硅酸盐学报

电极颗粒力-化学耦合接触分析

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龙永一 , 赵莹

硅酸盐学报 | 电化学储能材料计算与设计专题—研究论文 2025,53(7): 1856-1864

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硅酸盐学报 |电化学储能材料计算与设计专题—研究论文 2025 , 53 (7) : 1856 -1864

电极颗粒力-化学耦合接触分析

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龙永一, 赵莹

作者信息

同济大学航空航天与力学学院，上海 200092

通讯作者:

赵莹（1988—），女，博士，研究员。

作者简介:

龙永一（2002—），男，硕士研究生。

Chemo-mechanical Contact Analysis of Electrode Active Particles

Yongyi LONG, Ying ZHAO

Affiliations

School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

Corresponding Author:

ZHAO Ying (1988-), female, Ph.D., Professor. E-mail: 19531@tongji.edu.cn

LONG Yongyi (2002-), male, Master candidate. E-mail: longyy@tongji.edu.cn

出版时间: 2025-07-20 doi: 10.14062/j.issn.0454-5648.20240853

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摘要

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锂电池电极颗粒在充放电过程中伴随着变形，当变形过大时，颗粒与颗粒之间会产生接触，甚至相互挤压，导致颗粒破碎，影响电池的电化学性能。传统固体接触问题的数值求解方法基于拉格朗日描述，需要复杂的接触检测算法来实现接触约束，对于具有复杂形貌的颗粒在发生大变形时的接触行为不能准确捕捉，导致对于颗粒间相互作用预估不准，甚至发生错误判断。为解决这些问题，基于相场法，在欧拉描述下，建立了考虑力-化学耦合的锂电池颗粒模型，实现了锂电池充放电过程中接触检测的简化和固体间的接触分析，并以线弹性的赫兹接触问题为例，展示该方法在接触计算中的精度。通过仿真模拟了电极颗粒锂化膨胀发生接触的过程，并探究了不同条件下不同形貌的电极颗粒在发生接触时的应力集中情况，获得了电极颗粒在相互挤压时容易发生力学损伤的部位。

关键词

锂电池 / 电极颗粒 / 固体接触 / 欧拉描述 / 相场法

Abstract

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Introduction

In lithium-ion batteries, electrode active particles are used to store and release lithium ions. The insertion and extraction of lithium ions are accompanied by a local deformation of the electrode active material, which can lead to mechanical degradation. Studies on the chemo-mechanical behavior of electrode particles can favor to improve the capacity and cycle life of batteries. Silicon has a super high capacity as an anode and is considered as a promising electrode material. However, its excessively high volume change rate hinders the further development of silicon electrodes. Two main reasons lead to mechanical failure of silicon electrode particles, i.e., the non-uniform volume change due to Li-ion concentration gradient, and the contact between particles upon lithium insertion induced volume expansion. Contacts between elastic deformable parts with simple morphologies are investigated based on the Hertz theory, which mainly analyzes contacts via calculating the contact area and indentation depth. Simulations of solids are mainly based on the Lagrangian description, which requires to create multiple systems and inter-system connections that are computationally complex. A phase-field model is developed with Eulerian description that can conveniently identify and distinguish the inside and outside of an object by the value of a variable "order parameter". In addition, some examples for calculation the contact between electrode particles with different morphologies are also calculated to explore the ability of the proposed method.

Methods

The calculation model is based on 3 equations, i.e., the equilibrium equation, Cahn-Hilliard equation and the reference map equation. After splitting the Cahn-Hilliard equation into two parts, 4 variables v, Ф, μ, ξ need to be calculated. The constitutive law is calculated through ξ and contact force is calculated through the Ф of the contact bodies. Deformation gradient is decomposed into elastic part and lithium-intercalation-induced part. The elastic part is constructed on neo-Hookean theory, and lithium-intercalation-induced part is calculated through the concentration of Li. Elastic constants are also functions of the concentration as Si and Li both contribute to it. 4 PDEs are generated, including the Cahn-Hilliard equation, the equilibrium equation and the evolution equation of ξ. After applying boundary conditions, the PDEs are transformed to weak forms. The simulations are performed by the finite element method.

Results and discussion

A simple elastic contact problem is simulated to verify the feasibility and accuracy of the method. The result is compared with the Hertz theory. The lithiation of electrode particles is then simulated. The electrode particles are initialized as cylinders with regular and irregular profiles. The figure of von Mises stress shows that the contact between particles with regular profile is equivalent to the contact between a nanowire and rigid plane. And particles show different behaviors when they start lithiation at different durations. Particles with irregular circle profile shows a higher stress when the contact with rigid plane while the stress is lower when contacting with other particles. That is because particles rotate when the irregular profiles contact, which releases part of the stress and expands the contact area. To exclude the effects of rotation, considering that friction and binder can impede rotation, an example of 1/4 electrode particles is simulated. Particle rotation has a significant effect on stress relief, especially in the final stages of expansion, where the maximum stress can be reduced by approximately 1/3. Finally, simulations are performed with a reference to the actual electrode particle morphology. The internal stress in the particles becomes stable at a certain point and no longer increases significantly with deeper lithiation.

Conclusions

The simulation modeling of the contact between solids was implemented based on the phase-field method, and its feasibility and accuracy were verified through a simple example. Subsequently, the simulations of the contact problem of the lithiation of electrode particles were carried out to investigate the deformation and stress state of electrode particles with different shapes when the contact occurs to show the region where mechanical degradation might occur. The simulation of electrode particles' lithiation showed different behaviors when the profile changed. This was because particles with irregular profile rotate when contacts occured so that concave surface and convex surface coupled. However, smaller contact area resulted in higher stress when concave surface contacted with rigid plane. The final simulations were performed with a reference to the morphology of the electrode particles in the real situation. These simulations could provide a reference for the study of the lithiation behavior of electrode particles in Li-ion batteries, showing the possible sites of mechanical damage or fracture of the electrode particles when they squeezed against each other, which in turn could be expected to contribute to the optimal design of Li-ion batteries in the future.

Key words

lithium-ion battery / electrode particle / solid contact / Eulerian description / phase-field method

引用本文

龙永一, 赵莹. 电极颗粒力-化学耦合接触分析. 硅酸盐学报, 2025 , 53 (7) : 1856 -1864 . DOI: 10.14062/j.issn.0454-5648.20240853

Yongyi LONG, Ying ZHAO. Chemo-mechanical Contact Analysis of Electrode Active Particles[J]. Journal of the Chinese Ceramic Society, 2025 , 53 (7) : 1856 -1864 . DOI: 10.14062/j.issn.0454-5648.20240853

基金

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国家自然科学基金(12472175)

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2025年第53卷第7期

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文章信息

doi: 10.14062/j.issn.0454-5648.20240853

接收时间：2025-01-02
首发时间：2026-10-21
出版时间：2025-07-20

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出版历史

收稿日期：2025-01-02
修回日期：2025-02-01

基金

国家自然科学基金(12472175)

作者信息

同济大学航空航天与力学学院，上海 200092

通讯作者:

赵莹（1988—），女，博士，研究员。

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20240853

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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