1. Different scales of diffusion-induced stress in lithium-ion batteries

2. Relationship between volume change ratio of graphite and SOC^[9]

3. Radial stress and tangential stress in the active particle^[12]

4. Lithiation process of the spherical silicon particle^[14]

5. (a) Nanowire particle and its lithiation process^[23]; (b) Initial state and lithiation expansion state of nanowire particle with initial delamination defect^[25]; (c) Initial state and lithiation expansion state of nanowire particle with mechanical clamping^[26]

6. (a) Solid sphere particle with carbon-coated shell^[31]; (b) Lithium concentration distribution of carbon-coated solid sphere particle and hollow sphere particle during lithiation^[32]; (c) Nanotube particle with carbon-coated shell^[33]

7. (a) Delithiation process of spherical particle with two-phase deintercalation mechanism^[35]; (b) Surface tangential stress of spherical particle during lithiation process with two-phase deintercalation mechanism^[36], the hollow circle, solid circle, asterisk and star represent the initial dimensionless sizes of the particles as 0.01, 0.1, 1.0 and 10.0, respectively; (c) Relationship between critical dimension and discharge rate^[42]

8. (a) Lithium concentration distribution in the multi-particle model at 60% Depth of Discharge (DOD)^[46,47]; (b) Multi-particle model considering homogeneous matrix and single-particle-matrix representative unit^[48]; (c) Multi-particle-matrix electrode structure considering homogeneous matrix and diffusion-induced stress distribution of active particles during 1C discharge^[50]

9. (a) Multi-particle model established by X-ray scanning, (Black: The active particles and the binder; Blue: The electrolyte)^[53]; (b) Diffusion-induced stress distribution of multi-particle model when fully charged at 1C rate^[54]

10. Schematic diagrams of models

11. (a) Initial state and lithiation deformation of the double-layer electrode considering plasticity of the current collector^[62]; (b) Symmetrical electrode model composed of graphite active layers and copper current collector^[63]; (c) Relationship between the elastic modulus of graphite and silicon and SOC^[69]

12. (a) Double-layer silicon electrode cracks to form silicon islands (above), and double-layer electrode model of a silicon island constrained by a current collector (below)^[73]; (b) Diffusion-induced stress distribution of the double-layer electrodes of silicon islands with initial defects after lithiation, the length ratios of the long and short axes of the initial defects are 0.2, 0.4, 0.6, 0.8 and 1, respectively^[75]

13. Failure of particles in the NMC311 positive electrode^[77]

14. Scanning electron micrographs of a silicon-carbon composite anode

15. Crack propagation of a silicon electrode^[80]

16. (a) Diffusion-induced stress in the graphite anode during the first 3 cycles^[85]; (b) Evolution of diffusion-induced stress in a Ge electrode during lithiation and delithiation, the arrows represent the moment when the electrode fractures^[86]

17. Distribution of diffusion-induced stress in the cell unit during discharge, DOD are (a) 8%, (b) 54%, (c) 67% and (d) 100%, respectively^[90]

18. Surface pressure during charge and discharge of a prismatic cell ^[93]

19. (a) Experimental schematic diagram of the external constraint and EIS test^[94]; (b) Impedance as a function of cycle times at different external pressures^[95]; (c) Effect of external constraints on cycle lifetime of the cell, of which blue, green, yellow and red lines representing external constraints of 0, 0.05, 0.5 and 5 MPa, respectively^[96]; (d) SOH as a function of cycle times, of which blue, red, yellow, and purple lines representing no external constraint, constant thickness constraint, elastic element constraint, and constant force spring constraint, respectively^[97]

20. Deformation of jelly roll after charge and discharge cycles (a) X-ray scan result and (b) Laser microscope result^[101]

Table 1. Factors affecting diffusion-induced stress in a single particle model

Table 2. Failure phenomenon of cell and their corresponding mechanism