Peukert equation for determining the remaining capacity of lead-acid and Lithium-ion batteries. J Power Sources 155(2):395–400
Peukert W (1897) Über die abhängigkeit der kapazität von der entladestromstärke bei bleiakkumulatoren. Elektrotech Z 20:20–21
Chen M, Rincon-Mora G (2006) Accurate electrical battery model capable of predicting runtime and IV performance. IEEE Trans Energy Conver 21(2):504–511
Fares RL, Webber ME (2015) Combining a dynamic battery model with high-resolution smart grid data to assess microgrid islanding lifetime. Appl Energy 137:482–489
Rong P, Member S, Pedram M (2006) An analytical model for predicting the remaining battery capacity of Lithium-ion batteries. IEEE Trans VlSI Syst 14(5):441–451
von Srbik MT, Marinescu M, Martinez-Botas RF, Offer GJ (2016) A physically meaningful equivalent circuit network model of a Lithium-ion battery accounting for local electrochemical and thermal behaviour, variable double layer capacitance and degradation. J Power Sources 325:171–184
Widanage WD, Barai A, Chouchelamane GH, Uddin K, McGordon A, Marco J, Jennings P (2016) Design and use of multisine signals for Li-ion battery equivalent circuit modelling. Part II: model estimation. J Power Sources 324:61–69
He H, Xiong R, Fan J (2011) Evaluation of Lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach. Energies 4:582–598
Gao L, Liu S, Dougal RA (2002) Dynamic Lithium-ion battery model for system simulation. IEEE Trans Compon Pack Technol 25(3):495–505
Buller S, Thele M (2005) Impedance-based simulation models of supercapacitors and Li-ion batteries for power electronic applications. IEEE Trans Ind Appl 41(3):742–747
Gold S (1997) A PSPICE macromodel for Lithium-ion batteries. In: The 12th annual battery conference on applications and advances, pp 215–222
Fotouhi A, Auger DJ, Propp K, Longo S, Wild M (2016) A review on electric vehicle battery modelling: from Lithium-ion toward Lithium–Sulphur. Renew Sustain Energy Rev 56:1008–1021
De Groot SR, Mazur P (1984) Non-equilibrium thermodynamics. Dover, New York
DeHoff R (2006) Thermodynamic in material science. CRC Press, Taylor
Gurtin ME, Fried E, Anand L (2010) The mechanics and thermodynamics of continua. Cambridge University Press, Cambridge
Shell S (2015) Thermodynamics and statistical mechanics: an integrated approach. Cambridge University Press, Cambridge
Tadmor EB, Miller RE, Elliott RS (2011) Continuum mechanics and thermodynamics: from fundamental concepts to governing equations. Cambridge University Press, Cambridge
Tagade P, Hariharan KS, Basu S, Verma MKS, Kolake SM, Song T, Oh D, Yeo T, Doo SK (2016) Bayesian calibration for electrochemical thermal model of Lithium-ion cells. J Power Sources 320:296–309
Edouard C, Petit M, Forgez C, Bernard J, Revel R (2016) Parameter sensitivity analysis of a simplified electrochemical and thermal model for Li-ion batteries aging. J Power Sources 325:482–494
Bard AJ, Faulkner LR (2000) Electrochemical methods: fundamentals and applications, 2nd edn. Wiley, New York
Bower AF, Guduru PM, Sethuraman VA (2011) A finite strain model of stress, diffusion, plastic flow and electrochemical reactions in a Lithium-ion half-cell. J Mech Phys Solids 59:804–828
Aurbach A (2002) The role of surface films on electrodes in Li-ion batteries. In: van Schalkwijk W, Scrosati B (eds) Advances in Lithium-ion batteries. Kluwer Academic, New York
Bower AF, Guduru PR, Chason E (2015) Analytical solutions for composition and stress in spherical elastic-plastic Lithium-ion electrode particles containing a propagating phase boundary. Int J Solids Struct 69–70:328–342
Chon MJ, Sethuraman VA, McCormick A, Srinivasan V, Guduru PR (2011) Real-time measurement of stress and damage evolution during initial lithiation of crystalline silicon. Phys Rev Lett 107:045503
Arora P, White RE, Doyle M (1998) Capacity fade mechanisms and side reactions in Lithium-ion batteries. J Electrochem Soc 145(10):3647–3667
Marom R, Amalraj SF, Leifer N, Jacob D, Aurbach D (2011) A review of advanced and practical Lithium battery materials. J Mater Chem 21:9938–9954
Sarre G, Blanchard P, Broussely M (2004) Aging of Lithium-ion batteries. J Power Sources 127:65–71
Vetter J, Novak P, Wagner MR, Veit C, Moeller KC, Besenhard JO, Winter M, Wohlfahrt-Mehrens M, Vogler C, Hammouche A (2005) Ageing mechanisms in Lithium-ion batteries. J Power Sources 147(1–2):269–281
Wohlfart-Mehrens M, Vogler C, Garche J (2004) Aging mechanism of Lithium cathode materials. J Power Sources 127:58–64
Swallow JG, Woodford WH, McGrogan FP, Ferralis N, Chiang YM, Van Vliet KJ (2014) Effect of electrochemical charging on elastoplastic properties and fracture toughness of \({\rm Li}_{x}{\rm CoO}_{2}\). J Electrochem Soc 161(11):F3084–F3090
Swallow JG, Woodford WH, Chen Y, Lu Q, Kim JJ, Chen D, Chiang YM, Carter WC, Yildiz B, Tuller HL, Van Vliet KJ (2014) Chemomechanics of ionically conductive ceramics for electrical energy conversion and storage. J Electroceram 32:3–27
David WIF, Thackeray MM, De Picciotto LA, Goodenough JB (1987) Structure refinement of the spinel-related phases \({\rm Li}_{2}{\rm Mn}_{2}{\rm O}_{4}\) and \({\rm Li}_{0.2}{\rm Mn}_{2}{\rm O}_{4}\). J Solid State Chem 67(2):316–323
Ohzuku T, Iwakoshi Y, Sawai K (1993) Formation of Lithium-graphite intercalation compounds in nonaqueous electrolytes and their application as a negative electrode for a Lithium ion (shuttlecock) cell. J Electrochem Soc 140(9):2490–2498
