Over the last few decades, rechargeable lithium-ion batteries have been extensively used in portable instruments due to their high energy density and low self-discharge rate. Recently, lithium-ion batteries have emerged as the most promising candidate for electric vehicles and stationary energy storage. However, the maximum energy that lithium-ion batteries store decreases as they are used because of various irreversible degradation mechanisms. The mechanical properties of the electrode layers inside the battery highly influence the battery's performance. There is, however, a fundamental lack of understanding of the mechanical properties of electrodes and how they evolve during electrochemical cycling, which makes it a necessity to characterize their mechanical behavior for mesoscopic and macroscopic level modeling. Lithium-ion batteries are complex systems to understand, and various processes and their interactions make battery modeling challenging. This thesis contributes to understanding the mechanical behavior of electrodes in lithium-ion batteries and provides methods for the design and efficient modeling of battery systems.

        In Paper A and Paper B, the macroscopic mechanical behavior of active layers in the electrodes is investigated using U-shape bending tests. The active layers are porous and a different tensile and compressive behavior is captured by performing tests on single side coated dry electrodes. The experiments reveal that the active layer is stiffer in compression as compared to tension. The compressive stiffness increases with bending strain whereas the tensile stiffness is almost independent of the bending strain. A very low value of modulus of the active layer (1-5 GPa) is measured in comparison to the metal foils (70-110 GPa) and the active particles (50-200 GPa) which shows that the electrode properties are governed majorly by the binders present in the active layers. The time-dependent and hysteresis effects are also captured by the method which circumvents the flaws of many other test methods presented in the literature.  

        Paper C focuses on characterizing the layer-level evolution of mechanical and electrochemical properties of a Ni-rich positive electrode during early-stage electrochemical cycling, along with complementary cross-section analyses to understand the relationship between macroscopic and microscopic changes. Macroscopic constitutive properties were measured using the U-shaped bending test method developed in papers A and B, which revealed that the compressive modulus was primarily influenced by the porous structure and binder properties. It decreased notably with electrolyte wetting but increased with cycling and aging. Electrochemical impedance spectra showed an increase in local resistance near the particle-electrolyte interface with early-stage aging, which was likely due to secondary particle grain separation and carbon black redistribution. Cross-section analyses reveal significant variations in particle properties between pristine and cycled samples, including particle swelling, compression of the binder phase, and increased particle contact, contributing to the rise in the elastic modulus of the porous layer during cycling.

        In Paper D and Paper E, we present a multiscale homogenization method that couples mechanics and electrochemistry at the particle, electrode, and battery scales. The active materials of lithium-ion battery electrodes exhibit volume change during lithium intercalation or deintercalation. A lithium concentration gradient develops inside particles, as well as inside the active layer. The developed stress due to deformations further affects solid diffusion.  We utilized models that have already been developed to couple particle and electrode layer levels. Electric vehicle battery packs consist of numerous battery modules, each of which includes multiple battery cells composed of electrode, separator, and current collector layers. A finite element model capable of capturing stresses at the layer level would need to be very large to account for all the details. The mechanical coupling between the electrode and the battery level is achieved by homogenization of the layered battery using three-dimensional laminate theory, which greatly reduces the number of finite elements required for stress simulations in batteries. After obtaining a homogenized solution, layer-level stresses can be determined in a post-processing step. The method accurately predicts stresses on various scales and captures the effects of external battery loadings, cycling rates, and mechanical parameters. The efficiency of the method is demonstrated by comparing it to detailed finite element computations. The simulations indicate that layer-wise stresses, such as pressure, can be predicted as functions of position and time, providing insights into the inhomogeneous aging state of the battery.

Under de senaste decennierna har uppladdningsbara litiumjonbatterier använts flitigt i bärbara instrument på grund av deras höga energitäthet och låga självurladdningshastighet. Just nu ses en kraftig ökning av eldrivna fordon. Den maximala energin som litiumjonbatterier kan lagra minskar dock med tiden på grund av olika irreversibla nedbrytningsmekanismer. De mekaniska egenskaperna hos elektrodskikten inuti batteriet påverkar här i hög grad batteriets prestanda. Det finns dock en bristande kunskap om elektrodernas mekaniska egenskaper och hur de utvecklas under elektrokemisk cykling. Behovet av nya experimentella och teoretiska metoder för karaktärisering på mikro- och makroskalor är stort. Litiumjonbatterier är komplexa system att förstå, och olika processer och deras interaktioner gör batterimodellering utmanande. Denna avhandling bidrar till en ökad förståelse av elektrodernas mekaniska beteende i litiumjonbatterier. Även metoder för design och effektiv modellering av batterisystem presenteras.

