Table 1
Summary of lithium battery simulation methods, including computational material science, electrochemical simulation, thermal simulation and mechanical simulation
| Methods/Models | Descriptions | Applications | Software | |
| Computational material science | Ab initio calculation | • Based on quantum mechanics, density functional theory (DFT) describes the electronic structure of materials by solving the Schrödinger equation in an approximate form. It replaces the complex many-electron wavefunction with an electron density functional, significantly reducing computational complexity. The method is parameter-free, meaning it does not rely on experimental data, and can provide fundamental insights into electronic structures, bonding interactions, energy levels, and material stability. | • Electronic structure analysis • Interface stability • Ion intercalation/Extraction |
• VASP • Quantum ESPRESSO • Materials Studio • PWmat |
| Molecular dynamics | • Uses Newton’s laws of motion to simulate the time evolution of a system of atoms or molecules. Each atom’s motion is determined by interatomic forces derived from a predefined force field, which describes the potential energy as a function of atomic positions. MD allows for the study of atomic-scale dynamic processes such as diffusion, solvation, thermal stability, and mechanical deformation. Simulations can be either classical (using empirical force fields) or ab initio MD (where forces are calculated from quantum mechanical principles like DFT). | • Ion diffusion in solid/Liquid electrolytes • SEI film formation and solvation effects • Electrode-electrolyte interface stability |
• LAMMPS • GROMAC • Materials Studio |
|
| Monte Carlo | • A stochastic (random sampling) method based on probability theory and statistical mechanics. MC is used to explore the energy landscape and thermodynamic properties of a system by generating many random configurations and accepting or rejecting them based on an energy criterion (e.g., Metropolis algorithm). Unlike MD, MC does not simulate time-dependent processes but excels at predicting phase transitions, equilibrium states, and material stability in large-scale systems. | • Electrode materials phase transitions and stability • Electrode particle structural evolution |
• Gibbs • LAMMPS |
|
| Calculation of phase diagrams | • A thermodynamic modeling approach that integrates experimental data and theoretical calculations to determine the phase stability and thermodynamic properties of multi-component systems. It relies on Gibbs free energy minimization and uses empirical databases to predict phase diagrams, material compositions, and reaction equilibria. CALPHAD is widely used for designing battery materials with optimized stability and performance. | • Phase diagrams of battery materials • Battery materials thermodynamic stability |
• Thermo-Calc • JMatPro |
|
| Phase field method | • A continuum modeling approach that describes the evolution of phase boundaries using partial differential equations (PDEs). PFM represents different phases within a system using a continuous order parameter, which changes smoothly across interfaces. The method incorporates thermodynamic and kinetic equations (such as Cahn-Hilliard or Allen-Cahn equations) to model microstructural evolution, phase transformations, stress distributions, and interfacial dynamics. PFM is particularly useful for studying electrode microstructure evolution, mechanical degradation, and SEI layer growth in lithium batteries. | • Particle cracking, stress distribution • Electrode microstructural changes |
• COMSOL Multiphysics • MOOSE • OpenPhase |
|
| Electrochemical simulations | Pseudo-two-dimensional (P2D) model | • The Pseudo-two-dimensional (P2D) model combines porous electrode theory and concentrated solution theory. It simplifies the three-dimensional lithium-ion battery system to two dimensions, mainly considering ion transport in the electrode thickness and particle radial directions. P2D describes lithium-ion movement in electrolyte pores and solid-phase diffusion within electrode particles, along with electrochemical reactions at the electrode-electrolyte interface. | • Electrode material screening • Charge-discharge behavior simulation • Low/High-temperature performance analysis • SEI growth dynamics • Lifetime degradation mechanism research • Aging model analysis |
• COMSOL Multiphysics • Simcenter STAR-CCM+ • Battery Design Studio (BDS) • PyBaMM • Electroder |
| 2D/3D porous lectrode model | • The porous electrode model is based on porous electrode theory, treating the electrode as a porous medium with solid active materials and pores. It uses equations like Nernst- Planck to describe ion transport in the liquid-phase electrolyte within pores, considering concentration gradients and electric fields. Fick’s laws are applied to model solid-phase diffusion of lithium ions inside electrode particles. | • Electrode microstructure optimization • Solid-phase diffusion limitation analysis • Electrode polarization analysis |