Ohzuku T, Matoba N, Sawai K (2001) Direct evidence on anomalous expansion of graphite-negative electrodes on first charge by dilatometry. J Power Sources, 97–98:73–77. Proceedings of the 10th international meeting on Lithium batteries
Wang H, Jang YI, Huang B, Sadoway DR, Chiang YM (1999) TEM study of electrochemical cycling-induced damage and disorder in \({{\rm LiCoO}}_{2}\) cathodes for rechargeable Lithium batteries. J Electrochem Soc 146(2):473–480
Tucker MC, Reimer JA, Cairns EJ (2002) A study of capacity fade in metal-substituted Lithium manganese oxide spinels. J Electrochem Soc 149(5):A574–A585
Lim MR, Cho WI, Kim KB (2001) Preparation and characterization of gold-codeposited \({{\rm LiMn}}_{2}{{\rm O}}_{4}\) electrodes. J Power Sources 92(1–2):168–176
Wang D, Wu X, Wang Z, Chen L (2005) Cracking causing cyclic instability of \({{\rm LiFePO}}_{4}\) cathode material. J Power Sources 140(1):125–128
Gabrisch H, Wilcox J, Doeff MM (2008) TEM study of fracturing in spherical and plate-like \({\text{ LiFePO }}_{4}\) particles. Electrochem Solid-State Lett 11(3):A25–A29
Kostecki R, McLarnon F (2003) Microprobe study of the effect of Li intercalation on the structure of graphite. J Power Sources, 119–121:550–554. Selected papers presented at the 11th international meeting on Lithium batteries
Hardwick LJ, Marcinek M, Beer L, Kerr JB, Kostecki R (2008) An investigation of the effect of graphite degradation on irreversible capacity in Lithium-ion cells. J Electrochem Soc 155(6):A442–A447
Markervich E, Salitra G, Levi MD, Aurbach D (2005) Capacity fading of lithiated graphite electrodes studied by a combination of electroanalytical methods, raman spectroscopy and SEM. J Power Sources, 146(1–2):146–150. Selected papers presented at the 12th international meeting on Lithium batteries12th international meeting on Lithium batteries
Beaulieu LY, Eberman KW, Turner RL, Krause LJ, Dahn JR (2001) Colossal reversible volume changes in Lithium alloys. Electrochem Solid-State Lett 4(9):A137–A140
Tang M, Albertus P, Newman J (2009) Two-dimensional modeling of Lithium deposition during cell charging. J Electrochem Soc 156:A390–A399
Finegan DP, Scheel M, Robinson JB, Tjaden B, Hunt I, Mason TJ, Millichamp J, Di Michiel M, Offer GJ, Hinds G, Brett DJL, Shearing PR (2015) In-operando high-speed tomography of Lithium-ion batteries during thermal runaway. Nat Commun 6:04
Salvadori A, Grazioli D, Geers MGD, Danilov D, Notten PHL (2015) A novel approach in modeling ionic transport in the electrolyte of (Li-ion) batteries. J Power Sources 293:892–911
Salvadori A, Grazioli D, Magri M, Geers MGD, Danilov D, Notten PHL (2015) On the role of saturation in modeling ionic transport in the electrolyte of (Li-ion) batteries. J Power Sources 294:696–710
Zhang SS (2007) A review on the separators of liquid electrolyte Li-ion batteries. J Power Sources 164:351–364
Wu W, Xiao X, Huang X, Yan S (2014) A multiphysics model for the in situ stress analysis of the separator in a lithium-ion battery cell. Comput Mater Sci 83:127–136
Valoen LR, Reimers JN (2005) Transport properties of \({{\rm LiPF}}_{6}\)-based Li-ion battery electrolytes. J Electrochem Soc 152(5):A882–A891
Bauer G, Gravemeier V, Wall WA (2011) A 3 D finite element approach for the coupled numerical simulation of electrochemical systems and fluid flow. Int J Numer Meth Eng 86:1339–1359
Bauer G, Gravemeier V, Wall WA (2012) A stabilized finite element method for the numerical simulation of multi-ion transport in electrochemical systems. Comput Method Appl Mech Eng 223–224:199–210
Latz A, Zausch J (2015) Multiscale modeling of Li-ion batteries: thermal aspects. Beilstein J Nanotechnol 6:987–1007
Danilov D, Notten PHL (2008) Mathematical modeling of ionic transport in the electrolyte of Li-ion batteries. Electrochim Acta 53:5569–5578
Newman J, Thomas-Alyea KE (2004) Electrochemical systems. John Wiley and Sons B.V, New York
Bazant MZ, Chu KT, Bayly BJ (2005) Current-voltage relations for elecrochemical thin films. SIAM J Appl Math 65:1463–1484
Dickinson EJF, Limon-Petersen JG, Compton RG (2011) The electroneutrality approximation in electrochemistry. J Solid State Electr 15:1335–1345
Salvadori A, Bosco E, Grazioli D (2014) A computational homogenization approach for Li-ion battery cells. Part 1: formulation. J Mech Phys Solids 65:114–137
Salvadori A, Grazioli D, Geers MGD (2015) Governing equations for a two-scale analysis of Li-ion battery cells. Int J Solids Struct 59:90–109
Djian D, Alloin F, Martinet S, Lignier H, Sanchez JY (2007) Lithium-ion batteries with high charge rate capacity: influence of the porous separator. J Power Sources 172:416–421
Huang X (2011) Separator technologies for Lithium-ion batteries. J Solid State Electr 15:649–662
Abraham KME (1993) Directions in secondary Lithium battery research and development. Electrochim Acta 38:1233–1248
Bruggeman DAG (1935) Berechnung verschiedener physikallischer konstanten von heterogenen substanzen. Ann Phys-Leipzig 24:636–664
MacMullin RB, Muccini GA (1956) Characteristics of porous beds and structures. AIChE J 2:393–403
Patel KK, Paulsen JM, Desilvestro J (2003) Numerical simulation of porous networks in relation to battery electrodes and separators. J Power Sources 122:144–152
Thorat IV, Stephenson DE, Zacharias NA, Zaghib K, Harb JN, Wheeler DR (2009) Quantifying tortuosity in porous Li-ion battery materials. J Power Sources 188:592–600
Xiao X, Wu W, Huang X (2010) A multi-scale approach for the stress analysis of polymeric separators in a Li-ion battery. J Power Sources 195:7649–7660
