Conformal Decomposition Finite Element Method Research Articles

(Invited) Impact of Mesoscale Morphology on Electrode Performance through Multi-Physics Simulations

While lithium-ion battery electrodes are manufactured in large-scale, high-speed, roll-to-roll manufacturing processes, it is the morphology of the particle and conductive binder structures that greatly affect macroscale properties and can vary significantly as a function of manufacturing conditions. This relationship is particularly true in the extremely fast (dis)charge environments relevant for electrification of our vehicle fleet, where the short time scales probe ever smaller length scales and increase the impact of ionic and charge transport limitations. To explore the process-structure-property relationship, we employ mesoscale finite element simulations of the three-phase particle-conductive binder-electrolyte composite of NMC cathodes. Particle and conductive binder domain mesostructures are derived from both x-ray computed tomography imaging and simulated using discrete element methods. The Conformal Decomposition Finite Element Method is applied to create conformal three-phase finite element discretizations of these mesostructures. Effective properties including electrical conductivity, tortuosity, and mechanical modulus are calculated and compared to experimentally measured values. Coupled electrochemical-mechanical simulations of cathode discharge are performed and validated against half-cell experimental data. We focus on how the conductive binder domain morphology affects electrode performance. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

A higher-order conformal decomposition finite element method for plane B-rep geometries

A higher-order accurate conformal decomposition finite element method (CDFEM) is proposed, using an explicit boundary description of the domain. A level-set concept is introduced which converts the explicit B-rep geometry based on NURBSs to an implicit representation. This concept also applies to higher-order fictitious domain methods (FDMs) which are often based on implicit descriptions. In the proposed CDFEM, an arbitrary, non-conforming background mesh is introduced and manipulated to capture non-smooth features of the boundary such as corners and to ensure shape-regular elements. Elements that are cut by the boundary are decomposed into conforming sub-elements. The final mesh composed by higher-order Lagrange elements enables higher-order accurate approximations in the context of the FEM. Special emphasis is on the fact that NURBSs feature reduced continuity between knot spans which must be properly considered in the mesh generation, not only at corners.

A computational model for molten corium spreading and solidification

When the core is breached during a severe nuclear accident, a molten mixture of nuclear fuel, cladding, and structural supports is discharged from the reactor vessel. This molten mixture of ceramic and metal is often referred to as “corium”. Predicting the flow and solidification of corium poses challenges for numerical models due to the presence of large Peclet numbers when convective transport dominates the physics. Here, we utilize a control volume finite-element method (CVEM) discretization to stabilize the advection dominated flow and heat transport. This CVFEM approach is coupled with the conformal decomposition finite-element method (CDFEM), which tracks the corium/air interface on an existing background mesh. CDFEM is a sharp-interface method, allowing the direct discretization of the corium front. This CVFEM-CDFEM approach is used to model the spreading of molten corium in both two- and three-dimensions. The CVFEM approach is briefly motivated in a comparison with a streamwise upwind/Petrov-Galerkin (SUPG) stabilized finite-element method, which was not able to suppress spurious temperature oscillations in the simulations. Our model is compared directly with the FARO L26 corium spreading experiments and with previous numerical simulations, showing both quantitative and qualitative agreement with those studies.

A verified conformal decomposition finite element method for implicit, many-material geometries

As computing power rapidly increases, quickly creating a representative and accurate discretization of complex geometries arises as a major hurdle towards achieving a next generation simulation capability. Component definitions may be in the form of solid (CAD) models or derived from 3D computed tomography (CT) data, and creating a surface-conformal discretization may be required to resolve complex interfacial physics. The Conformal Decomposition Finite Element Methods (CDFEM) has been shown to be an efficient algorithm for creating conformal tetrahedral discretizations of these implicit geometries without manual mesh generation.In this work we describe an extension to CDFEM to accurately resolve the intersections of many materials within a simulation domain. This capability is demonstrated on both an analytical geometry and an image-based CT mesostructure representation consisting of hundreds of individual particles. Effective geometric and transport properties are the calculated quantities of interest. Solution verification is performed, showing CDFEM to be optimally convergent in nearly all cases. Representative volume element (RVE) size is also explored and per-sample variability quantified. Relatively large domains and small elements are required to reduce uncertainty, with recommended meshes of nearly 10 million elements still containing upwards of 30% uncertainty in certain effective properties. This work instills confidence in the applicability of CDFEM to provide insight into the behaviors of complex composite materials and provides recommendations on domain and mesh requirements.