        I de bilagda rapporterna A och B undersöks det makroskopiska mekaniska beteendet hos aktiva skikt i elektroder med hjälp av böjprovning med U-formade provstavar. De aktiva skikten är porösa och skillnader i drag- och tryckbeteende fångas upp genom att utföra tester på ensidigt belagda torra elektroder. Experimenten visar att det aktiva lagret är styvare i kompression jämfört med dragning. Kompressionstyvheten ökar med töjningsnivån medan dragstyvheten är nästan oberoende av töjning. De uppmätta E-modulerna för det aktiva skiktet (1-5 GPa ) är låga i jämförelse med metallfolierna (70-110 GPa ) och de aktiva partiklarna (50-200 GPa ) vilket visar att elektrodegenskaperna huvudsakligen styrs av bindemedlen som finns i de aktiva skikten. Tidsberoende effekter och hystereser fångas också upp av den använda mätmetoden som även kringgår de begränsningar som alternativa testmetoder uppvisar. 

        I rapport C karakteriseras utvecklingen av mekaniska och elektrokemiska egenskaper som funktion av antalet laddningscykler i en positiv elektrod. För att bättre förstå orsaken till förändringar av egenskaper genomfördes parallella mikroskopiundersökningar. Makroskopiska konstitutiva egenskaper uppmättes med den böjprovningsmetod som utvecklades i rapporterna A och B. Resultaten visar att kompressionsmodulen främst påverkas av den porösa strukturen och bindemedlets egenskaper. Styvheten minskade märkbart efter vätning med elektrodvätska och därpå följande torkning. Med ökande antal laddningscykler ökade styvheten åter i jämförelse med denna referensnivå. Elektrokemiska impedansspektra visade på en ökning av lokal resistans nära partikel-elektrolytgränsytorna vid tidig åldring, vilket sannolikt berodde på sekundär kornseparation i elektrodpartiklarna samt omfördelning av kolpartiklar i bindemedlet. Mikroskopianalyser visade på betydande variationer i partikelegenskaper mellan virgina och cykliska prover. Förändringar i partikelstorlek och form kunde konstateras vilka kunde korreleras till utvecklingen av kompressionsstyvhet i den porösa elektroden. 

        I rapporterna D och E presenteras en flerskalig homogeniseringsmetod som kopplar mekanik och elektrokemi på partikel-, elektrod- och batteriskala. De aktiva materialen i litiumjonbatteriets elektroder uppvisar volymförändringar vid laddning och urladdning. En gradient i koncentrationen av litium utvecklas såväl inuti partiklar som inom elektrodskiktet under laddning eller urladdning. Dessa gradienter leder till mekaniska spänningar som i sin tur påverkar diffusionen av litium. För modellering av diffusion och därtill hörande litiumkoncentrationer applicerades är väl etablerad modell från litteraturen. Batteripaket för elfordon består av ett stort antal batterimoduler, som var och en innehåller flera battericeller vilka i sin tur består av många elektrod-, separator- och metallskikt. En finit elementmodell som kan fånga spänningar på skiktnivåer skulle behöva vara mycket stor för att ta hänsyn till alla variationer på små skalor. I rapporterna D och E utvecklas i stället en modell för homogenisering av det skiktade batteriet med hjälp av tredimensionell laminatteori. På detta sätt kan antalet frihetsgrader och därigenom beräkningskostnad för en finit elementmodell kraftigt reduceras. Baserat på en homogeniserad lösning kan spänningar på skiktnivå bestämmas i efterhand. Metoden förutsäger spänningar på olika skalor och fångar effekterna av laddningshastighet, extern mekanisk belastning och de ingående skiktens mekaniska egenskaper. Metodens effektivitet demonstreras genom att jämföra den med detaljerade finita elementberäkningar. Simuleringarna indikerar att skiktspänningar, såsom tryck, kan förutsägas som funktioner av position och tid, vilket ger insikter om åldrande i olika deler av ett batteri.

The effects of electrochemical aging on the mechanical properties of electrodes in lithium-ion batteries are challenging to measure and are largely unknown. Mechanochemical degradation processes occur at different scales within an electrode and understanding the correlation between the degradation of mechanical properties, electrochemical aging, and morphological changes is crucial for mitigating battery performance degradation. This paper explores the evolution of mechanical and electrochemical properties at the layer level in a Ni-rich positive electrode during the initial stages of electrochemical cycling. The investigation involves complementary cross-section analyses aimed at unraveling the connection between observed changes on both macroscopic and microscopic scales. The macroscopic constitutive properties were assessed using a U-shaped bending test method that had been previously developed. The compressive modulus exhibited substantial dependency on both the porous structure and binder properties. It experienced a notable reduction with electrolyte wetting but demonstrated an increase with cycling and aging. During the initial stages of aging, electrochemical impedance spectra revealed increased local resistance near the particle–electrolyte interface. This is likely attributable to factors such as secondary particle grain separation and the redistribution of carbon black. The swelling of particles, compression of the binder phase, and enhanced particle contact were identified as probable factors adding to the elevation of the elastic modulus within the porous layer as a result of cycling.

