[1] [1] REDDY M V, MAUGER A, JULIEN C M, et al. Brief history of early lithium-battery development[J]. Materials, 2020, 13(8): 1884.

[2] [2] LI M, LU J, CHEN Z W, et al. 30 years of lithium-ion batteries[J]. Adv Mater, 2018，30(33): e1800561.

[3] [3] GOODENOUGH J B, KIM Y. Challenges for rechargeable Li batteries[J]. Chem Mater, 2010, 22(3): 587–603.

[4] [4] BABU B. Self-discharge in rechargeable electrochemical energy storage devices[J]. Energy Storage Mater, 2024, 67: 103261.

[5] [5] LI J, FANG Q H, WU H, et al. Investigation into diffusion induced plastic deformation behavior in hollow lithium ion battery electrode revealed by analytical model and atomistic simulation[J]. Electrochim Acta, 2015, 178: 597–607.

[6] [6] MUKHOPADHYAY A, SHELDON B W. Deformation and stress in electrode materials for Li-ion batteries[J]. Prog Mater Sci, 2014, 63: 58–116.

[7] [7] XU R, ZHAO K J. Mechanical interactions regulated kinetics and morphology of composite electrodes in Li-ion batteries[J]. Extreme Mech Lett, 2016, 8: 13–21.

[8] [8] JANGID M K, MUKHOPADHYAY A. Real-time monitoring of stress development during electrochemical cycling of electrode materials for Li-ion batteries: Overview and perspectives[J]. J Mater Chem A, 2019, 7(41): 23679–23726.

[9] [9] HONG Y H, ZHENG J Q, DENG D R, et al. Heterogeneous aging of large-scale flexible lithium-ion batteries based on micro-heterostructures and simulation[J]. Int J Energy Res, 2020, 44(14): 12112–12125.

[10] [10] JI L, GUO P Z, WU P Y. Computational and experimental observation of Li-ion concentration distribution and diffusion-induced stress in porous battery electrodes[J]. Energy Technol, 2017, 5(9): 1702–1711.

[11] [11] WANG Q J, ZHU D. Hertz theory: Contact of spherical surfaces[M]//Encyclopedia of Tribology. Boston, MA: Springer US, 2013: 1654–1662.

[12] [12] BENSON D J, OKAZAWA S. Contact in a multi-material Eulerian finite element formulation[J]. Comput Meth Appl Mech Eng, 2004, 193(39–41): 4277–4298.

[13] [13] WRIGGERS P. Computational Contact Mechanics[M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006.

[14] [14] XIAO H, BRUHNS O T, MEYERS A. Thermodynamic laws and consistent Eulerian formulation of finite elastoplasticity with thermal effects[J]. J Mech Phys Solids, 2007, 55(2): 338–365.

[15] [15] PLOHR B J, SHARP D H. A conservative Eulerian formulation of the equations for elastic flow[J]. Adv Appl Math, 1988, 9(4): 481–499.

[16] [16] LIU C, WALKINGTON N J. An eulerian description of fluids containing visco-elastic particles[J]. Arch Ration Mech Anal, 2001, 159(3): 229–252.

[17] [17] TRANGENSTEIN J A, COLELLA P. A higher-order Godunov method for modeling finite deformation in elastic-plastic solids[J]. Commun Pure Appl Math, 1991, 44(1): 41–100.

[18] [18] NARAYAN S, ANAND L. A large deformation elastic–viscoplastic model for lithium[J]. Extreme Mech Lett, 2018, 24: 21–29.

[19] [19] OSHER S, FEDKIW R. Level set methods and dynamic implicit surfaces[M]. New York: Springer, 2003.

[20] [20] HIRT C W, NICHOLS B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. J Comput Phys, 1981, 39(1): 201–225.

[21] [21] ANDERSON D M, MCFADDEN G B, WHEELER A A. Diffuse-interface methods in fluid mechanics[J]. Annu Rev Fluid Mech, 1998, 30: 139–165.

[22] [22] SUN Y, BECKERMANN C. Sharp interface tracking using the phase-field equation[J]. J Comput Phys, 2007, 220(2): 626–653.

[23] [23] ZHAO Y. Phase-field modeling of electro-chemo-mechanical behavior of li-ion battery electrodes[D]. Darmstadt, Germany: Technische Universitaet Darmstadt, 2017.

[24] [24] CAHN J W, HILLIARD J E. Free energy of a nonuniform system. I. interfacial free energy[J]. J Chem Phys, 1958, 28(2): 258–267.

[25] [25] LOREZ F, PUNDIR M, KAMMER D S. Eulerian framework for contact between solids represented as phase fields[J]. Comput Meth Appl Mech Eng, 2024, 418: 116497.

[26] [26] Provatas N, Elder K. Spatial Variations and Interfaces[C]//Phase-Field Methods in Materials Science and Engineering. John Wiley & Sons, Ltd, 2010: 27–32.

[27] [27] ZHAO Y, XU B X, STEIN P, et al. Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles[J]. Comput Meth Appl Mech Eng, 2016, 312: 428–446.

[28] [28] DI LEO C V, REJOVITZKY E, ANAND L. Diffusion–deformation theory for amorphous silicon anodes: The role of plastic deformation on electrochemical performance[J]. Int J Solids Struct, 2015, 67: 283–296.

[29] [29] SETHURAMAN V A, CHON M J, SHIMSHAK M, et al.In situmeasurement of biaxial modulus of Si anode for Li-ion batteries[J]. Electrochem Commun, 2010, 12(11): 1614–1617.

[30] [30] KAMRIN K, RYCROFT C H, NAVE J C. Reference map technique for finite-strain elasticity and fluid–solid interaction[J]. J Mech Phys Solids, 2012, 60(11): 1952–1969.

[31] [31] Anders L, Kent-Andre M, Garth W. Automated Solution of Differential Equations by the Finite Element Method[M]. SpringerLink, 2012.

[32] [32] Abraham D P, Dees D W, Knuth J, et al. Diagnostic examination of Generation 2 lithium-ion cells and assessment of performance degradation mechanisms [C/OL]. 2005: ANL-05/21, 861617