A chemo-mechanics framework for elastic solids with surface stress

Gao, Xiang; Fang, Daining; Qu, Jianmin

doi:10.1098/rspa.2015.0366

Cited by 15 publications

(3 citation statements)

References 28 publications

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“…Several studies have attempted to apply surface stress theory to energy storage materials and lithium-ion batteries. A general chemo-mechanics theory for elastic solids with surface stress was proposed by Gao et al [29]. However, for lithium-ion batteries, in particular, Cheng and Verbrugge [30] have shown that both the magnitude and distribution of stresses can be significantly affected by surface mechanics for nanoscale particles.…”

Section: Introductionmentioning

confidence: 99%

An Investigation of Surface Stress on the Fracture Mechanics Behavior of Classical and Phase-Separating Planar Electrodes

Mahmoudy¹,

Haftbaradaran²

2021

Preprint

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Although lithium-ion batteries have extensively been used in various applications because of their high energy capacity, fracture and failure, the by-products of large strains and stresses caused by fast charging and discharging need yet to be addressed. The size effects on the mechanical behavior of the nano-sized structures are significant; however, the classical elasticity theory may not consider such effects. On the other hand, surface stress theory, as a robust and potential theory, is suitable in considering size effects in nano-scale structures. Therefore, in this paper, in order to involve the surface stress effects on the fracture behavior of Li-ion batteries, the following steps are taken. Firstly, a phase-field model is used to determine the evolution of the concentration profile. Subsequently, the stress distribution is obtained by using the surface stress theory combined with chemical equations for a planar electrode. Afterward, by using the weight function method for an edge crack in the plate, the stress intensity factor is derived for all time steps and possible crack lengths during the process. It is found that with increasing phase boundary thickness parameter or decreasing phase-separation phenomenon, the surface mechanics parameters become more influential. Furthermore, in the presence of positive surface stress, the diffusion-induced stress distribution decreases, which in turn reduces the stress intensity factor. In addition, in this paper, the two states of surface stress are compared either for elastic or total strain. Concerning stresses and concentrations, the results indicate a big difference at the beginning of the deintercalation process showing, in particular, 2% for stresses, but the differences diminish gradually.

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Section: Introductionmentioning

confidence: 99%

An Investigation of Surface Stress on the Fracture Mechanics Behavior of Classical and Phase-Separating Planar Electrodes

Mahmoudy¹,

Haftbaradaran²

2021

Preprint

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“…Beside design perspectives, nano-wires and nano-tubes have enhanced electrochemical performance due to their robust electrical contact with the metallic current collector which enable each particle to contribute to the capacity [43,44]. A number of studies indicate the prominence of surface stress in nano-particles [52] as the prime reason behind their structural durability [53][54][55][56][57][58][59][60]. Furthermore, the effect of surface stress is dependent on the particle size (with decrease in particle size surface stress effect increases [61,62]), as well as the charging rate (with increase in charging rate, surface stress effect increases) [56].…”

Section: Introductionmentioning

confidence: 99%

Rethinking battery degradation in presence of surface effects: mechanical versus electrochemical peformance mediated by charging condition

Sengupta¹,

Chakraborty²

2021

Preprint

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Surface stresses, in nano-sized anode particles undergoing chemomechanical interactions, have a relaxing effect on the diffusion-induced stresses thus improving the mechanical endurance of the particles, whereas, the compressive effect of surface stresses degrades the electrochemical performance. However, this straightforward prediction of an improved mechanical performance is challenged in this work. Silicon nanowires undergoing huge volumetric changes during lithiation, may undergo significant axial length-increase, which serves as an important criterion in determining the mechanical performance of SiNWs. Interestingly, surface stresses tend to reduce the length-increase under potentiostatic charging condition, but under galvanostatic charging, the length-increase gets enhanced, thus degrading the mechanical performance of the SiNWs. To further make the study more inclusive, the nanowire is modelled with a constraining material at its core, and a competitive analysis is presented for the overall performance of the anode particles under the combined effects of surface stresses and constraining material. The mathematical model is based on large deformation theory, considering two-way coupling of diffusion-induced stresses and stressenhanced diffusion. It is hoped that this study will provide a fresh perspective in designing next-generation lithium-ion battery particles.

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“…Due to the nonlinearity and coupling nature of this problem, Haftbaradaran and Qu [14] obtained the asymptotic solutions for three fundamental two-dimensional problems using a perturbation method. Gao et al [15] derived the governing equations for three-dimensional chemo-mechanical problems accounting for surface stresses. Similarly, a perturbation method is used and the nonlinear governing equations are reduced to a system of linear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Perturbation solutions of the diffusive chemo-mechanical coupling problem without a failure of local Fick’s law

Shen

Wan

2019

Mathematics and Mechanics of Solids

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Silicon electrodes of lithium-ion batteries have a remarkable diffusive chemo-mechanical coupling effect during lithiation and delithiation. In order to study the variation of stresses and concentration distribution in the electrode, a nonlinear partial differential equation for the concentration is usually derived using the thermal analogy method and Fick’s laws, in the case without a failure of local Fick’s law. However, due to the nonlinearity of the equation and the boundary conditions, it is generally difficult to get the analytic solution. In this paper, by using the dimensionless quantities, the perturbation solutions are obtained for two fundamental problems, that is, the semi-infinite and the cylinder, which appears to be semi-analytic and easy for the numerical calculation. The results match with the numerical solutions very well, when the charge current density is controlled in a relatively appropriate range. The semi-analytic solutions show that the compressive stress promotes the diffusion of lithium in the electrode during lithiation, which cannot be neglected, compared with the condition without considering the coupling effect.

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A chemo-mechanics framework for elastic solids with surface stress

Cited by 15 publications

References 28 publications

An Investigation of Surface Stress on the Fracture Mechanics Behavior of Classical and Phase-Separating Planar Electrodes

An Investigation of Surface Stress on the Fracture Mechanics Behavior of Classical and Phase-Separating Planar Electrodes

Rethinking battery degradation in presence of surface effects: mechanical versus electrochemical peformance mediated by charging condition

Perturbation solutions of the diffusive chemo-mechanical coupling problem without a failure of local Fick’s law

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