Discrete Element Method Model Research Articles

Deformation and Frictional Failure of Granular Media in 3D Analog and Numerical Experiments

AbstractFrictional sliding along grain boundaries in brittle shear zones can result in the fragmentation of individual grains, which ultimately can impact slip dynamics. During deformation at small scales, stick–slip motion can occur between grains when existing force chains break due to grain rearrangement or failure, resulting in frictional sliding of granular material. The rearrangement of the grains leads to dilation of the granular package, reducing the shear stress and subsequently leading to slip. Here, we conduct physical experiments employing HydroOrbs, an elasto-plastic material, to investigate grain comminution in granular media under simple shear conditions. Our findings demonstrate that the degree of grain comminution is dependent on both the normal force and the size of the grains. Using the experimental setup, we benchmark Discrete Element Method (DEM) numerical models, which are capable of simulating the movement, rotation, and fracturing of elasto-plastic grains subjected to simple shear. The DEM models successfully replicate both grain comminution patterns and horizontal force fluctuations observed in our physical experiments. They show that increasing normal forces correlate with higher horizontal forces and more fractured grains. The ability of our DEM models to accurately reproduce experimental results opens up new avenues for investigating various parameter spaces that may not be accessible through traditional laboratory experiments, for example, in assessing how internal friction or cohesion affect deformation in granular systems.

Prediction of burden distribution and electrical resistance in submerged arc furnaces using discrete element method modelling

A computational model of a submerged arc furnace (SAF) used in the production of ferrochrome is presented. The model's intended use is to investigate the extent to which intrinsic and extrinsic properties of the raw materials affect burden distribution and electrical resistance within the furnace. The model is built on the discrete element method and calculates the mechanical interactions of particle distributions resulting from the flow motion of typical raw materials used in the smelting of chromium ore. This model excludes the effects of thermodynamics, furnace chemistry, and heat transfer. It illustrates how the consumption of materials (chromite pellets, flux, and reductant) is affected by changes in electrode length, reductant fractions, and reductant sizing and density during the formation of a reductant bed. The resistance calculation algorithm developed by Mintek was applied to construct networks developed from particle contacts, which can quantitatively generate estimates of the electrode-to-electrode and electrode-to-bath electrical conduction conditions.

A Discrete Element Model of High-Pressure Torsion Test to Assess the Effect of Particle Characteristics in the Interface

Abstract Sand particles have been used since the early stages of the railway industry to increase adhesion at the wheel–rail contact. However, there is a limited understanding of how sand particle characteristics affect the tribological performance of the wheel–rail contact. In this work, the high-pressure torsion test used as a small-scale simulation of the interface is numerically modeled using the discrete element method (DEM). The DEM model is then utilized to investigate the effect of different particle characteristics on the frictional performance of wheel–rail contact which can provide more insight into micromechanical observations. The effects of various particle characteristics including their size, their number, the number of fragments the particles break into, and the parameters defining the behavior of the bonds between particle fragments on the coefficient of traction (COT) are systematically investigated. Results show that, in dry contacts, the coefficient of traction decreases when the size or number of sand particles increases. This can be attributed to the formation of weak shear bands between the fragments. Further investigation is needed for wet- and leaf-contaminated contacts. It is also found that the COT is more sensitive to the stiffness of the bond between the fragments of a broken particle compared to the strength of the bond. A limiting value for bond strength was identified, beyond which the sand particles exhibited ductile behavior rather than the expected brittle fracture. The findings from this study can be useful for future research on adhesion management in wheel–rail contact and the modeling approach can be scaled up to the full contact.