Pinson MB, Bazant MZ (2013) Theory of SEI formation in rechargeable batteries: capacity fade, accelerated aging and lifetime prediction. J Electrochem Soc 160(2):A243–A250
Long JW, Dunn B, Rolison DR, White HS (2004) Three-dimensional battery architectures. Chem Rev 104:4463–4492
Kim JG, Son B, Mukherjee S, Schuppert N, Bates A, Kwon O, Choi MJ, Chung HY, Park S (2015) A review of lithium and non-lithium based solid state batteries. J Power Sources 282:299–322
Robinson AL (2014) Solid-state batteries enter EV fray. MRS Bull 39:1046–1047
Scrosati B, Vincent CA (2000) Polymer electrolytes: the key to Lithium polymer batteries. MRS Bull 3:28–30
Park M, Zhang X, Chung M, Less GB, Sastry AM (2010) A review of conduction phenomena in Li-ion batteries. J Power Sources 195(24):7904–7929
Fabre SD, Guy-Bouyssou D, Bouillon P, Le Cras F, Delacourta C (2012) Charge/discharge simulation of an all-solid-state thin-film battery using a one-dimensional model. J Electrochem Soc 159(2):A104–A115
Thangadurai V, Narayanan S, Pinzaru D (2014) Garnet-type solid-state fast Li ion conductors for Li batteries: critical review. Chem Soc Rev 43:4714–4727
Dudney NJ, Neudecker BJ (1999) Solid state thin-film lithium battery systems. Curr Opin Solid State Mater Sci 4:479–482
Danilov D, Niessen RAH, Notten PHL (2011) Modeling all-solid-state Li-ion batteries. J Electrochem Soc 158(3):A215–A222
Wang Y, Liu B, Li Q, Cartmell S, Ferrara S, Deng ZD, Xiao J (2015) Lithium and Lithium ion batteries for applications in microelectronic devices: a review. J Power Sources 286:330–345
Watanabe M, Ogata N (1988) Ionic conductivity of polymer electrolytes and future applications. Br Polym J 20(3):181–192
Hallinan DT Jr, Balsara NP (2013) Polymer electrolytes. Annu Rev Mater Res 43:503–525
Johansson P (2015) Computational modelling of polymer electrolytes: what do 30 years of research efforts provide us today? Electrochim Acta 175:42–46
Natsiavas PP, Weinberg K, Rosato D, Ortiz M (2016) Effect of prestress on the stability of electrode-electrolyte interfaces during charging in Lithium batteries. J Mech Phys Solids 95:92–111
Bucci G, Chiang Y-M, Craig Carter W (2016) Formulation of the coupled electrochemical-mechanical boundary-value problem, with applications to transport of multiple charged species. Acta Mater 104:33–51
Thomas KE, Newman J, Darling RM (2002) Matematical modeling of Lithium batteries. In: van Schalkwijk W, Scrosati B (eds) Advances in Lithium-ion batteries. Kluwer Academic, New York
Newman JS, Tobias CW (1962) Theoretical analysis of current distribution in porous electrodes. J Electrochem Soc 109(12):1183–1191
Newman J, Tiedemann WM (1975) Porous-electrode theory with battery applications. AIChE J 21(1):25–41
Doyle M, Newman J (1995) The use of mathematical modeling in the design of Lithium/polymer battery systems. Electrochim Acta 40(13):2191–2196
Doyle M, Fuller TF, Newman J (1993) Modeling of galvanostatic charge and discharge of the Lithium/polymer/insertion cell. J Electrochem Soc 140:1526–1533
Fuller TF, Doyle M, Newman J (1994) Simulation and optimization of the dual Lithium ion insertion cell. J Electrochem Soc 141(1):1–10
Garcia RE, Chiang YM, Carter WC, Limthongkul P, Bishop CM (2005) Microstructural modeling and design of rechargeable Lithium-ion batteries. J Electrochem Soc 152:255–263
West K, Jacobsen T, Atlung S (1982) Modeling of porous insertion electrodes with liquid electrolyte. J Electrochem Soc 129(7):1480–1485
Christensen J (2010) Modeling diffusion-induced stress in Li-ion cells with porous electrodes. J Electrochem Soc 157:366–380
Ramadesigan V, Northrop PWC, De S, Santhanagopalan S, Braatz RD, Subramanian VR (2012) Modeling and simulation of Lithium-ion batteries from a systems engineering perspective. J Electrochem Soc 159(3):R31–R45
Atlung S, West K, Jacobsen T (1979) Dynamic aspects of solid solution cathodes for electrochemical power sources. J Electrochem Soc 126(8):1311–1321
Doyle M, Newman J, Gozdz AS, Schmutz CN, Tarascon JM (1996) Comparison of modeling predictions with experimental data from plastic Lithium ion cells. J Electrochem Soc 143(6):1890–1903
Arora P, Doyle M, Gozdz AS, White RE, Newman J (2000) Comparison between computer simulations and experimental data for high-rate discharges of plastic Lithium-ion batteries. J Power Sources 88(2):219–231
Smekens J, Paulsen J, Yang W, Omar N, Deconinck J, Hubin A, Van Mierlo J (2015) A modified multiphysics model for Lithium-ion batteries with a \({{\rm Li}}_{x}{{\rm Ni}}_{1/3}{{\rm Mn}}_{1/3}{{\rm Co}}_{1/3}{{\rm O}}_{2}\) electrode. Electrochim Acta 174:615–624
Mukhopadhyay A, Sheldon BV (2014) Deformation and stress in electrode materials for Li-ion batteries. Prog Mater Sci 63:58–116
Fuller TF, Doyle M, Newman J (1994) Relaxation phenomena in Lithium-ion-insertion cells. J Electrochem Soc 141(4):982–990
Doyle M, Fuentes Y (2003) Computer simulations of a Lithium-ion polymer battery and implications for higher capacity next-generation battery designs. J Electrochem Soc 150(6):A706–A713
Pramanik S, Anwar S (2016) Electrochemical model based charge optimization for Lithium-ion batteries. J Power Sources 313:164–177
Thomas KE, Newman J (2003) Thermal modeling of porous insertion electrodes. J Electrochem Soc 150(2):A176–A192
Renganathan S, Sikha G, Santhanagopalan S, White RE (2010) Theoretical analysis of stresses in a Lithium ion cell. J Electrochem Soc 157:155–163
