A multiplicative finite strain deformation for diffusion-induced stress: An incremental approach

Understanding the evolution of lithium concentration and stresses in electrode materials during electrochemical cycling is of paramount importance in studying the fundamental mechanisms contributing to the structural degradation of lithiated electrode materials. In this work, we use the change rate of the volume of a host material in analyzing diffusion-induced volume expansion and obtain the volume expansion as an exponential function of the concentration of solute atoms and the coefficient of linear expansion in contrast to the widely used linear relation between the diffusion-induced volume expansion and the coefficient of linear expansion. Using the principle of multiplicative decomposition in the framework of elastic deformation and thermodynamic free energies, we derive the constitutive relation for diffusion-induced finite deformation of elastic materials. The symmetric Piola-Kirchhoff stress is an exponential function of the coefficient of linear expansion and the concentration of solute atoms. Incorporating the change of strain field with the change in the number of solute atoms in Helmholtz free energy, we derive the chemical potential of the solute atoms in the host material the same as the one given by Li et al. (Zeitschrift fur PhysikalischeChemie, 49 (1966) 271-290). Numerical results for the lithiation of a spherical silicon electrode reveal that the spatial distributions of lithium concentration and stresses for small dimensionless time (dilute solution) exhibit similar trends to the corresponding ones calculated from the theory of linear elasticity and nonlinear characteristics for large dimen-sionless time (concentrated solution).

Automated summary

Understanding the evolution of lithium concentration and stresses in electrode materials during electrochemical cycling is crucial for studying the degradation mechanisms of lithiated electrode materials. This study analyzes the diffusion-induced volume expansion by the change rate of the host material's volume and establishes an exponential relationship between volume expansion, concentration of solute atoms, and coefficient of linear expansion. The constitutive relation for diffusion-induced finite deformation of elastic materials is derived using the principle of multiplicative decomposition. The spatial distributions of lithium concentration and stresses in a spherical silicon electrode are found to exhibit similar trends to those calculated from linear elasticity theory and nonlinear characteristics.