A comprehensive diffusion-induced stress coupled multiscale modeling and analysis in hard-carbon electrodes of Li-ion batteries

Particle fracture due to diffusion-induced stress (DIS) in electrodes is a key factor for lithium-ion battery (LIB) failure. Among many ways to minimize DIS, optimization of particle size and C-rates using state of charge (SOC) dependent varying properties can be a noble approach. Herein, a comprehensive multiscale modeling approach has been proposed to optimize the particle size by studying the DIS in hard carbon (HC) particles as the potential anode materials for high-energy LIBs. To accomplish this, density functional theory (DFT) was used to calculate the SOC dependent coefficient of volume expansion (CVE). Similarly, SOC dependent diffusivity and elastic modulus are calculated via molecular dynamics (MD) simulations. These results are transferred to a continuum model to examine the evolution of concentrations and DISs in hard carbon particles of radius 100-1000 nm lithiated at various C-rates (1C, 2C, 5C, and 10C). Our model successfully incorporates the variation of Li+ diffusivity and elastic modulus with SOC and tracks stress relaxation and volume expansion in the particles during lithiation. An optimized particle size has been recommended for hard carbon, considering both stresses for different C-rates. Our study provides a more realistic multiscale modeling framework for optimizing the DIS and can act as a guiding method towards achieving an optimum particle size so that capacity fading due to cracking can be avoided.