Arunachalam H, Onori S, Battiato I (2015) On veracity of macroscopic Lithium-ion battery models. J Electrochem Soc 10:A1940–A1951
Garcia RE, Chiang YM (2007) Spatially resolved modeling of microstructurally complex battery architectures. J Electrochem Soc 154(9):A856–A864
Wang CW, Sastry AM (2007) Mesoscale modeling of a Li-ion polymer cell. J Electrochem Soc 154:A1035–A1047
Purkayastha RT, McMeeking RM (2012) An integrated 2-D model of a Lithium ion battery: the effect of material parameters and morphology on storage particle stress. Comput Mech 50:209–227
Stern O (1924) Zur theorie der elektrolytischen doppelschicht. Z Elektrochem 30:508–516
Chapman DL (1913) A contribution to the theory of electrocapillarity. Lond Edinb Dublin Philos Mag J Sci 25:475–481
Gouy M (1910) Sur la constitution de la charge electrique a la surface d’un electrolyte. J Phys Theory Appl 9(1):457–468
Hamann CH, Hamnett A, Vielstich W (2007) Electrochemistry. Wiley, New York
Bazant MZ, Kilic MS, Storey B, Ajdari A (2009) Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Adv Colloid Interfac 152:48–88
Biesheuvel PM, van Soestbergenb M, Bazant MZ (2009) Imposed currents in galvanic cells. Electrochim Acta 54:4857–4871
Marcicki J, Conlisk AT, Rizzoni G (2014) A Lithium-ion battery model including electrical double layer effects. J Power Sources 125:157–169
Bazant MZ, Thornton K, Ajdari A (2004) Diffuse-charge dynamics in electrochemical systems. Phys Rev E 70:021506
Frumkin A, Petry O, Damaskin B (1970) The notion of the electrode charge and the Lippmann equation. J Electroanal Chem 27(1):81–100
Rubi JM, Kjelstrup S (2003) Mesoscopic nonequilibrium thermodynamics gives the same thermodynamic basis to Butler–Volmer and Nernst equations. J Phys Chem B 107:13471–13477
Bower AF, Guduru PM (2012) A simple finite element model of diffusion, finite deformation, plasticity and fracture in Lithium ion insertion electrode materials. Model Simul Mater Sci Eng 20:045004
Bucci G, Nadimpalli SPV, Sethuraman VA, Bower AF, Guduru PR (2014) Measurement and modeling of the mechanical and electrochemical response of amorphous Si thin film electrodes during cyclic lithiation. J Mech Phys Solids 62:276–294
Dao TS, Vyasarayani CP, McPhee J (2012) Simplification and order reduction of Lithium-ion battery model based on porous-electrode theory. J Power Sources 198:329–337
Streeter I, Compton RG (2008) Numerical simulation of potential step chronoamperometry at low concentrations of supporting electrolyte. J Phys Chem C 112:13716–13728
Dreyer W, Guhlke C, Landstorfer M (2014) A mixture theory of electrolytes containing solvation effects. Electrochem Commun 43:75–78
Gillman A, Amadio G, Matouš K, Jackson TL (2015) Third-order thermo-mechanical properties for packs of platonic solids using statistical micromechanics. Proc R Soc A 241:20150060
Cheng YT, Verbrugge MW (2009) Evolution of stress within a spherical insertion electrode particle under potentiostatic and galvanostatic operation. J Power Sources 190:453–460
Cheng YT, Verbrugge MW (2010) Diffusion-induced stress, interfacial charge transfer, and criteria for avoiding crack initiation of electrode particles. J Electrochem Soc 4:508–516
Christensen J, Newman J (2006) Stress generation and fracture in Lithium insertion materials. J Solid State Electr 10:293–319
Cui Z, Gao F, Qu J (2012) A finite deformation stress-dependent chemical potential and its applications to Lithium ion batteries. J Mech Phys Solids 60:1280–1295
Deshpande R, Cheng YT, Verbrugge MW (2010) Modeling diffusion-induced stress in nanowire electrode structures. J Power Sources 195:5081–5088
Deshpande R, Cheng YT, Verbrugge MW, Timmons A (2011) Diffusion induced stresses and strain energy in a phase-transforming spherical electrode particle. J Electrochem Soc 158(6):A718–A724
Golmon S, Maute K, Lee SH, Dunn ML (2010) Stress generation in silicon particles during Lithium insertion. Appl Phys Lett 97:033111
Miehe C, Dal H (2015) Computational electro-chemo-mechanics of Lithium-ion battery electrodes at finite strains. Comput Mech 55:303–325
Purkayastha RT, McMeeking RM (2013) A parameter study of intercalation of Lithium into storage particles in a Lithium-ion battery. Comput Mater Sci 80:2–14
Zhang X, Sastry AM, Shyy W (2008) Intercalation-induced stress and heat generation within single Lithium-ion battery chatode particles. J Electrochem Soc 155(7):A542–A552
Zhang X, Shyy W, Sastry AM (2007) Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. J Electrochem Soc 154:A910–A916
Zhao K, Pharr M, Cai S, Vlassak JJ, Suo Z (2011) Large plastic deformation in high-capacity Lithium-ion batteries caused by charge and discharge. J Am Ceram Soc 94(S1):S226–S235
Awarke A, Lauer S, Wittler M, Pischinger S (2011) Quantifying the effects of strains on the conductivity and porosity of \({{\rm LiFePO}}_{4}\) based Li-ion composite cathodes using a multi-scale approach. Comput Mater Sci 50(3):871–879
Gupta A, Seo JH, Zhang X, Du W, Sastry AM, Shyy W (2011) Effective transport properties of \({{\rm LiMn}}_{2}{{\rm O}}_{4}\) electrode via particle-scale modeling. J Electrochem Soc 158(5):A487–A497
Roberts SA, Brunini VE, Long KN, Grillet AM (2014) A framework for three-dimensional mesoscale modeling of anisotropic swelling and mechanical deformation in Lithium-ion electrodes. J Electrochem Soc 161(11):F3052–F3059
Stershic AJ, Simunovic S, Nanda J (2015) Modeling the evolution of Lithium-ion particle contact distributions using a fabric tensor approach. J Power Sources 297:540–550