The association of acute and chronic somatic disease, depressive symptoms and neurotransmitter precursor monamine levels

A higher-order accurate conformal decomposition finite element method (CDFEM) is proposed, using an explicit boundary description of the domain. A level-set concept is introduced which converts the explicit B-rep geometry based on NURBSs to an implicit representation. This concept also applies to higher-order fictitious domain methods (FDMs) which are often based on implicit descriptions. In the proposed CDFEM, an arbitrary, non-conforming background mesh is introduced and manipulated to capture non-smooth features of the boundary such as corners and to ensure shape-regular elements. Elements that are cut by the boundary are decomposed into conforming sub-elements. The final mesh composed by higher-order Lagrange elements enables higher-order accurate approximations in the context of the FEM. Special emphasis is on the fact that NURBSs feature reduced continuity between knot spans which must be properly considered in the mesh generation, not only at corners.

Advances and Application of Conformal Mesoscale Modeling to Battery Electrodes

Advances in x-ray computed tomography (XCT) with sub-micron resolution and millimeters of field-of-view have enabled imaging of battery electrodes in sufficient detail to elucidate the mesostructure of the percolated particle network. Most often the secondary conductive binder phase is not visible using XCT and its structure can only be observed using electron-based techniques (e.g. scanning electron microscopy), which typically have a field-of-view too small for meaningful reconstructions. This secondary phase, however, is thought to be critically important for understanding electrode performance at the mesoscale. We have developed a computational approach to creating computable three-dimensional (3D) mesoscale representations of the active material (particle), conductive binder, and electrolyte/void phases. This approach is built upon the Conformal Decomposition Finite Element Method (CDFEM) and combines 3D XCT image data for the active material phase and a novel “binder bridge” placement algorithm for the conductive binder. This approach enables the calculation of effective transport properties, such as electrical and ionic conductivity and mechanical moduli, that can be upscaled to macroscale battery simulations. Coupled electrochemical and mechanical simulations can also be performed to predict (dis)charge performance and degradation mechanisms of the electrode. In this work, we discuss the computational requirements, in terms of mesh resolution and domain size, to reasonably minimize computational errors. We also compare our “binder bridge” approach to other approaches in the literature, including a popular stochastic representation. The effect of nano-porosity within the conductive binder phase is explored. As part of this comparison, we explore the differences between smooth and voxelated particle representations along with differences between finite element and finite volume methods. Finally, we discuss upscaling of some of these effective properties into functional forms that can be implemented in macroscale battery simulation platforms. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Coupled Electrochemistry and Mechanics in Mesoscale Simulation of NMC Cathodes

Analysis of lithium-ion battery performance and degradation presents many multi-physics challenges as we look to understand the plethora of coupled mechanisms occurring within a single electrode. Electrochemical reactions in the active material introduce mechanical stresses as cathode particles swell upon lithium intercalation. Over numerous charge-discharge cycles, this behavior can lead to mechanical degradation, and thus, capacity fade. The presence of a secondary conductive binder phase additionally complicates these mechanisms, altering ionic and electronic conduction pathways, masking available surface area for reaction, and buffering mechanical contacts. As these mechanisms are largely governed by effects at the mesoscale (structures of 100s of active material particles joined by binder), we focus our computational efforts on resolved cathode mesostructures. In this talk, we will present a variety of different simulations which study half-cell performance at constant current discharge. The Conformal Decomposition Finite Element Method (CDFEM) algorithm is used to generate conformal mesoscale meshes of particle, conductive binder, and electrolyte phases, derived directly from 3D computed tomography data of NMC333 cathodes. This mesoscale approach for coupled electrochemical and mechanical simulations allows exploration of phenomena at the particle scale, while also providing insight on macroscale effective properties. Here, we will discuss the manifestation of local stresses from lithiation-induced swelling, as well as the impact of concentration gradients and local mesostructure on half-cell discharge curves and other macroscopic behavior. Additionally, we will investigate the influence of manufacturing processes on cell performance by studying a range of calendering pressures and binder loading fractions. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Formulation and computation of dynamic, interface-compatible Whitney complexes in three dimensions