In this study, we developed a robust methodology for extracting the mechanical properties of individual components in complex systems such as Li-ion battery electrodes and provided quantitative values that can be used as input for modelling and lifetime estimation of Li-ion batteries. We employed micromechanical testing techniques, including micropillar compression, microcantilever bending, and nanoindentation, to measure the mechanical properties of the PVdF binder phase in the active layer. We discovered that nanoindentation tends to overestimate the modulus due to uncertainty associated with the test volume and initial large compression strains, while the micropillar compression technique provides more accurate modulus data with a narrower spread. Additionally, the yield stress of the binder phase can be evaluated using micropillar compression. Our obtained modulus values were in the range of 2.5–4.4 GPa, and the yield stress was in the range of 162–270 MPa. By microcantilever bending tests, we determined that the binder–particle interface often fails before the binder itself, suggesting that the interface significantly influences the failure mechanics. Overall, our results indicate that the microcantilever bending tests provide moduli estimates that agree with those obtained from micropillar compression tests. We also qualitatively examined the binder-particle and binder-current collector interfaces, further emphasising the significance of our methodology and the obtained quantitative values.

Battery packs in electric vehicles consist of several battery modules, each containing several battery cells with numerous layers (electrodes, separators and current collector layers. A finite element model that can capture the stresses on the layer level would be extremely large in order to resolve the details. In the present paper, a novel homogenization method is presented which is based on three-dimensional laminate theory. The number of finite elements for the simulation of stresses in batteries can in this way be drastically reduced. Based on a homogenized solution, layer-level stresses can then be determined in a post-processing step. The present formulation is adaptive and fast, eliminating the need to model individual layers. It allows for non-linear elastic behavior of active layers that undergo swelling and separator layers as well as elastic-plastic behavior of current collectors. Three realistic battery structures subjected to swelling in electrode layers have been simulated: 1. free jellyroll, 2. jellyroll enclosed by a stiff enclosure, and 3. battery module consisting of 10 cells. The presented homogenized method allows for the inclusion of battery cells as parts of larger models representing vehicle structures and facilitates studying the interaction between batteries and surrounding structures.

The stress-strain relationship of a dry lithium-ion graphite anode coating has been characterized by a bending test method. The method is based on U-shaped bending of single-side coated electrodes, which enables separate measurements of tensile and compressive properties of the electrode coating. The experiments reveal that the elastic modulus of the anode coating in compression is higher than the elastic modulus in tension and that the compressive stiffness increases with strain level. Contrary, the tensile modulus is approximately independent of strain. The quantitative results for compressive modulus, and in particular the stiffening effect with increasing strain, are believed to be new to the battery research community. The measured stiffness of the anode coating is compared to previously reported results for a cathode coating. It is found that the anode coating is stiffer in compression compared to the cathode coating despite a much larger particle stiffness of the cathode material in comparison to the anode. It is concluded that differences in porosity are the main reason for the observed behavior. The method also successfully captures the hysteresis effects, both in tension and compression, that are present due to the polymeric binder and the evolution of microstructural contacts. Relaxation experiments are as well conducted to characterize the time-dependent properties of the anode coating, and the response is modeled by a Prony series.

Models that consistently couple particle, electrode, and battery level mechanics and electrochemistry are rare inliterature. Within a battery, there are hundreds of layers of electrodes and the inherent multiscale structure ofelectrodes makes battery level simulations computationally very expensive. This paper presents a multiscalehomogenization method that couples mechanics and electrochemistry at the particle, electrode, and batteryscales. The method is divided into two parts. Firstly, an electrochemical/mechanical model for a one-dimensionalperiodic element is applied to determine particle and electrode layer swelling as functions of time and position.Secondly, the layered structure of the battery is homogenized by the use of three-dimensional laminate theory.The homogenized material model can be applied in finite element calculations on the battery level. Layer levelstresses can in a second step be back-calculated. The accuracy and efficiency of the method are demonstrated bycomparisons to detailed finite element computations where each layer is individually modeled. Predictions ofelectrode layer stresses are also favorably compared to impedance measurements of electrode layers at differentelectrode positions. It is furthermore demonstrated that the effects of external battery loadings like batterystacks, casings, and external pressure easily can be captured by the model.