Ender M, Joos J, Carraro T, Ivers-Tiffee E (2011) Three dimensional reconstruction of a composite cathode for Lithium-ion cells. Electrochem Commun 13(2):166–168
Hutzenlaub T, Thiele S, Zengerle R, Ziegler C (2012) Three-dimensional reconstruction of a \({{\rm LiCoO}}_{2}\) Li-ion battery cathode. Electrochem Solid State Lett 15(3):A33–A36
Hutzenlaub T, Thiele S, Paust R, Spotnitz RM, Zengerle R, Walchshofer C (2014) Three dimensional electrochemical Li-ion battery modeling featuring a focused ion-beam/scanning electrode microscopy based three-phase reconstruction of a \({{\rm LiCoO}}_{2}\) cathode. Electrochim Acta 115:131–139
Malave V, Berger J, Zhu H, Kee RJ (2014) A computational model of the mechanical behavior within reconstructed \({{\rm Li}}_{x}{{\rm CoO}}_{2}\) Li-ion battery cathode particles. Electrochim Acta 130:707–717
Malave V, Berger JR, Martin PA (2014) Concentration-dependent chemical expansion in Lithium-ion battery cathode particles. J Appl Mech 81(9):091005
Stephenson DE, Hartman EM, Harb JN, Wheeler DR (2007) Modeling of particle-particle interactions in porous cathodes for Lithium-ion batteries. J Electrochem Soc 154:A1146–A1155
Wieser C, Prill T, Schladitz K (2015) Multiscale simulation process and application to additives in porous composite battery electrodes. J Power Sources 277:64–75
Babu SK, Mohamed AI, Whitacre JF, Litster S (2015) Multiple imaging mode X-ray computed tomography for distinguishing active and inactive phases in Lithium-ion battery cathodes. J Power Sources 283:314–319
Shearing PR, Howard LE, Jorgensen P, Brandon NP, Harris SJ (2010) Characterization of the 3-dimensional microstructure of a graphite negative electrode from a Li-ion battery. Electrochem Commun 12(3):374–377
Zielke L, Hutzenlaub T, Wheeler DR, Manke I, Arlt T, Paust N, Zengerle R, Thiele S (2014) A combination of X-Ray tomography and carbon binder modeling: reconstructing the three phases of \({{\rm LiCoO}}_{2}\) Li-ion battery cathodes. Adv Energy Mater 4(8):1301617
Zielke L, Hutzenlaub T, Wheeler DR, Chao CW, Manke I, Hilger A, Paust N, Zengerle R, Thiele S (2015) Three-phase multiscale modeling of a \({{\rm LiCoO}}_{2}\) cathode: combining the advantages of FIB–SEM imaging and X-Ray tomography. Adv Energy Mater 5:1401612
Wilson JR, Cronin JS, Barnett SA, Harris SJ (2011) Measurements of three-dimensional microstructure in a \({{\rm LiCoO}}_{2}\) positive electrode. J Power Sources 196:3443–3447
Liu Z, Cronin JS, Chen-Wiegart Y, Wilson JR, Yakal-Kremski KJ, Wang J, Faber KT, Barnett SA (2013) Three-dimensional morphological measurements of \({{\rm LiCoO}}_{2}\) and \({{\rm LiCoO}}_{2}/{{\rm Li}}({{\rm Ni}}_{1/3}{{\rm Mn}}_{1/3}{{\rm Co}}_{1/3}){{\rm O}}_{2}\) Lithium-ion battery cathodes. J Power Sources 227:267–274
Wiedemann AH, Goldin GM, Barnett SA, Zhu H, Kee RJ (2013) Effects of three-dimensional cathode microstructure on the performance of Lithium-ion battery cathodes. Electrochim Acta 88:580–588
Liu Z, Chen-Wiegart Y, Wang J, Barnett SA, Faber KT (2016) Three-phase 3d reconstructions of a \({{\rm LiCoO}}_{2}\) cathode via FIB–SEM tomography. Microsc Microanal 22:140–148
Newman J, Tiedemann WM (1995) Temperature rise in a battery module with constant heat generation. J Electrochem Soc 142(4):1054–1057
Pals CR, Newman J (1995) Thermal modeling of the Lithium/polymer battery. J Electrochem Soc 142(10):3274–3281
Rao L, Newman J (1997) Heat-generation rate and general energy balance for insertion battery systems. J Electrochem Soc 144(8):2697–2704
Jhua CY, Wang YW, Wen CY, Shu CM (2012) Thermal runaway potential of \({{\rm LiCoO}}_{2}\) and \({{\rm Li(Ni}}_{1/3}{{\rm Co}}_{1/3}{{\rm Mn}}_{1/3}){{\rm O}}_{2}\) batteries determined with adiabatic calorimetry methodology. Appl Energy 100:127–131
Abada S, Marlair G, Lecocq A, Petit M, Sauvant-Moynot V, Huet F (2016) Safety focused modeling of Lithium-ion batteries: a review. J Power Sources 306:178–192
Fleckenstein M, Bohlen O, Roscher MA, Baeker B (2011) Current density and state of charge inhomogeneities in Li-ion battery cells with \({{\rm LiFePO}}_{4}\) as cathode material due to temperature gradients. J Power Sources 196:4769–4778
Latz A, Zausch J (2011) Thermodynamic consistent transport theory of Li-ion batteries. J Power Sources 196:3296–3302
Rothe S, Schmidt JH, Hartmann S (2015) Analytical and numerical treatment of electro-thermo-mechanical coupling. Arch Appl Mech 85:1245–1264
Baghdadi I, Briat O, Delétage JY, Gyan P, Vinassa JM (2016) Lithium battery aging model based on Dakin’s degradation approach. J Power Sources 325:273–285
Darling R, Newman J (1998) Modeling side reactions in composite \({{\rm Li}}_{y}{{\rm Mn}}_{2}{{\rm O}}_{4}\) electrodes. J Electrochem Soc 145(3):990–998
Belt JR, Ho CD, Motloch CG, Miller TJ, Duong TQ (2003) A capacity and power fade study of Li-ion cells during life cycle testing. J Power Sources 123(2):241–246
Bloom I, Cole BW, Sohn JJ, Jones SA, Polzin EG, Battaglia VS, Henriksen GL, Motloch C, Richardson R, Unkelhaeuser T, Ingersoll D, Case HL (2001) An accelerated calendar and cycle life study of Li-ion cells. J Power Sources 101(2):238–247
Asakura K, Shimomura M, Shodai T (2003) Study of life evaluation methods for Li-ion batteries for backup applications. J Power Sources, 119–121:902–905. Selected papers presented at the 11th international meeting on Lithium batteries
Safari M, Delacourt C (2011) Simulation-based analysis of aging phenomena in a commercial graphite/\({{\rm LiFePO}}_{4}\) cell. J Electrochem Soc 158(12):A1436–A1447