A discrete De Rham complex enables compatible, structure-preserving discretizations for a broad range of partial differential equations problems. Such discretizations can correctly reproduce the physics of interface problems, provided the grid conforms to the interface. However, large deformations, complex geometries, and evolving interfaces makes generation of such grids difficult. We develop and demonstrate two formally equivalent approaches that, for a given background mesh, dynamically construct an interface-conforming discrete De Rham complex. Both approaches start by dividing cut elements into interface-conforming subelements but differ in how they build the finite element basis on these subelements. The first approach discards the existing non-conforming basis of the parent element and replaces it by a dynamic set of degrees of freedom of the same kind. The second approach defines the interface-conforming degrees of freedom on the subelements as superpositions of the basis functions of the parent element. These approaches generalize the Conformal Decomposition Finite Element Method (CDFEM) and the extended finite element method with algebraic constraints (XFEM-AC), respectively, across the De Rham complex.

Higher-order conformal decomposition FEM (CDFEM)

A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative for fictitious domain and extended finite element methods. The domain of interest is immersed in a background mesh composed by higher-order elements. The zero-level sets are identified and meshed followed by a decomposition of the cut background elements into conforming sub-elements. Adaptivity is a crucial ingredient of the method to guarantee the success of the mesh generation. It ensures the successful decomposition of cut elements and enables improved geometry descriptions and approximations. It is confirmed that higher-order accurate results with optimal convergence rates are achieved with the proposed conformal decomposition finite element method (CDFEM).

Mechanical and Electrochemical Response of a LiCoO2 Cathode using Reconstructed Microstructures

As LiCoO2 cathodes are charged, delithiation of the LiCoO2 active material leads to an increase in the lattice spacing, causing swelling of the particles. When these particles are packed into a bicontinuous, percolated network, as is the case in a battery electrode, this swelling leads to the generation of significant mechanical stress. In this study we performed coupled electrochemical-mechanical simulations of the charging of a LiCoO2 cathode in order to elucidate the mechanisms of stress generation and the effect of charge rate and microstructure on these stresses. Energy dispersive spectroscopy combined with scanning electron microscopy imaging was used to create 3D reconstructions of a LiCoO2 cathode, and the Conformal Decomposition Finite Element Method is used to automatically generate computational meshes on this reconstructed microstructure. Replacement of the ideal solution Fickian diffusion model, typically used in battery simulations, with a more general non-ideal solution model shows substantially smaller gradients of lithium within particles than is typically observed in the literature. Using this more general model, lithium gradients only appear at states of charge where the open-circuit voltage is relatively constant. While lithium gradients do affect the mechanical stress state in the particles, the maximum stresses are always found in the fully-charged state and are strongly affected by the local details of the microstructure and particle-to-particle contacts. These coupled electrochemical-mechanical simulations begin to yield insight into the partitioning of volume change between reducing pore space and macroscopically swelling the electrode. Finally, preliminary studies that include the presence of the polymeric binder suggest that it can greatly impact stress generation and that it is an important area for future research.

Mesoscale Modeling and Simulation of Composition, Manufacturing, and Microstructure Effects on Electrical Conduction in Thermal Battery Cathodes