The stress-strain relationship of a dry lithium-ion graphite anode coating has been characterized by a bending test method. The method is based on U-shaped bending of single-side coated electrodes, which enables separate measurements of tensile and compressive properties of the electrode coating. The experiments reveal that the elastic modulus of the anode coating in compression is higher than the elastic modulus in tension and that the compressive stiffness increases with strain level. Contrary, the tensile modulus is approximately independent of strain. The quantitative results for compressive modulus, and in particular the stiffening effect with increasing strain, are believed to be new to the battery research community. The measured stiffness of the anode coating is compared to previously reported results for a cathode coating. It is found that the anode coating is stiffer in compression compared to the cathode coating despite a much larger particle stiffness of the cathode material in comparison to the anode. It is concluded that differences in porosity are the main reason for the observed behavior. The method also successfully captures the hysteresis effects, both in tension and compression, that are present due to the polymeric binder and the evolution of microstructural contacts. Relaxation experiments are as well conducted to characterize the time-dependent properties of the anode r coating, and the response is modeled by a Prony series. 

Over the last few decades, rechargeable lithium-ion batteries have been extensively used in portable instruments due to their high energy density and low self-discharge rate. Recently, lithium-ion batteries have emerged as the most promising candidate for electric vehicles and stationary energy storage. However, the maximum energy that lithium-ion batteries can store decreases as they are used because of various irreversible degradation mechanisms. Lithium-ion batteries are complex systems to understand, and various processes and their interactions are responsible for the degradation over time. The mechanical integrity and stability of the electrode layers inside the battery highly influence the battery performance, which makes it a necessity to characterize the mechanical behavior of electrode active layers for mesoscopic and macroscopic level modeling.

In papers 1 and 2, the macroscopic mechanical behavior of active layers in the electrodes is investigated using U-shape bending tests. The active layers are porous and a different tensile and compressive behavior is captured by performing tests on single side coated dry specimens. The experiments reveal that the active layer is stiffer in compression as compared to tension. The compressive stiffness increases with bending strain whereas the tensile stiffness is almost independent of the bending strain. A very low value of modulus of the active layer (1-5 GPa) is measured in comparison to the metal foils (70-110 GPa) and the active particles (50-200 GPa) which shows that the electrode properties are governed majorly by the binders present in the active layers.  The time-dependent and hysteresis effects are also captured by the method which circumvents the flaws of many other test methods presented in the literature.  

In paper 3, we present a multiscale homogenization method that couples mechanics and electrochemistry at the particle, electrode, and battery scales. The active materials of lithium-ion battery electrodes exhibit volume change during lithium intercalation or deintercalation. A lithium concentration gradient develops inside particles, as well as inside the active layer. The developed stress due to deformations further affects solid diffusion.  We utilized models that have already been developed to couple particle and electrode layer levels. The mechanical coupling between the electrode and the battery level is achieved by homogenization of the layered battery using three-dimensional laminate theory.  By application of the model, we demonstrate that the stresses on all considered scales can be predicted from the homogenized model. It is furthermore demonstrated that the effects of external battery loadings like battery stacks, casings, and external pressure can be captured by the model. The model can also capture the effect of various electrochemical cycling rates and mechanical parameters like layer thicknesses, stiffnesses, and swelling properties. The presented multi-scale model is fast, accurate and the efficiency of the method is demonstrated by comparisons to detailed finite element computations where each layer is individually modeled. 

Presently used experimental techniques for the characterization of tensile and compressive behavior of active layers in lithiumionbatteries have limitations of different kinds. This is particularly true for measurements of compressive properties.Furthermore, the characterizations of time-dependent stress-strain behavior are largely missing. In order to characterize thestress-strain relationship for a dry cathode active layer in lithium-ion batteries, a mechanical testing method is presented thatpreviously has been applied to the testing of optical fibers. The method is based on U-shaped bending of single-side coatedaluminum foils, which enables separate measurements of tensile and compressive properties. In particular, the method has clearadvantages for measurements of compressive properties in comparison to previously reported techniques. Relaxation experimentsare also conducted in order to characterize the time-dependent properties of the dry active layer and to check if these effectscould explain the measured hysteresis. It is found that the elastic modulus in compression is significantly larger than the elasticmodulus in tension and that the compressive modulus increases with strain level. Contrary, the tensile modulus is approximatelyindependent of strain. Furthermore, hysteresis effects are present at loading-unloading measurements, both for tension andcompression. The low values of the measured elastic moduli show that the electrode properties are largely controlled by thebinder and carbon additives. It is concluded that the development of particle-particle contacts most likely is the reason for thehigher modulus in compression in comparison to tension. The time-dependent effects are significant, primarily for shorter timescales, which explains the relaxation behavior, but they cannot fully explain the hysteresis effects. Most likely non-linear micromechanismsdo contribute as well.