Wu YP, Rahm E, Holze R (2003) Carbon anode materials for Lithium ion batteries. J Power Sources 114(2):228–236
Fong R, von Sacken U, Dahn JR (1990) Studies of Lithium intercalation into carbons using nonaqueous electrochemical cells. J Electrochem Soc 137(7):2009–2013
Christensen J, Newman J (2004) A mathematical model for the Lithium-ion negative electrode solid electrolyte interphase. J Electrochem Soc 151(11):A1977–A1988
Deng J, Wagner GJ, Muller RP (2013) Phase field modeling of solid electrolyte interface formation in Lithium ion batteries. J Electrochem Soc 160(3):A487–A496
Li D, Danilov D, Zhang Z, Chen H, Yang Y, Notten PHL (2015) Modeling the SEI-formation on graphite electrodes in \({{\rm LiFePO}}_{4}\) batteries. J Electrochem Soc 162(6):A858–A869
Liu L, Park J, Lin X, Sastry AM, Lu W (2014) A thermal-electrochemical model that gives spatial-dependent growth of solid electrolyte interphase in a Li-ion battery. J Power Sources 268:482–490
Nie M, Chalasani D, Abraham DP, Chen Y, Bose A, Lucht BL (2013) Lithium ion battery graphite solid electrolyte interphase revealed by microscopy and spectroscopy. J Phys Chem C 117:1257–1267
Ploehn HJ, Ramadass P, White RE (2004) Solvent diffusion model for aging of Lithium-ion battery cells. J Electrochem Soc 151(3):A456–A462
Rejovitzky E, Di Leo CV, Anand L (2015) A theory and a simulation capability for the growth of a solid electrolyte interphase layer at an anode particle in a Li-ion battery. J Mech Phys Solids 78:210–230
Shin H, Park J, Han S, Sastry AM, Lu W (2015) Component-/structure-dependent elasticity of solid electrolyte interphase layer in Li-ion batteries: experimental and computational studies. J Power Sources 277:169–179
Shin H, Park J, Sastry AM, Lu W (2015) Degradation of the solid electrolyte interphase induced by the deposition of manganese ions. J Power Sources 284:416–427
Tang M, Lu S, Newman J (2012) Experimental and theoretical investigation of solid-electrolyte-interphase formation mechanisms on glassy carbon. J Electrochem Soc 159(11):A1775–A1785
Xie Y, Li J, Yuan C (2014) Multiphysics modeling of Lithium ion battery capacity fading process with solid-electrolyte interphase growth by elementary reaction kinetics. J Power Sources 248:172–179
Ekström H, Lindbergh G (2015) A model for predicting capacity fade due to SEI formation in a commercial graphite/\({{\rm LiFePO}}_{4}\) cell. J Electrochem Soc 162(6):A1003–A1007
Bothe D (2011) On the Maxwell–Stefan approach to multicomponent diffusion. Prog Nonlin 80:81–93
Lam SH (2006) Multicomponent diffusion revisited. Phys Fluids 18:073101
Cheng YT, Verbrugge MW (2008) The influence of surface mechanics on diffusion induced stresses within spherical nanoparticles. J Appl Phys 104:083521
Higa K, Srinivasan V (2015) Stress and strain in silicon electrode models. J Electrochem Soc 162(6):A1111–A1122
Huggins RA, Nix WD (2000) decrepitation model for capacity loss during cycling of alloys in rechargeable electrochemical systems. Ionics 6:57–63
Zhao K, Pharr M, Cai S, Vlassak JJ, Suo Z (2010) Fracture of electrodes in Lithium-ion batteries caused fast charging. J Appl Phys 108:073517
Aifantis KE, Dempsey JP (2005) Stable crack growth in nanostructured Li-batteries. J Power Sources 143:203–211
Aifantis KE, Hackney SA, Dempsey JP (2007) Design criteria for nanostructured Li-ion batteries. J Power Sources 165:874–879
Hu Y, Zhao X, Suo Z (2010) Averting cracks caused by insertion reaction in Lithium-ion batteries. J Mater Res 25(6):1007–1010
Ryu I, Choi JW, Cui Y, Nix WD (2011) Size-dependent fracture of Si nanowire battery anodes. J Mech Phys Solids 59:1717–1730
Woodford H, Chiang YM, Carter WC (2010) Electrochemical shock of intercalation electrodes: a fracture mechanics analysis. J Electrochem Soc 157(10):A1052–A1059
Zhao K, Pharr M, Vlassak JJ, Suo Z (2011) Inelastic hosts as electrodes for high-capacity Lithium-ion batteries. J Appl Phys 109:016110
Salvadori A (2008) A plasticity framework for (linear elastic) fracture mechanics. J Mech Phys Solids 56:2092–2116
Salvadori A (2010) Crack kinking in brittle materials. J Mech Phys Solids 58:1835–1846
Salvadori A, Fantoni F (2013) Minimum theorems in 3D incremental linear elastic fracture mechanics. Int J Fract 184(1):57–74
Salvador A, Fantoni F (2016) Fracture propagation in brittle materials as a standard dissipative process: general theorems and crack tracking algorithms. J Mech Phys Solids 59:121–144
Salvadori A, Giacomini A (2013) The most dangerous flaw orientation in brittle materials and structures. Int J Fract 183(1):19–28
Bhandakkar TK, Gao H (2010) Cohesive modeling of crack nucleation under diffusion induced stresses in a thin strip: implications on the critical size for flaw tolerant battery electrodes. Int J Solids Struct 47:1424–1434
Bhandakkar TK, Gao H (2011) Cohesive modeling of crack nucleation in a cylindrical electrode under axisymmetric diffusion induced stresses. Int J Solids Struct 48:2304–2309
Miehe C, Schaenzel LM, Ulmer H (2015) Phase field modeling of fracture in multi-physics problems. Part I. balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids. Comput Method Appl Mech Eng 294:449–485
Miehe C, Hofacker M, Schaenzel LM, Aldakheel F (2015) Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic–plastic solids. Comput Method Appl Mech Eng 294:486–522
Miehe C, Dal H, Raina A (2016) A phase field model for chemo-mechanical induced fracture in Lithium-ion battery electrode particles. Int J Numer Meth Eng 106(9):683–711