Variability and loss of uniqueness of numerical solutions in FEM×DEM modeling with second gradient enhancement

AbstractIn the last decade, a new multi‐scale FEM×DEM approach has been developed using Finite Element Method (FEM) coupled with Discrete Element Method (DEM) as a constitutive law to account for the specificities of the mechanical behavior of granular materials. In FEM×DEM model, a DEM calculation is performed on a particle assembly (volume element—VE) at each Gauss point. Recent publications have demonstrated that FEM×DEM approach naturally captures the discrete and anisotropic nature of granular materials. Despite its advantages, FEM×DEM with classical FEM, suffers from mesh dependency, especially when material enters softening phase and exhibits strain localization. To overcome this limitation, FEM×DEM model has been enriched by incorporating a local second gradient model. Nevertheless, the existence of multiple possible solutions is observed. In this paper, we study the variability and loss of uniqueness of numerical solutions to a boundary value problem. Different VEs with equivalent mechanical properties are generated and used to model the pressuremeter tests by means of FEM×DEM. The modeling results show a great variability of the numerical results, both in shape of borehole and in different modes of shear bands. For the same VE, the loss of uniqueness of numerical solutions is evidenced by a slight modification of loading history at the level of the internal pressure applied to the borehole. Finally, we show that when a certain heterogeneity is introduced by using different VEs within the same BVP, even if the uniqueness of the solution is not guaranteed, the set of possible solutions seems more restrained.

Modeling and simulation of anisotropic cross-linked cellulose fiber networks with an out-of-plane topography

Non-woven cellulose fiber networks of low areal density are widely used in many industrial applications and consumer products. A discrete element method (DEM) modeling framework is advanced to simulate the formation of strongly anisotropic cellulose fiber network sheets in the dilute limit with simplified hydrodynamic and hydroelastic interactions. Our modeling accounts for in-plane fiber orientation and viscous drag indirectly by using theories developed by Niskanen (2018 Fundamentals of Papermaking, Trans. 9th Pulp and Paper Fundamental Research Symp. Cambridge, 1989 (FRC) pp 275–308) and Cox (1970 J. Fluid Mech. 44 791–810) respectively. Networks formed on a patterned and flat substrate are simulated for different fiber types, and their tensile response is used to assess the influence of the out-of-plane topographical pattern, specifically, on their stiffness and strength. Sheets with the same grammage and thickness, but composed with a higher fraction of softwood fiber (longer fibers with large diameter), have higher strength and higher strain to failure compared to sheets made from hardwood fibers (short fibers with small diameter). However, varying the fiber fraction produces only an insignificant variation in the initial sheet stiffness. The above simulation predictions are confirmed experimentally for sheets comprised of fibers with different ratios of Eucalyptus kraft and Northern Bleached Softwood Kraft fibers. Sheets with out-of-plane topography show an unsymmetric mass distribution, lower tensile stiffness, and lower tensile strength compared to those formed on a flat substrate. The additional fiber deformation modes activated by the out-of-plane topography, such as bending and twisting, explain these differences in the sheet mechanical characteristics.

Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure, this study proposed a novel approach combining numerical simulation and machine learning algorithms. Initially, 3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional (3D) discrete element method (DEM) were conducted to construct a database. In this process, the positions of the particles were randomly altered, and the particle assemblages changed. Interestingly, besides confirming the influence of particle size distribution parameters, the stress-strain curves differed despite an identical gradation size statistic when the particle position varied. Subsequently, the obtained data were partitioned into training, validation, and testing datasets at a 7:2:1 ratio. To convert the DEM model into a multi-dimensional matrix that computers can recognize, the 3D DEM models were first sliced to extract multi-layer two-dimensional (2D) cross-sectional data. Redundant information was then eliminated via gray processing, and the data were stacked to form a new 3D matrix representing the granular soil's fabric. Subsequently, utilizing the Python language and Pytorch framework, a 3D convolutional neural networks (CNNs) model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil's fabric. The mean squared error (MSE) function was utilized to assess the loss value during the training process. When the learning rate (LR) fell within the range of 10-5-10-1, and the batch sizes (BSs) were 4, 8, 16, 32, and 64, the loss value stabilized after 100 training epochs in the training and validation dataset. For BS = 32 and LR = 10-3, the loss reached a minimum. In the testing set, a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error (MAPE) of 4.43% under the optimized condition, demonstrating the accuracy of this approach. Thus, by combining DEM and CNNs, the variation of soil's mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

Study on strain localization of frozen sand based on uniaxial compression test and discrete element simulation

