Lithium-ion batteries have the advantages of high energy density, high working voltage, low self-discharge rate, and fast charging. They are widely used in various fields related to national defense industry and human life. After considerable efforts in developing the domestic battery industry, China has built a strong foundation in battery research and production. However, owing to the lack of battery computing models and design software, the design of novel batteries is still based on experience. Thus, relevant quantitative theoretical models and algorithm implementations are urgently needed. Lithium-ion battery systems have complex multiphysics coupling characteristics and multiscale characteristics in time and space. Unclear multifield coupling mechanisms related to lithiation and delithiation, the hard scale transitions in time and space, and the lack of design software are the main factors preventing the commercialization of novel materials in next-generation high-energy-density batteries. Herein, we propose a multiscale theoretical model and algorithm realization using the coupling of the electrochemomechanical behaviors of the batteries, including ① electrochemomechanical coupling theory of electrodes in lithium-ion batteries, ② finite element realization of multifield coupling behavior at various scales, ③ concurrent and hierarchical multiscale theoretical and numerical models of electrodes, and ④ electrochemomechanical behavior of the interface between the electrode and electrolyte.
WU Yikun. Multiscale and multiphysics theoretical model and computational method for lithium-ion batteries[J]. Energy Storage Science and Technology, 2023, 12(7): 2141-2154
Fig. 1
(a) Decomposition of total deformation[24]; (b) Stress distribution on the reference state and current state[23]; (c) Concentration and stress distribution in the electrode particle[27]; (d) Anisotropic expansion and the stress distribution of the Si electrode[21]
Fig. 4
(a) Mori-Tanaka method to related the electrode and the active partical[60]; (b) The relations of parameters at different scale in the electrode[57]; (c) Three typical scale in the battery[56]
Fig. 5
(a) Geometric model with 1050 particles based on CT[71]; (b), (c) 3D geometric model of based on FIB-SEM[73-74]; (d) The simulation scheme of the particles based on the FIB-SEM and CT[75]
Fig. 10
(a) Schematic of an ion intercalation and deintercalation reaction which is pictured as a process of transferring electron between the graphite electrode and lithium ion in the electrolyte solution; (b) Simulation box of the electrochemical double layer model includes the mechanical deformations; (c) The relationship between solvent reorganization energy and strain at different potentials; (d) The relationship between potential and mechanical strain
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... 然而对于新型高容量电极来说,小变形弹性假设已经无法满足实际要求,因此发展基于有限变形理论下的力/化耦合理论逐渐成为广大科研工作者的重点.Newman等[14]较早地提出基于当前构型下的球形颗粒应力分布.而对于硅基负极这种新型高容量电池,许多研究表明,不管是晶体硅还是无定形硅,在嵌锂过程中都会产生塑性变形[15-20].为了描述这一现象,大变形弹塑性力化双向耦合理论模型纷纷建立[21-31].与小变形理论不同的是,大变形通常将变形梯度进行Lee分解[32]: F = FeFcFp,其中弹性变形梯度( Fe)、塑性变形梯度( Fp)以及嵌锂膨胀导致的化学本征变形梯度( Fc).变形梯度分解如图1(a)所示,实际发生的过程是由初始构型变化到当前构型,但为了方便分解,假设了一个中间构型,也就是由当前构型卸载得到的,也可称为卸载构型.如果每点附近的区域都完全卸载,那么由于不可逆的塑性变形,各微元之间不会连续呈现出图中碎裂的状态.但实际上,微元不可能做到完全卸载,只能卸载到残余应力状态,并通过各自的旋转组成一个连续体.因此中间构型在实际中是不存在的,只是为了分解应变梯度假设出来的一个构型. ...
1
... 然而对于新型高容量电极来说,小变形弹性假设已经无法满足实际要求,因此发展基于有限变形理论下的力/化耦合理论逐渐成为广大科研工作者的重点.Newman等[14]较早地提出基于当前构型下的球形颗粒应力分布.而对于硅基负极这种新型高容量电池,许多研究表明,不管是晶体硅还是无定形硅,在嵌锂过程中都会产生塑性变形[15-20].为了描述这一现象,大变形弹塑性力化双向耦合理论模型纷纷建立[21-31].与小变形理论不同的是,大变形通常将变形梯度进行Lee分解[32]: F = FeFcFp,其中弹性变形梯度( Fe)、塑性变形梯度( Fp)以及嵌锂膨胀导致的化学本征变形梯度( Fc).变形梯度分解如图1(a)所示,实际发生的过程是由初始构型变化到当前构型,但为了方便分解,假设了一个中间构型,也就是由当前构型卸载得到的,也可称为卸载构型.如果每点附近的区域都完全卸载,那么由于不可逆的塑性变形,各微元之间不会连续呈现出图中碎裂的状态.但实际上,微元不可能做到完全卸载,只能卸载到残余应力状态,并通过各自的旋转组成一个连续体.因此中间构型在实际中是不存在的,只是为了分解应变梯度假设出来的一个构型. ...