• COMSOL Multiphysics • Simcenter STAR-CCM+ • Simcenter Amesim • Electroder |
|
| Reduced-order electrochemical models | • Reduced-order electrochemical models (ROMs) are simplified versions of high-fidelity electrochemical models (e.g., P2D model) that retain key physical mechanisms while significantly reducing computational complexity. Classic ROMs include the single particle model (SPM), which assumes electrodes are represented by a single spherical particle and ignores electrolyte concentration gradients, making it suitable for real-time state estimation and control. The extended single particle model (ESPM) enhances SPM by incorporating electrolyte dynamics, improving accuracy. Polynomial approximation models further simplify calculations by fitting lithium-ion concentration profiles with polynomials. | • Real-time state estimation • Fault diagnosis • Charge-discharge control • State estimation algorithm development |
• COMSOL Multiphysics • MATLAB/Simulink • GT-AutoLion • Battery Design Studio (BDS) • VEBsim |
|
| Equivalent circuit models (ECMs) | • Equivalent circuit models (ECMs) represent a battery as an electrical circuit made up of basic elements like resistors, capacitors, and voltage sources. Rooted in circuit theory, they use Kirchhoff’s laws to describe the relationship between battery voltage, current, and state-of-charge. For instance, the Randles circuit, a common ECM, includes elements such as charge-transfer resistance and double-layer capacitance, which are used to fit electrochemical impedance spectroscopy data. ECMs simplify the complex electrochemical processes in a battery, enabling quick and practical analysis of battery behavior, especially in battery management systems for tasks like state-of-charge estimation. | • State of charge (SOC) estimation • State of health (SOH) monitoring • State of power (SOP) prediction • Fast charging control • Polarization analysis • Battery life prediction |
• MATLAB/Simulink • GT-AutoLion • Simcenter Amesim • PyBaMM |
|
| Mechanical simulations | Cell structural mechanics simulations | • Structural mechanics simulations, often using finite element methods, analyze the mechanical behavior of battery components. They apply principles like Hooke’s law for elastic materials and consider factors such as stress, strain, and loading conditions. | • Vibration simulation • Impact simulation • Extrusion simulation |
• Abaqus • ANSYS Mechanical • LS-DYNA • RADIOSS |
| Expansion force model | • Expansion force models in the context of lithium-ion batteries aim to describe and predict the forces generated due to volume changes during battery operation. These models consider factors such as lithium-ion insertion/extraction in electrode materials, which cause expansion and contraction. They typically use principles of material mechanics and electrochemistry, taking into account parameters like electrode porosity, particle size, and the mechanical properties of materials. By quantifying expansion forces, these models help in understanding the mechanical stress on battery components, crucial for designing batteries with enhanced structural integrity and lifespan. | • Mechanical safety evaluation • Capacity fade prediction • SOC and SOH estimation |
• COMSOL Multiphysics • ANSYS Mechanical • Abaqus • GT-Autolion |
|
| Pack extrusion model (multi-scale contact mechanics model) | • The lithium-ion battery extrusion simulation model is based on continuum mechanics. It uses the finite element method to discretize the model, takes into account the non-linear characteristics of materials, contact and friction phenomena, and through the multi-physics coupling theory (such as electrochemical-mechanical coupling), it simulates the mechanical response and performance evolution of lithium-ion batteries under extrusion. | • Battery pack structural integrity assessment • Internal short circuit and thermal runaway prediction • Safety standard compliance verification |
• Abaqus • ANSYS Mechanical • LS-DYNA |
|
| Pack vibration model (modal-fatigue coupling model) | • The battery pack vibration model provides critical insights into the dynamic behavior of battery systems, enabling robust design and compliance with industry standards. By combining advanced simulation tools with experimental validation, engineers can ensure the reliability and durability of battery packs under real-world vibration conditions. | • Battery pack modal analysis • Random vibration analysis • Fatigue life assessment • Electrical performance analysis under vibration environment |
• Abaqus • ANSYS Mechanical • LS-DYNA |
|