Strain localization has always been an important subject in frozen soil mechanics and engineering. To evaluate the development of local strain and the formation of shear bands in frozen soil, uniaxial compression tests have been conducted on frozen sand at various temperatures and particle grades. The strain localization evolution law of the frozen soil is analyzed utilizing the digital image correlation (DIC) method. The test results reveal that the entire process of shear band generation, development, and formation in frozen soil can be well captured. Within the testing temperature and particle grade range in this study, in comparison to particle grade, temperature exerts a more pronounced influence on the shear band angle which increases as temperature decreases. It is discovered that the width of the shear band increases with the decrease in temperature and the increase in mean particle diameter d50. Subsequently, a discrete element method (DEM) model is developed to examine the microscopic mechanical characteristics of frozen sand in uniaxial compression tests. The reliability of the DEM model is verified through comparative analysis with test results. Besides, the development law of the strain localization of the frozen soil obtained by the numerical simulation is revealed based on the quantitative analysis of the rotational angle, bonding state, and displacement of the soil particle during the shearing process.

Spatter-flow interaction behavior under protective gas flow parameters and scanning directions

Spattering is a common issue in selective laser melting (PBF-LB), causing contamination of the powder bed and negatively affecting product quality. One solution to this problem is introducing an inert gas flow that can remove spatter particles. The gas flow's characteristics and interaction with spatter particles depend on process parameters and involve a multi-physical field coupling process. However, current research mainly focuses on spattering behavior under single process conditions and lacks systematic exploration of gas flow characteristics and their interaction with spattering. This paper investigates the gas flow-spatter interaction process in PBF-LB, constructing a coupled model of Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM). The model investigates the effects of inlet height, inlet flow velocity and laser scanning direction on the deposition and removal of spattered particles. The study reveals that flow velocity and inlet height affect the dynamic behavior of spattering by altering the flow distribution, while the laser scanning direction influences spatter dynamics by changing the direction of spatter ejects. The rate of spatter removal increases as the angle between the scanning direction and flow direction, and the flow velocity, increase. Conversely, it decreases as the inlet height increases. This work provides theoretical understanding of the interaction between gas flow characteristics and spattering, which is significant for optimizing printing process parameters and improving printing quality.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method (DEM) modelling. The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions. A side wall node loading method is used to exert bi-directional shear of various angles. The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials. However, the relationship between bi-directional shear and mechanical responses relies on loading conditions, i.e. constant vertical stress or constant volume conditions. The stress states induced by static shear consolidation are affected by loading angles, which are enlarged by subsequent shear, consistent with the relationship between bi-directional shear and principal stresses. It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials. The presence of bi-directional principal stress rotation (PSR) is demonstrated, which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction. Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts, but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts. It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions. Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined, providing further insights into understanding granular behaviour under bi-directional shear.

Evaluation and improvement of Gay-Berne interaction potential to simulate 3D DLVO interaction of clay particles

This paper first presents a set of DLVO-based energy-separation functions for a pair of finite uniformly charged square platelets of infinitesimal thickness in three elementary configurations: face-to-face, edge-to-edge, and edge-to-face. The novel dataset was generated by summing the electrostatic interaction energy computed numerically by solving the non-linear 3D Poisson-Boltzmann equation and the van der Waals interaction energy calculated analytically. The dataset aims to inform qualitatively and quantitatively the energy/force separation functions used in the Discrete Element Method (DEM) and Coarse-Grained Molecular Dynamics (CGMD) modelling of clays. The same dataset was then used to calibrate and evaluate two Gay-Berne (GB)-type potentials: i) a DLVO-adapted Gay-Berne potential, where the Born-van der Waals branches of the underlying Lennard-Jones (LJ) potential are replaced with van der Waals-Columbic branches to represent DLVO interactions; ii) the Mie potential, where the exponents of the two energy terms are ‘unlocked’ instead of being set equal to 12 and 6 as per the original LJ potential. It is shown that the orientation parameter, µ, and the anisotropy parameter, ν, need to be different from µ = 2 and ν = 1 as adopted in CGMD clay modelling to capture the progression of the shape of the pair energy-separation function from face-to-face to edge-to-face and edge-to-edge configuration. It is also shown that the MIE potential (with exponents m = 3 and n = 1.5) better captures the slow decay of the electrostatic repulsive energy component of the DLVO potential energy Coulombic branch of the interaction potential compared to the DLVO-adapted GB potential, which embeds the Lennard-Jones (LJ) exponents m = 12 and n = 6.