Zuo P, Zhao YP (2015) A phase field model coupling Lithium diffusion and stress evolution with crack propagation and application in Lithium ion batteries. Phys Chem Chem Phys 17:287–297
Miehe C, Mauthe S (2016) Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media. Comput Method Appl Mech Eng 304:619–655
Zhao Y, Xu BX, Stein P, Gross D (2016) Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles. Comput Method Appl Mech Eng 14:1–28
Klinsmann M, Rosato D, Kamlah M, McMeeking RM (2016) Modeling crack growth during Li extraction in storage particles using a fracture phase field approach. J Electrochem Soc 163(2):A102–A118
O’Connor DT, Welland MJ, Liu WK, Voorhees PV (2016) Phase transformation and fracture in single \({{\rm Li}}_{x}{{\rm FePO}}_{4}\) cathode particles: a phase-field approach to Li-ion intercalation and fracture. Model Simul Mater Sci Eng 24(3):035020
Klinsmann M, Rosato D, Kamlah M, McMeeking RM (2016) Modeling crack growth during Li insertion in storage particles using a fracture phase field approach. J Mech Phys Solids 92:313–344
Christensen J, Newman J (2006) A mathematical model of stress generation and fracture in Lithium manganese oxide. J Electrochem Soc 153(6):A1019–A1030
Verbrugge MW, Cheng YT (2009) Stress and strain-energy distributions within diffusion-controlled insertion-electrode particles subjected to periodic potential excitations. J Electrochem Soc 156:A927–A937
Gao YF, Zhou M (2011) Strong stress-enhanced diffusion in amorphus Lithium alloy nanowire electrodes. J Appl Phys 109:014310
Li JCM (1978) Physical chemistry of some microstructural phenomena. Metall Trans 9A:1353–1380
Prussin S (1961) Generation and distribution of dislocations by solute diffusion. J Appl Phys 32(10):1876–1881
Lee S, Wang WL, Chen JR (2000) Diffusion-induced stresses in a hollow cylinder: constant surface stresses. Mater Chem Phys 64(2):123–130
Yang F (2005) Interaction between diffusion and chemical stresses. Mater Sci Eng A 409:153–159
Larche F, Cahn JW (1973) A linear theory of thermochemical equilibrium under stress. Acta Metall Mater 21:1051–1063
Larche F, Cahn JW (1978) Non linear theory of thermochemical equilibrium under stress. Acta Metall Mater 26:53–60
Purkayastha RT, McMeeking RM (2012) A linearized model for Lithium ion batteries and maps for their performance and failure. J Appl Mech 79:1–16
Seo JH, Chung M, Park M, Han SW, Zhang X, Sastry AM (2011) Generation of realistic structures and simulations of internal stress: a numerical/AFM study of \({{\rm LiMn}}_{2}{{\rm O}}_{4}\) particles. J Electrochem Soc 158(4):A434–A442
Wu CH (2001) The role of Eshelby stress in composition-generated and stress-assisted diffusion. J Mech Phys Solids 49(8):1771–1794
Haftbaradaran H, Song J, Curtin WA, Gao H (2011) Continuum and atomistic models of strongly coupled diffusion, stress, and solute concentration. J Power Sources 196:361–370
Wang JW, He Y, Fan F, Liu XH, Xia S, Liu Y, Harris CT, Li H, Huang JY, Mao SX, Zhu T (2013) Two-phase electrochemical lithiation in amorphous silicon. Nano Lett 13(2):709–715
Brassart L, Zhao K, Suo Z (2013) Cyclic plasticity and shakedown in high-capacity electrodes of Lithium-ion batteries. Int J SolidS Struct 50:1120–1129
Sethuraman VA, Srinivasan V, Bower AF, Guduru PR (2010) In situ measurements of stress-potential coupling in lithiated silicon. J Electrochem Soc 157:1253–1261
Wang J, Chen-Wiegart Y, Wang J (2014) In operando tracking phase transformation evolution of Lithium iron phosphate with hard X-ray microscopy. Nat Commun 5:1453–1459
Chen G, Song X, Richardson TJ (2006) Electron microscopy study of the \({{\rm LiFePO}}_{4}\) to \({{\rm FePO}}_{4}\) phase transition. Electrochem Solid State Lett 9:A295
Laffont L, Delacourt C, Gibot P, Wu M, Kooyman P, Masquelier C, Tarascon J (2006) Study of the \({{\rm LiFePO}}_{4}/{{\rm FePO}}_{4}\) two-phase system by high-resolution electron energy loss spectroscopy. Chem Mater 18(23):5520–5529
Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys 28:258–267
Thornton K, Agren J, Voorhees PW (2003) Modelling the evolution of phase boundaries in solids at the meso-and nano-scales. Acta Mater 51(19):5675–5710
Srinivasan V, Newman J (2004) Discharge model for the Lithium iron-phosphate electrode. J Electrochem Soc 151(10):A1517–A1529
Subramanian VR, Ploehn HJ, White RE (2000) Shrinking core model for the discharge of a metal hydride electrode. J Electrochem Soc 147(8):2868–2873
Zhang Q, White RE (2007) Moving boundary model for the discharge of a \({{\rm LiCoO}}_{2}\) electrode. J Electrochem Soc 154(6):A587–A596
Gao F, Hong W (2016) Phase-field model for the two-phase lithiation of silicon. J Mech Phys Solids 94:18–32
Singh GK, Ceder G, Bazant MZ (2008) Intercalation dynamics in rechargeable battery materials: general theory and phase-transformation waves in \({{\rm LiFePO}}_{4}\). Electrochim Acta 53:7599–7613
Burch D, Singh GK, Ceder G, Bazant MZ (2008) Phase-transformation wave dynamics in \({{\rm LiFePO}}_{4}\). Solid State Phenom 139:95–100
Han BC, Van der Ven A, Morgan D, Ceder G (2004) Electrochemical modeling of intercalation processes with phase field models. Electrochim Acta 49(26):4691–4699
Tang M, Craig Carter W, Belak JF, Chiang YM (2010) Modeling the competing phase transition pathways in nanoscale olivine electrodes. Electrochim Acta 56(2):969–976