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... 对于新一代高容量电极材料来说,如何实现有限变形、质量扩散以及塑性问题的数值模拟是对科研工作者的主要挑战.在一些研究中,得益于商业软件ABAQUS平台针对非线性问题的鲁棒性与可操作性优势,基于其二次开发功能的相关数值方法得以建立[40-43].其中,亚利桑那州立大学的姜汉卿课题组[44]基于ABAQUS二次开发程序在连续介质尺度模拟了有限变形和质量扩散全耦合问题.该方法巧妙地借助热传导与质量扩散控制方程在形式上的相似,通过将质量扩散问题与ABAQUS中自带力学/热传导相类比,借用力/热耦合单元以及热传导子程序UMATHT来实现扩散模拟.同时,开发UMAT、UEXPAN以及UFLUX 3个子程序来分别进行变形梯度 F 的读取、化学膨胀应变的定义以及流量边界条件的施加.Yang等[45]采用同样的方法研究了二维硅电极面内裂纹对其界面脱黏的影响.还有一些学者单独采用UMATHT子程序来进行扩散与弹塑性耦合模拟[18, 21, 46].相对于借用ABAQUS自带的力/热耦合单元,一些学者通过自己开发力/化耦合用户自定义单元来实现该复杂问题的数值模拟.其中,中科院魏宇杰老师课题组[31]发展了较大塑性变形情况下力/电/化强耦合模型,并通过开发相应的力/电/化强耦合有限元单元,较为准确地描述了薄膜电极应力的演化情况.根据多光束实验得到的基底曲率演化规律,该方法可以较为准确地获取电极材料在循环过程中的材料参数.除了借用商业平台外,Bower等[47]采用一种对于微小改进的标准B-bar方法来避免单元自锁现象,并且采用了混合单元,考虑了应力梯度引起的扩散现象.Gao等[48]也提出了一种混合有限元模型,以数值方式评估静水压力.在有限元法之外,还有一些其他计算方法来解决特定的问题.比如,Gritton等[49]采用物质点法(MPM)来描述硅负极中应力相关化学势与扩散诱导应力.物质点法最大的优势在于,在解决大变形问题时不存在由于网格畸变而导致的错误.高华健院士课题组[50]通过原子模拟硅电极中应力对于嵌锂的影响.此外,由于电极活性颗粒是离散分布的,因此离散元多用于电极颗粒的仿真分析[51-53].Smith等[54]通过离散元方法研究了极片在不同辊压条件下结构的演变.总的来说,数值计算方法对于理解多物理场耦合机理有着至关重要的地位,然而对于多孔极片综合性的力/电/电化学耦合的通用性计算方法还较为缺失,同时计算方法的准确性与高效性还有待提高. ...
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... 然而对于新型高容量电极来说,小变形弹性假设已经无法满足实际要求,因此发展基于有限变形理论下的力/化耦合理论逐渐成为广大科研工作者的重点.Newman等[14]较早地提出基于当前构型下的球形颗粒应力分布.而对于硅基负极这种新型高容量电池,许多研究表明,不管是晶体硅还是无定形硅,在嵌锂过程中都会产生塑性变形[15-20].为了描述这一现象,大变形弹塑性力化双向耦合理论模型纷纷建立[21-31].与小变形理论不同的是,大变形通常将变形梯度进行Lee分解[32]: F = FeFcFp,其中弹性变形梯度( Fe)、塑性变形梯度( Fp)以及嵌锂膨胀导致的化学本征变形梯度( Fc).变形梯度分解如图1(a)所示,实际发生的过程是由初始构型变化到当前构型,但为了方便分解,假设了一个中间构型,也就是由当前构型卸载得到的,也可称为卸载构型.如果每点附近的区域都完全卸载,那么由于不可逆的塑性变形,各微元之间不会连续呈现出图中碎裂的状态.但实际上,微元不可能做到完全卸载,只能卸载到残余应力状态,并通过各自的旋转组成一个连续体.因此中间构型在实际中是不存在的,只是为了分解应变梯度假设出来的一个构型. ...