Discrete Element Model Building and Optimization of Tomato Stalks at Harvest

The mechanical properties of tomato stalk, relevant to the harvesting and crushing of tomato vines, significantly impact its harvesting quality and efficiency. Establishing a simulation model, which accurately mirrors these properties, is foundational for designing related mechanical components. The discrete element method models tomato stalk harvesting and is optimized through mechanical tests and simulations. A blend of Plackett–Burman, steepest ascent, and central composite design modeling identified three contact model parameters influencing the maximum stalk shear force. The optimal values of these three parameters were a normal stiffness of 1.04 × 1010 N m−3, tangential stiffness of 7.59 × 109 N m−3, and bond radius of 1.06 mm. The relative error in the simulated versus measured shear force was <1%, affirming the model’s accuracy in characterizing cutting properties. These findings lay the theoretical groundwork for numerical simulations of tomato-stalk-related equipment.

Experimental and numerical analyses of crushing resistance of unbound road materials

ABSTRACT Aggregate breakage in unbound pavement layers can lead to pavement distresses that affect their functionality and service life. Thus understanding the mechanics and clarifying the factors affecting materials breakage resistance are important for ensuring adequate performance of these layers. In this study, aggregate breakage in unbound granular materials (UGM) is investigated experimentally and numerically. Experimentally, aggregate breakage under uniaxial compression is examined for two UGMs prepared with the same aggregate type but different gradations. To capture the experimentally observed influence of gradation and load magnitude on aggregate breakage, a Discrete Element Method (DEM) model was developed, based on granular mechanics particle contact and failure laws. A simple procedure to identify the contact and failure law parameters from experiments is proposed. With those parameters, the model’s capability of capturing the effect of gradation and loading on the aggregate breakage in UGM is evaluated. Based on comparison with experimental findings, it is shown that the model can capture macro-scale properties of UGM, such as its deformation response under uniaxial compression, as well as the amount of aggregate breakage in the material.

Optimizing Retention Bunkers in Copper Mines with Numerical Methods and Gradient Descent

This study examines the optimization of ore receiving bins in underground copper mines, targeting the reduction of rapid wear and tear on bin components. The investigation identifies the primary wear contributors as the force exerted by the accumulated ore and the velocity at which ore particles move. By altering design and operational parameters, the objective is to decrease wear at key points such as transfer areas, thereby improving the efficiency and service life of retention bunkers. A Discrete Element Method (DEM) model of the bin was created and validated against actual mining conditions to study the impact of material flow on wear. The optimization approach used a constrained gradient descent algorithm to minimize factors like particle velocity and pressure force, while maintaining the efficiency of the bin. The findings provide valuable insights for the future design enhancements, potentially improving the operational performance of retention bunkers in the mining industry.

Numerical investigation on the densification of granulated porous indium tin oxide powders before compaction

Dense and uniform initial packing structures of powders are of key significance in powder metallurgy process, which can provide the precondition for the fabrication of high-performance components with low cost and high efficiency. In this paper, the packing densification of indium tin oxide (ITO) granulated micro powders with continuous size distributions and internal porosity under three-dimensional vibrations was numerically investigated by discrete element method (DEM). Firstly, the DEM model was validated by physical experiments, and the contact parameters between particles and the porosity therein were determined. Then the effects of operating parameters on the macro/micro properties (e.g., packing density, coordination number (CN), pores, and forces) of the packing structures were analyzed. Results show that the mean CN cannot intuitively reflect the packing structure due to the complex and varied inter-particle contacts caused by the inhomogeneity of the particle size in a multi-sized granular system. Additionally, the excellent packing structure of porous ITO particles is always obtained from low amplitude when the vibration intensity is the same. Corresponding mechanism analyses reveal that higher amplitude normally causes strong convective diffusion, leading to more pores in the packing. This increases the probability of wedging effect occurring during settling, thereby reducing the packing density. However, optimal packing quality with low amplitude can only be achieved when coupled with high frequency. Therefore, applying vibration is an effective way to achieve dense packing of porous spherical particles, especially at low amplitude and high-frequency operating conditions.

