Fig. 1

(a) Various practical problems in lithium-ion batteries involve the coupling of electrical-chemical-mechanical-thermal effects; (b) which is mathematically represented by the coupling of partial differential equations[9]"

Fig. 2

(a) In double polymer electrolyte and organic-inorganic composite double polymer electrolyte, the concentration distribution of lithium ion evolves with time [14]; (b) The current density distribution of porous electrolyte membrane with multilayer nano sheet interface phase [15]; (c) The potential distribution at the electrolyte cavity, the metal boundaries within the cavity at different deposition times, and the deposition current [19]; (d) The von Mises Plane stress analysis, and the corresponding electric potential field and the ion flux density in the Solid-state cell [21]; (e) Potential distribution and lithium flux distribution in the electrolyte/solid electrolyte interface/lithium negative electrode system when there is no/no mixed conductive interface phase Li5Sn2 [22]"

Fig. 3

(a) Li+ transport path and simulation of Li+ concentration distribution in thick electrode [33]; (b) Lithium concentration distribution of three carbon binder domain states at different discharge capacities [36]; (c) Lithium ion concentration distributions of solid electrolyte (up) and CEI (down) in contact with cathode NCM under [37]; (d) Distribution of lithium ion concentration, volume strain, and von Mises stress in positive electrode particles during charge-discharge cycling [38]; (e) The reaction degrees of positive-solvent reaction for various cathode materials (left); Heat generation rates due to different exothermic reactions for the LiMn2O4 cell during 255 ℃ and 275 ℃ (middle), and for LiFePO4 during 275 ℃ (right) [45]"

Fig. 4

(a) The size dependence of the fracture of silicon nanoparticles during the lithiation process (above); When the particle size D of silicon nanoparticles under the critical Dc ≈150 nm, silicon nanoparticles will not crack or fracture upon first lithiation; while D increases, the ratio of surface thickness to particle size (t/D) decreases, indicating the advancing entrance into the first fracture (middle); Stress relaxation due to surface cracking with the cross section of radii R0 and R0/2, respectively; the crack lengths are 0.1R0 in both cases (below, Red represents full lithiation, and blue represents unlithiated)[47]; (b) The lithiation states (left) and the corresponding maximum in-plane principal stress in the cross sections (right) of〈100〉and〈112〉at various lithiation snapshots[48]; (c) For hierarchical porous Si nanoparticles, volume changes during lithiation and delithiation are mainly accommodated by inward Li breathing, causing negligible exterior volume change[49](Red: fully lithiated, blue: unlithiated)"

Fig. 5

(a) Current density distributions on lithium metal surfaces with different heights (h), widths (w) and ridge lengths (LR)[53]; (b) The morphology evolution of BLi, RGLi and FGLi electrodes [58]; (c) Morphology and uniformity of lithium deposition at different applied current densities [62]; (d) Schematic of lithium deposition behavior at different exchange current densities (top) and simulated deposition cross-section (bottom) [64]"

Fig. 6

(a) Lithium deposition morphology with different SEI coverage [66]; (b) Lithium deposition morphology on LiRAP- ASEI/Cu (top) and Cu foil (bottom) [67]; (c) Von Mises stress distribution and failure time of SEI interfacial films with different pd; (d) Von Mises stress distribution and failure time of SEI interfacial films with different ESEI[69]"

Fig. 7

(a) Simulate the heating process of the battery [76]; (b) Simulating the thermal process after the battery is punctured [78]; (c) Simulating the thermal expansion under different discharge currents and depths of discharge [80]"

Fig. 8

The detailed fault causes of lithium-ion batteries under mechanical, electrical and thermal abuse conditions (from the real world to the laboratory)[81]"

Fig. 9

Applying COMSOL Multiphysics for multi-scale problems in batteries"

Fig. 10

Research on practical problems by combining COMSOL Multiphysics simulation and experimental characterization"

Fig. 11

The analysis of publications in the field of COMSOL Multiphysics using the Science Citation Index (SCI), including (a) the annual trend of SCI publications; (b) density maps of SCI publications from major research countries; (c) keyword and contribution networks; and (d) the keyword and contribution networks related to lithium-ion batteries"