Tang M, Huang H-Y, Meethong N, Kao Y-H, Carter WC, Chiang Y-M (2009) Model for the particle size, overpotential, and strain dependence of phase transition pathways in storage electrodes: application to nanoscale olivines. Chem Mater 21(8):1557–1571
Cogswell DA, Bazant MZ (2012) Coherency strain and the kinetics of phase separation in \({{\rm LiFePO}}_{4}\) nanoparticles. ACS Nano 6(3):2215–2225
Anand L (2012) A Cahn–Hilliard-type theory for species diffusion coupled with large elastic-plastic deformations. J Mech Phys Solids 60(12):1983–2002
Di Leo C, Rejovitzky E, Anand L (2014) A Cahn-Hilliard-type phase-field theory for species diffusion coupled with large elastic deformations: application to phase-separating Li-ion electrode materials. J Mech Phys Solids 70:1–29
Areias P, Samaniego E, Rabczuk T (2016) A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity. Comput Mech 57(2):339–351
Huang S, Fan F, Li J, Zhang S, Zhu T (2013) Stress generation during lithiation of high-capacity electrode particles in Lithium ion batteries. Acta Mater 61:4354–4364
Yang H, Fan F, Liang W, Guo X, Zhu T, Zhang S (2014) A chemo-mechanical model of lithiation in silicon. J Mech Phys Solids 70:349–361
Drozdov AD (2014) A model for the mechanical response of electrode particles induced by Lithium diffusion in Li-ion batteries. Acta Mech 225:2987–3005
Drozdov AD (2014) Viscoplastic response of electrode particles in Li-ion batteries driven by insertion of Lithium. Int J Solids Struct 51:690–705
Cui Z, Gao F, Qu J (2013) Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in Lithium ion batteries. J Mech Phys Solids 61:293–310
Zhao K, Pharr M, Wan Q, Wang WL, Kaxiras E, Vlassak JJ, Suo Z (2012) Concurrent reaction and plasticity during initial lithiation of crystalline silicon in Lithium-ion batteries. J Electrochem Soc 159:A238–A243
Yang H, Huang S, Huang X, Fan F, Liang W, Liu XH, Chen LQ, Huang JY, Li J, Zhu T, Zhang S (2012) Orientation-dependent interfacial mobility governs the anisotropic swelling in lithiated silicon nanowires. Nano Lett 12(4):1953–1958
Drugan WJ, Willis JR (1996) A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J Mech Phys Solids 44(4):497–524
Shan Z, Gokhale AM (2002) Representative volume element for non-uniform micro-structure. Comput Mater Sci 24(3):361–379
Swaminathan S, Ghosh S, Pagano NJ (2006) Statistically equivalent representative volume elements for unidirectional composite microstructures: part I-without damage. J Compos Mater 40(7):583–604
Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties. Springer, New York
Willis JR (1980) Elasticity theory of composites. Defense Technical Information Center, Report Date : MAR 1980
Stephenson DE, Walker BC, Skelton CB, Gorzkowski EP, Rowenhorst DJ, Wheeler DR (2011) Modeling 3D microstructure and ion transport in porous Li-ion battery electrodes. J Electrochem Soc 158:A781–A789
Ferguson TR, Bazant MZ (2012) Nonequilibrium thermodynamics of porous electrodes. J Electrochem Soc 159(12):A1967–A1985
Schmuck M, Bazant MZ (2015) Homogenization of the Poisson–Nernst–Planck equations for ion transport in charged porous media. SIAM J Appl Math 75(3):1369–1401
Lee S, Sastry AM, Park J (2016) Study on microstructures of electrodes in Lithium-ion batteries using variational multi-scale enrichment. J Power Sources 315:96–110
Golmon S, Maute K, Dunn ML (2009) Numerical modeling of electrochemical-mechanical interactions in Lithium polymer batteries. Comput Struct 87:1567–1579
Golmon S, Maute K, Dunn ML (2012) Multiscale design optimization of Lithium ion batteries using adjoint sensitivity analysis. Int J Numer Meth Eng 92:475–494
Golmon S, Maute K, Dunn ML (2014) A design optimization methodology for \({{\rm Li}}^{+}\) batteries. J Power Sources 253:239–250
Allu S, Kalnaus S, Simunovic S, Nanda J, Turner JA, Pannala S (2016) A three-dimensional meso-macroscopic model for Li-ion intercalation batteries. J Power Sources 325:42–50
Suquet PM (1985) Local and global aspects in the mathematical theory of plasticity. In: Sawczuk A, Bianchi G (eds) Plasticity today: modeling, methods and applications. Elsevier Applied Science Publishers, London, pp 279–310
Geers MGD, Kouznetsova VG, Brekelmans WAM (2010) Multi-scale computational homogenization. J Comput Appl Math 234:2175–2182
Kovetz A (1989) The principles of electromagnetic theory. Cambridge University Press, Cambridge
Huggins RA (2010) Energy storage. Springer, New York
Franco AA, Doublet ML, Bessler WGB (eds) (2016) physical multiscale modeling and numerical symulation of electrochemical devices for energy conversion and storage. Springer, London
Rahman MA, Anwar S, Izadian A (2016) Electrochemical model parameter identification of a Lithium-ion battery using particle swarm optimization method. J Power Sources 307:86–97
Takahashi K, Higa K, Mair S, Chintapalli M, Balsara N, Srinivasan V (2016) Mechanical degradation of graphite/PVDF composite electrodes: a model-experimental study. J Electrochem Soc 163(3):A385–A395
Acknowledgments
We express our deep gratitude to Prof. B. Scrosati, who inspired us and proposed to write this review. He also revised part of the manuscript. FIB–SEM analyses in Fig. 4 were made in cooperation with J. Pauls, A. Mukasyan, J. Schaefer, and K. Matouš at the University of Notre Dame, USA.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grazioli, D., Magri, M. & Salvadori, A. Computational modeling of Li-ion batteries. Comput Mech 58, 889–909 (2016). https://doi.org/10.1007/s00466-016-1325-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-016-1325-8