A novel grain growth algorithm for grain-based models for investigating the complex behavior of crystalline rock

The mineralogical composition and microstructure of crystalline rock affect its mechanical properties. However, it is challenging to analyze and quantify the associated mechanisms using experimental methods. A potential solution to this problem is to apply microscopic simulation methods, such as a combination of the discrete element method and grain-based model (GBM). A prerequisite for microscopic simulations is to accurately reproduce the microscopic features, especially the interactions between grains. Inspired by the crystallization of polycrystalline rocks, a novel grain growth algorithm that constructs a GBM by simulating the sequential crystallization process is proposed in this paper. The results of comprehensive analyses show that the proposed modeling method can accurately reproduce the mineralogical compositions, euhedral-to-anhedral morphology transitions, and grain size distributions during different crystallization processes. By accurately reproducing the interlocking structure between grains, the proposed method can simulate typical mechanical behaviors, such as the nonlinear strength envelope, uniaxial compressive strength-to-tensile strength ratio, and bimodularity, which are consistent with the experimental findings. The effectiveness of this method in modeling porphyritic structures and grain-scale anisotropic textures is demonstrated, and the microscopic mechanism of fracture mode transition associated with the difference in grain structures is discussed.

Study on particle deposition in pipeline groove from gas–particle two-phase flow

In the process of particle–fluid flow, solid particles are easily deposited in pipes, which leads to collisions and abrasion, especially in pipelines with grooves. Therefore, some structural components are always designed above the groove to improve particle trajectories inside the groove in the pipeline. In the present study, the deposition of particles was analyzed in detail by means of experimental visualization, and Computational Fluid Dynamics and Discrete Element Method model (CFD-DEM) methods were used to investigate the motion and deposition of particles when both grooves and baffles are designed in the pipeline system. Finally, the effect of the baffle width on the deposition of particles in the groove was studied. The results show that the baffle width has a slight effect on the mass of particles deposited in the groove after the number of particles there stabilizes, but when the width of baffle is the same as that of the groove, the time it takes the particles to reach this stable state is shortest.

Water and mud inrush dynamics process simulation by using coarse-grained CFD-DEM method

Water and mud inrush disaster is a typical fluid-solid coupling problem, and its forecasting and prevention can reduce human and economic losses. In this work, a coarse-grained discrete element method and computational fluid dynamics model based on bonded particles is employed to investigate an inrush disaster happened in Foshan Metro Line 2. It's shown that the current model can simulate beam bending, and the differences from the analytical solution are 7% and 5% in deflection and maximum axial stress. This study also suggests that two-way coupling is in superior agreement with field observation than one-way coupling. The water pressure is highly influential as it increases from 0.15 MPa, 0.25 MPa, 0.35 MPa to 0.45 MPa inrush occurrence time varies from 28.0 s, 11.5 s, 7.5 s to 5.0 s, respectively. The current model is capable of simulating water and mud inrush, and may provide a framework for investigating this disaster in complex engineering scenarios.

Discrete Element Method Simulation of the Idaho Calcine Simulant for Hot Isostatic Pressing Canister-Filling Process: Part 1