| Pack impact model (ball impact) (transient impact-damage model) | • The lithium battery ball impact model theory aims to simulate the dynamic response and damage behavior of battery packs under high-speed impacts, such as steel ball collisions. The model is based on explicit dynamics theory, incorporating elastoplastic constitutive equations (e.g., the Johnson-Cook model) to describe material deformation characteristics under high strain rates. It predicts shell fracture and internal short-circuit risks using failure criteria (e.g., equivalent plastic strain or stress thresholds). The model typically employs the finite element method (FEM) or smoothed particle hydrodynamics (SPH) to capture key phenomena during the transient impact process, including stress wave propagation, material failure, and electrolyte leakage, providing quantitative insights for battery pack protection design. | • Battery pack structural integrity assessment • Electrolyte leakage risk assessment • Safety standard compliance verification |
• Abaqus • ANSYS Mechanical • LS-DYNA |
|
| Thermal simulations | Bernardi heat generation model | • The Bernardi heat generation model calculates heat generation in batteries by considering three main sources. Ohmic heating results from the resistance to current flow. Reaction heating comes from electrochemical reactions at the electrodes. Entropy-change heating is due to the entropy change associated with the reactions. By combining these components, the model provides a comprehensive way to estimate the total heat generation rate in a battery under various operating conditions, crucial for predicting thermal behavior and preventing thermal runaway. | • Total heat generation calculation • Cell thermal runaway critical conditions |
• COMSOL Multiphysics • MATLAB/Simulink • ThermoLi |
| Cell thermal model | • Battery cell thermal simulation focuses on analyzing the thermal behavior of individual battery cells during operation, including charging, discharging, and resting states. The temperature distribution within a cell significantly impacts its performance, safety, and lifespan. Key factors influencing cell temperature include internal heat generation (due to electrochemical reactions, Joule heating, and polarization) and external heat dissipation (via conduction, convection, and radiation). | • Fast charging strategy optimization • Battery temperature distribution calculation • Current overload analysis of cell connectors |
• COMSOL Multiphysics • Simcenter STAR-CCM+ • GT-AutoLion • ThermoLi |
|
| CFD thermal model (pack) | • CFD thermal simulations employ computational fluid dynamics techniques to solve the Navier-Stokes equations governing fluid flow and the energy equation for heat transfer simultaneously. By discretizing the fluid domain into a mesh, these simulations calculate the flow field of the cooling medium (air or liquid) around the battery. They also determine the temperature distribution within the battery and its surroundings. | • Air/liquid cooling flow field optimization • Battery pack thermal balance analysis |
• Simcenter STAR-CCM+ • ANSYS Fluent • Simcenter BDS • Icepak • ThermoLi |
|
| Thermal runaway model | • The lithium battery thermal runaway model theory aims to simulate the coupled thermal-electrochemical behavior of batteries under overheating conditions, providing critical insights into the initiation and propagation of thermal runaway. Thermal runaway temperature simulation captures the heat transfer within the cell and module using heat conduction equations, while gas generation models predict the release of flammable gases (e.g., electrolyte vapor) and their impact on internal pressure. | • Heat propagation analysis • Thermal runaway temperature rise calculation • Gas generation and pressure management |
• COMSOL Multiphysics • STAR-CCM+ • Simcenter BDS • Icepak • ThermoLi |
|
| Multi-physics coupling model | • The lithium battery multi-physics model theory aims to comprehensively describe the coupled electrochemical, thermal, and mechanical behaviors of batteries under complex operating conditions. The electro-mechanical coupling model analyzes the volume changes in electrodes caused by lithium-ion intercalation/deintercalation (e.g., silicon anode expansion up to 300%) and the resulting stress distribution, revealing the correlation between electrode crack propagation and capacity degradation. The thermo-mechanical coupling model incorporates thermal expansion coefficients and thermal stress equations to quantify material deformation and interface delamination risks induced by temperature gradients (e.g., tensile stress in NCM cathodes at high temperatures). The electrochemical-mechanical-thermal coupling model further itegrates the Butler-Volmer equation, heat generation models (e.g., Bernardi equation), and stress-diffusion equations to simulate the interactions among electrochemical reactions, heat generation, and mechanical stresses during charge/discharge processes, providing theoretical support for battery performance optimization and safety design. | • Operating condition adaptability assessment • Research on aging mechanism • Mechanical abuse simulation • Thermal runaway analysis |
• LS-DYNA • COMSOL Multiphysics • GT-AutoLion • Simcenter BDS • LIONSIMBA |
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