Li/FeS2 thermal batteries provide a stable, robust, and reliable power source capable of long-term electrical energy storage without performance degradation. These systems rely on a eutectic salt that melts at elevated temperature, activating the cell. When the electrolyte melts, the cathode becomes a suspension, with cathode particles suspended in a liquid molten salt. This suspension experiences mechanical deformation, or “slumping.” This slump changes the mechanical compression of the cell, as well as the tortuosity and electronic and ionic conductivity of the cell as the mesostructure of the cathode is reordered in response to the external compressive stress. The combined effect of deformation, component composition, and manufacturing conditions on electrical conduction has not been studied, yet the cathode electrical properties are critically important to battery performance. We present simulation results from a computer model validated with experiments to elucidate the effects of conduction in FeS2 cathode pellets when composition and manufacturing parameters are varied. Experimental validation was achieved through impedance spectroscopy measurements of pressed-powder cathode pellets. Pellets were manufactured in-house with variations in pellet density, FeS2 particle size distribution, and ratio of FeS2 to electrolyte content. Impedance measurements of solid-state pellets were taken at 25, 100, and 200°C before and after slumping. We observed that electrical conductivity increased with relative FeS2 content and decreased with the FeS2 particle size distribution, but that the density of the pellets did not demonstrate a clear effect. Slumped pellets exhibited greater electrical conductivity at all temperatures and pellet thickness decreased by 1.8% on average due to slumping. Sandia’s novel conformal decomposition finite element method (CDFEM) was applied to surface-meshed geometric representations of cathode microstructures generated from microcomputed tomography (MicroCT) reconstructions. MicroCT was performed on all pellet types before and after slumping, with approximately 0.5 μm pixel size achieved for >0.1 mm3 volumes. A particle surface mesh was generated for each volume using FEI Avizo software and combined with the CDFEM background mesh. Results from the SIERRA/Aria finite element code will be presented, including the effects of anisotropy, mesh size, system volume, and manufacturing conditions on electrical conduction through cathode models, and compared with the experimental trends that were observed in the laboratory. The understanding of manufacturing effects on battery performance is not well developed, and this effort represents a step forward in correlated and predicting performance of cells based upon observed manufacturing trends. Figure 1

A conformal decomposition finite element method for arbitrary discontinuities on moving interfaces

SUMMARYInterface capturing methods using enriched finite element formulations are well suited for solving multimaterial transport problems that contain weak or strong discontinuities. The conformal decomposition FEM decomposes multimaterial elements of a non‐conforming background mesh into sub‐elements that conform to material interfaces captured using a level set method. As the interface evolves, interfacial nodes move, and background nodes may change material. The present work describes approaches for handling moving interfaces in the context of the conformal decomposition FEM for both weakly and strongly discontinuous fields. Dynamic discretization methods using extrapolation and moving mesh approaches are considered and developed with first‐order and second‐order time integration methods. The moving mesh approach is demonstrated to be a stable method that preserves both weak and strong discontinuities on a variety of one‐dimensional and two‐dimensional test problems, while achieving the expected second‐order error convergence rate in space and time. Copyright © 2014 John Wiley & Sons, Ltd.

Toward application of conformal decomposition finite elements to non‐colloidal particle suspensions

SUMMARYParticle suspensions play an important role in many engineering applications, yet their behavior in a number of respects remains poorly understood. In conjunction with careful experiments, modeling and simulation of these systems can provide key insight into their complex behavior. However, these two‐phase systems pose the challenge of simultaneously, accurately, and efficiently capturing the complex geometric structure, kinematics, and dynamics of the particulate discrete phase and the discontinuities it introduces into the variables (e.g., velocity, pressure, density) of the continuous phase. To this end, a new conformal decomposition finite element method (CDFEM) is introduced for solid particles in a viscous fluid. The method is verified in several simple test problems that are representative of aspects of particle suspension behavior. In all cases, we find the CDFEM to perform accurately and efficiently leading to the conclusion that it forms a prime candidate for application to the full direct numerical simulation of particle suspensions. Copyright © 2012 John Wiley & Sons, Ltd.

A conformal decomposition finite element method for modeling stationary fluid interface problems

AbstractA method is developed for modeling fluid transport in domains that do not conform to the finite element mesh. One or more level set functions are used to describe the fluid domain. A background, non‐conformal mesh is decomposed into elements that conform to the level set interfaces. Enrichment takes place by adding nodes that lie on the interfaces. Unlike other enriched finite element methods, the proposed technique requires no changes to the underlying element assembly, element interpolation, or element quadrature. The complexity is entirely contained within the element decomposition routines. It is argued that the accuracy of the method is no less than that for eXtended Finite Element Methods (XFEM) with Heaviside enrichment. The accuracy is demonstrated using multiple numerical tests. In all cases, optimal rates of convergence are obtained for both volume and surface quantities. Jacobi preconditioning is shown to remove the ill‐conditioning that may result from the nearly degenerate conformal elements. Copyright © 2009 John Wiley & Sons, Ltd.