In preliminary engineering studies and equipment commissioning, readily available simulants with certain resemblances to the target waste, such as particle size, may be employed. However, for the validation of engineering processes, it is crucial to use simulants that closely replicate the physical and flow characteristics of the waste material, typically excluding radioactivity. The production of such simulants can entail significant costs. To facilitate the development of novel engineering solutions, the U.S. Department of Energy provided a nonradioactive alumina calcine simulant. This simulant was utilized to demonstrate a hot isostatic press (HIP) canister-filling system designed by Gravitas Technologies in Australia. The simulant was synthesized through a fluidized-bed calcination process, which mirrored the chemistry and procedure employed for the actual alumina Idaho calcine waste material. Consequently, the simulant exhibited physical properties akin to the actual calcine, including particle size distribution, bulk density, and flow properties. This first paper, Part 1, presents the powder characterization test results determined by a Freeman FT-4 rheometer and the calibration methods that determined a set of unique contact model parameters for dynamically simulating Idaho calcine simulant in a discrete element method (DEM) model. The second paper, Part 2, will present the dynamic simulations of two bulk material-handling scenarios in a full-scale, three-dimensional integrated HIP canister-filling system. The predicted results are compared with historical experimental results for validating the contact model. The contact model, which represents the particle-particle and particle-boundary interactions, was calibrated according to experimental data obtained from six calibration tests. This work aims to support future research with powder characterization experimental data and a calibrated DEM contact model to assist in developing processes for the safe handling and treatment of Idaho calcine waste.

Fracturing and Dome‐Shaped Surface Displacements Above Laccolith Intrusions: Insights From Discrete Element Method Modeling

AbstractInflation of viscous magma intrusions in Earth's shallow crust often induces strain and fracturing within heterogeneous host rocks and dome‐shaped ground deformation. Most geodetic models nevertheless consider homogeneous, isotropic, and linear‐elastic media wherein stress patterns indicate the potential for failure, but without simulating actual fracturing. We present a two‐dimensional Discrete Element Method (DEM) application to simulate magma recharge in a pre‐existing laccolith intrusion. In DEM models, fractures can propagate during simulations. We systematically investigate the effect of the host rock toughness (resistance to fracturing), stiffness (resistance to deformation) and the intrusion depth, on intrusion‐induced stress, strain, displacement and spatial fracture distribution. Our results show that the spatial fracture distribution varies between two end‐members: (a) for high stiffness or low toughness host rock or a shallow intrusion: extensive cracking, multiple vertical surface fractures propagating downward and two inward‐dipping highly cracked shear zones that connect the intrusion tip with the surface; and (b) for low stiffness or high toughness host rock or a deeper intrusion: limited cracking, one central vertical fracture initiated at the surface, and two inward‐dipping fractures at the intrusion tips. Abrupt increases in surface displacement magnitude occur in response to fracturing, even at constant magma injection rates. Our modeling application provides a novel approach to considering host rock mechanical strength and fracturing during viscous magma intrusion and associated dome‐shaped ground deformation, with important implications for interpreting geodetic signals at active volcanoes and the exploitation of geothermal reservoirs and mineral deposits.

An impact energy erosion model with an energy allocation rule for the discrete element method

Surface erosion caused by solid particle impact frequently occurs in engineering applications involving particulate flow. With the tremendous progress in computational technology, discrete element method (DEM)-based numerical methods have become a powerful means of studying surface erosion. However, the applicability of applied erosion models remains one of the critical challenges in DEM modelling to obtain satisfactory accuracy over a wide range of materials and impact conditions. In this study, an impact energy erosion model (IEEM) that evaluates erosive wear using accumulated impact energy during the impact process is developed. In IEEM, both cutting and deformation wear are considered. A calibration method of the specific energy that combines DEM simulations and abrasive jet tests is established. To quantitatively predict the erosive wear of the target surface eroded by different particles, an energy allocation rule based on the hardness ratio of the target surface to particles is proposed. Its rationality is thoroughly evaluated before embarking on DEM simulations. Subsequently, the accuracy of DEM simulations incorporated with IEEM and the energy allocation rule is comprehensively verified by comparing them with experimental data on ductile, brittle and semi-brittle materials. The results confirm that DEM simulations can reasonably predict the dependence of erosive wear on impact velocities, impact angles and erodent particle hardness, regardless of the material involved. The calibrated specific energy reflects the properties of the material and further determines the wear mechanism. Finally, the influence of critical DEM parameters on erosion prediction is studied. Generally, DEM incorporated with IEEM and the energy allocation rule provides a quantitative erosion prediction framework applicable to different materials and impact conditions. In the future, this framework has the potential to be applied to the erosion prediction of more systems.