Governing equations for a two-scale analysis of Li-ion battery cells

Salvadori, Alberto; Grazioli, Davide; Geers, Mgd Marc

doi:10.1016/j.ijsolstr.2015.01.014

Cited by 46 publications

(60 citation statements)

References 73 publications

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“…The set of continuity equations for mass and Maxwell's equations lead to a consistent model, with distinctive energy characteristics. Numerical examples show the robustness of the approach, which is well suited for multi-scale analyses [2,3].…”

Section: Introductionmentioning

confidence: 97%

“…[3] and in the present paper, Equation (2) is not used as a fundamental law. Instead, the electro-magnetics is explicitly taken into account via the electro-quasi-static formulation [25] of Maxwell's equations, which is summarized in Section 2.…”

Section: Introductionmentioning

confidence: 97%

“…The influence of the underlying microstructure on to macroscopic material properties is the goal of homogenization theory and recent publications have been devoted to computational homogenization for Li-ion batteries [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…In multi scale approaches [3], the electroneutrality assumption (2) cannot be used as in Newman's theory, since it does not allow to perform correct scales transitions. This is of major importance for researchers who want to understand and optimize the battery behavior with multi-scale models.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A multiscale-compatible approach in modeling ionic transport in the electrolyte of (Lithium ion) batteries

Salvadori

Grazioli

Geers

et al. 2015

Journal of Power Sources

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A multiscale-compatible approach in modeling ionic transport in the electrolyte of (Lithium ion) batteries

Salvadori

Grazioli

Geers

et al. 2015

Journal of Power Sources

Self Cite

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“…Which of these mechanisms is limiting depends on the applied current and the morphology of the electrodes [3]. To understand the complex interplay of the processes in batteries and to enable improved battery design, various models have been developed [4][5][6][7][8][9][10]. Using these models it is possible to design better battery management systems [4], decrease charging times [5], estimate the effect of side reactions on performance [6], and study what limits the performance of a battery [7].…”

Section: Introductionmentioning

confidence: 99%

Explaining key properties of lithiation in TiO2 -anatase Li-ion battery electrodes using phase-field modeling

Klerk

Vasileiadis

Smith

et al. 2017

Phys. Rev. Materials

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The improvement of Li-ion battery performance requires development of models that capture the essential physics and chemistry in Li-ion battery electrode materials. Phase-field modeling has recently been shown to have this ability, providing new opportunities to gain understanding of these complex systems. In this paper, a novel electrochemical phase-field model is presented that captures the thermodynamic and kinetic properties of lithium insertion in TiO 2 -anatase, a well-known and intensively studied Li-ion battery electrode material. Using a linear combination of two regular solution models, the two phase transitions during lithiation are described as lithiation of two separate lattices with different physical properties. Previous elaborate experimental work on lithiated anatase TiO 2 provides all parameters necessary for the phase-field simulations, giving the opportunity to gain fundamental insight in the lithiation of anatase and validate this phase-field model. The phase-field model captures the essential experimentally observed phenomena, rationalizing the impact of C rate, particle size, surface area, and the memory effect on the performance of anatase as a Li-ion battery electrode. Thereby a comprehensive physical picture of the lithiation of anatase TiO 2 is provided. The results of the simulations demonstrate that the performance of anatase is limited by the formation of the poor Li-ion diffusion in the Li 1 TiO 2 phase at the surface of the particles. Unlike other electrode materials, the kinetic limitations of individual anatase particles limit the performance of full electrodes. Hence, rather than improving the ionic and electronic network in electrodes, improving the performance of anatase TiO 2 electrodes requires preventing the formation of a blocking Li 1 TiO 2 phase at the surface of particles. Additionally, the qualitative agreement of the phase-field model, containing only parameters from literature, with a broad spectrum of experiments demonstrates the capabilities of phase-field models for understanding Li-ion electrode materials, and its promise for guiding the design of electrodes through a thorough understanding of material properties and their interactions.

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Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions

Kaessmair

Runesson

Steinmann

et al. 2021

Numerical Meth Engineering

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A variationally consistent model-based computational homogenization approach for transient chemomechanically coupled problems is developed based on the classical assumption of first-order prolongation of the displacement, chemical potential, and (ion) concentration fields within a representative volume element (RVE). The presence of the chemical potential and the concentration as primary global fields represents a mixed formulation, which has definite advantages. Nonstandard diffusion, governed by a Cahn-Hilliard type of gradient model, is considered under the restriction of miscibility. Weakly periodic boundary conditions on the pertinent fields provide the general variational setting for the uniquely solvable RVE-problem(s). These boundary conditions are introduced with a novel approach in order to control the stability of the boundary discretization, thereby circumventing the need to satisfy the LBB-condition: the penalty stabilized Lagrange multiplier formulation, which enforces stability at the cost of an additional Lagrange multiplier for each weakly periodic field (three fields for the current problem). In particular, a neat result is that the classical Neumann boundary condition is obtained when the penalty becomes very large. In the numerical examples, we investigate the following characteristics: the mesh convergence for different boundary approximations, the sensitivity for the choice of penalty parameter, and the influence of RVE-size on the macroscopic response.

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Governing equations for a two-scale analysis of Li-ion battery cells

Cited by 46 publications

References 73 publications

A multiscale-compatible approach in modeling ionic transport in the electrolyte of (Lithium ion) batteries

A multiscale-compatible approach in modeling ionic transport in the electrolyte of (Lithium ion) batteries

Explaining key properties of lithiation in TiO2 -anatase Li-ion battery electrodes using phase-field modeling

Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions

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