A computational homogenization approach for Li-ion battery cells: Part 1 – formulation

Salvadori, Alberto; Bosco, E.; Grazioli, Davide

doi:10.1016/j.jmps.2013.08.010

Cited by 72 publications

(57 citation statements)

References 54 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%

“…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%

“…The most common selection for such an additional relation in battery modeling is the electroneutrality condition c Li þ À c X À ¼ 0 (2) In several studies, originated by Newman [1] and collectively gathered in the terminology "porous electrode theory", condition (2) is used in lieu of Maxwell's law e see among others [12e18].…”

Section: Introductionmentioning

confidence: 99%

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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: 99%

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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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“…• porous media, for example, Su et al (2011) andZhuang et al (2015) • cellular materials, for example, Nguyen and Noels (2014) and Iltchev et al (2015) • soft matter, for example, Temizer (2014b) • polycrystalline metals, for example, Segurado and Llorca (2013) • technical textiles, for example, Fillep et al (2015) • granular materials, for example, Liu et al (2014) • trabecular bone, for example, Wierszycki et al (2014) • composite plates, for example, Helfen and Diebels (2014) • Li-ion battery cells, for example, Salvadori et al (2014) While CH is an extremely powerful multiscale technique, it comes along with a high computational cost. Nevertheless, CH is naturally parallelizable (Mosby and Matouš, 2015a) and the method has demonstrated excellent scalability as shown later in this chapter.…”

Section: Nonlinear Computational Homogenizationmentioning

confidence: 99%

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

Geers

Kouznetsova

Matouš

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This article focuses on computational multiscale methods for the mechanical response of nonlinear heterogeneous materials. After a short historical note, a brief overview is given of some recent activities in the field, with a particular focus on nonlinear homogenization methods. The two‐scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics. Model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis. High‐performance parallel multiscale implementations of the CH scheme are addressed in more detail.

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“…An increasing number of studies have focused on the formal derivation of continuum-scale models from micro-scale balance equations. [31][32][33][34][35] These studies reflect the need to validate reduced-order models and to elucidate the macroscopic response of microscale processes. Yet, to the best of our knowledge, no current work has rigorously established the conditions under which pore-scale equations describing electromigration, diffusion and reaction of lithium ions correctly upscale to the classical macroscopic porous-electrode equations.…”

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confidence: 99%

On Veracity of Macroscopic Lithium-Ion Battery Models

Arunachalam¹,

Onori²,

Battiato³

2015

J. Electrochem. Soc.

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Batteries are electrochemical energy storage devices that exhibit physico-chemical heterogeneity on a continuity of scales. As such, battery systems are amenable to mathematical descriptions on a multiplicity of scales that range from atomic to continuum. In this paper we present a new method to assess the veracity of macroscopic models of lithium-ion batteries. Macroscopic models treat the electrode as a continuum and are often employed to describe the mass and charge transfer of lithium since they are computational tractable and practical to model the system at the cell scale. Yet, they rely on a number of simplifications and assumptions that may be violated under given operating conditions. We use multiple-scale expansions to upscale the pore-scale Poisson-Nerst-Planck (PNP) equations and establish sufficient conditions under which macroscopic dual-continua mass and charge transport equations accurately represent pore-scale dynamics. We propose a new method to quantify the relative importance of three key pore-scale transport mechanisms (electromigration, diffusion and heterogenous reaction) by means of the electric Péclet (Pe) and Damköhler (Da) numbers in the electrolyte and the electrode phases. For the first time, applicability conditions of macroscopic models through a phase diagram in the (Da-Pe)-space are defined. Finally, we discuss how the new proposed tool can be used to assess the validity of macroscopic models across different battery chemistry and conditions of operation. In particular, a case study analysis is presented using commercial lithium-ion batteries that investigates the validity of Newman-type macroscopic models under temperature and current rate of charge/discharge variation. Predictive understanding of battery dynamical behavior still remains a major bottleneck in achieving diagnostic capabilities, safety, optimization and control of battery systems under different operating conditions. Such a difficulty arises from two main factors: i) nonlinearity of lithium-ion transport processes 1 and ii) battery systems multiscale structure that exhibits physicochemical heterogeneity on a continuity of scales (from the nanometer to the meter).2-5 Since the seminal work by Newman and Tiedemann, 6 where macroscopic ion transport equations were first formulated, a plethora of models have spurred in the past decades. They range from fully empirical approaches to generalizations of electrochemical models based on the porous electrode theory to account for concentrated solutions, 7,8 thermal effects 9 and capacity fade due to Solid-Electrolyte Interphase (SEI)-growth, [10][11][12] just to mention a few. In the past decade, ever increasing computational capabilities have fuelled the development of fully molecular/atomistic models and multiscale/multiphysics approaches. 13 For a thorough review on the topic, we refer the reader to Ref. 4. Microscale models 14,15 (e.g. molecular dynamics, kinetic Monte Carlo and pore-scale models) are theoretically robust, but are impractical as a predictive tool at t...

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A computational homogenization approach for Li-ion battery cells: Part 1 – formulation

Cited by 72 publications

References 54 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

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

On Veracity of Macroscopic Lithium-Ion Battery Models

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