5
... 然而对于新型高容量电极来说,小变形弹性假设已经无法满足实际要求,因此发展基于有限变形理论下的力/化耦合理论逐渐成为广大科研工作者的重点.Newman等[14]较早地提出基于当前构型下的球形颗粒应力分布.而对于硅基负极这种新型高容量电池,许多研究表明,不管是晶体硅还是无定形硅,在嵌锂过程中都会产生塑性变形[15-20].为了描述这一现象,大变形弹塑性力化双向耦合理论模型纷纷建立[21-31].与小变形理论不同的是,大变形通常将变形梯度进行Lee分解[32]: F = FeFcFp,其中弹性变形梯度( Fe)、塑性变形梯度( Fp)以及嵌锂膨胀导致的化学本征变形梯度( Fc).变形梯度分解如图1(a)所示,实际发生的过程是由初始构型变化到当前构型,但为了方便分解,假设了一个中间构型,也就是由当前构型卸载得到的,也可称为卸载构型.如果每点附近的区域都完全卸载,那么由于不可逆的塑性变形,各微元之间不会连续呈现出图中碎裂的状态.但实际上,微元不可能做到完全卸载,只能卸载到残余应力状态,并通过各自的旋转组成一个连续体.因此中间构型在实际中是不存在的,只是为了分解应变梯度假设出来的一个构型. ...
... [21](a) Decomposition of total deformation[24]; (b) Stress distribution on the reference state and current state[23]; (c) Concentration and stress distribution in the electrode particle[27]; (d) Anisotropic expansion and the stress distribution of the Si electrode[21]Fig. 1
(a) Decomposition of total deformation[24]; (b) Stress distribution on the reference state and current state[23]; (c) Concentration and stress distribution in the electrode particle[27]; (d) Anisotropic expansion and the stress distribution of the Si electrode[21]Fig. 1
... [23]; (c) Concentration and stress distribution in the electrode particle[27]; (d) Anisotropic expansion and the stress distribution of the Si electrode[21]Fig. 1
(a) Decomposition of total deformation[24]; (b) Stress distribution on the reference state and current state[23]; (c) Concentration and stress distribution in the electrode particle[27]; (d) Anisotropic expansion and the stress distribution of the Si electrode[21]Fig. 1
... [24]; (b) Stress distribution on the reference state and current state[23]; (c) Concentration and stress distribution in the electrode particle[27]; (d) Anisotropic expansion and the stress distribution of the Si electrode[21]Fig. 1
(a) Decomposition of total deformation[24]; (b) Stress distribution on the reference state and current state[23]; (c) Concentration and stress distribution in the electrode particle[27]; (d) Anisotropic expansion and the stress distribution of the Si electrode[21]Fig. 1
... [56](a) Mori-Tanaka method to related the electrode and the active partical[60]; (b) The relations of parameters at different scale in the electrode[57]; (c) Three typical scale in the battery[56]Fig. 4
... [57];(c) 3个尺度示意图以及相邻尺度间的参数传递[56](a) Mori-Tanaka method to related the electrode and the active partical[60]; (b) The relations of parameters at different scale in the electrode[57]; (c) Three typical scale in the battery[56]Fig. 4
... [60];(b) 微观尺度与宏观尺度间、电化学场与力学场之间的关键参数传递[57];(c) 3个尺度示意图以及相邻尺度间的参数传递[56](a) Mori-Tanaka method to related the electrode and the active partical[60]; (b) The relations of parameters at different scale in the electrode[57]; (c) Three typical scale in the battery[56]Fig. 4
... [71];(b)三维LiFePO4 正极FIB-SEM重构模型(绿色是LiFePO4;黑色是炭黑;透明的是孔隙)[73];(c) FIB-SEM正极重构模型[74];(d)通过FIB-SEM和CT重构得到的纳米导电剂与微米颗粒对电池性能影响的计算方案[75](a) Geometric model with 1050 particles based on CT[71]; (b), (c) 3D geometric model of based on FIB-SEM[73-74]; (d) The simulation scheme of the particles based on the FIB-SEM and CT[75]Fig. 53.2 并发多尺度方法
... [71]; (b), (c) 3D geometric model of based on FIB-SEM[73-74]; (d) The simulation scheme of the particles based on the FIB-SEM and CT[75]Fig. 53.2 并发多尺度方法
... [73];(c) FIB-SEM正极重构模型[74];(d)通过FIB-SEM和CT重构得到的纳米导电剂与微米颗粒对电池性能影响的计算方案[75](a) Geometric model with 1050 particles based on CT[71]; (b), (c) 3D geometric model of based on FIB-SEM[73-74]; (d) The simulation scheme of the particles based on the FIB-SEM and CT[75]Fig. 53.2 并发多尺度方法
... [74];(d)通过FIB-SEM和CT重构得到的纳米导电剂与微米颗粒对电池性能影响的计算方案[75](a) Geometric model with 1050 particles based on CT[71]; (b), (c) 3D geometric model of based on FIB-SEM[73-74]; (d) The simulation scheme of the particles based on the FIB-SEM and CT[75]Fig. 53.2 并发多尺度方法
... [75](a) Geometric model with 1050 particles based on CT[71]; (b), (c) 3D geometric model of based on FIB-SEM[73-74]; (d) The simulation scheme of the particles based on the FIB-SEM and CT[75]Fig. 53.2 并发多尺度方法