Method for simulating nanoindentation creep of calcium silicate hydrate gel based on discrete element model

Abstract

The application relates to a hydration calcium silicate gel nanoindentation creep simulation method based on a discrete element model. The method comprises the following steps: inputting a first indenter load in a holding stage into a target discrete element model established in advance for hydration calcium silicate gel, and determining a displacement change function of the indenter in the holding stage; based on the displacement change function, determining a contact area function of a nanoindentation at the end of the holding stage; and based on the indenter load, the displacement change function and the contact area function of the nanoindentation, determining a contact creep function of the hydration calcium silicate gel. The method can reduce the test cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cement-based material mechanics, in particular to a hydration calcium silicate gel nanoindentation creep simulation method based on a discrete element model. BACKGROUND

[0002] At present, it is generally believed that the creep performance of concrete is mainly related to calcium silicate hydrate (C-S-H). At present, the most important means for testing C-S-H creep is nanoindentation creep test, and the micro-creep parameters of C-S-H measured by this technology can be used as input parameters of a concrete multi-scale creep model.

[0003] However, the nanoindentation creep test technology has some shortcomings, for example: 1. The nanoindentation test equipment is expensive, and usually requires high-precision testing instruments and special laboratory environment; 2. The sample preparation of C-S-H is relatively complex, and it is necessary to ensure that the sample surface roughness is very low and has no obvious defects; 3. Factors such as microstructure, humidity conditions and loading mode of the sample may have a significant impact on the test results, and the repeatability is poor.

[0004] In summary, although the nanoindentation test technology is an effective method for characterizing the micro-creep performance of calcium silicate hydrate, its high cost and uncertainty of test data limit its wide application. SUMMARY

[0005] Therefore, it is necessary to provide a hydration calcium silicate gel nanoindentation creep simulation method based on a discrete element model, which can reduce the test cost.

[0006] In a first aspect, the present application provides a hydration calcium silicate gel nanoindentation creep simulation method based on a discrete element model, comprising:

[0007] inputting the first indenter load in the holding stage to the target discrete element model established in advance for the hydration calcium silicate gel, and determining the displacement change function of the indenter in the holding stage;

[0008] based on the displacement change function, determining the contact area function of the nanoindentation at the end of the holding stage;

[0009] based on the indenter load, the displacement change function and the contact area function of the nanoindentation, determining the contact creep function of the hydration calcium silicate gel.

[0010] In one embodiment, the process of establishing the above-mentioned target discrete element model comprises:

[0011] establishing an initial discrete element model for the hydration calcium silicate gel;

[0012] A viscous sliding creep mechanism is established in the initial discrete element model to obtain an intermediate discrete element model; the viscous sliding creep mechanism is used to change the contact relationship between particles in the initial discrete element model.

[0013] The intermediate discrete element model is calibrated to obtain the target discrete element model.

[0014] In one embodiment, the process of establishing the aforementioned intermediate discrete element model includes:

[0015] A second indenter load is applied to the initial discrete element model until the second indenter load reaches the target value.

[0016] For each particle in the initial discrete element model, iterative calculations are performed. In each iteration, the sliding velocity of the particle at the i-th time step is obtained. Based on the sliding velocity at the i-th time step, the friction coefficient of the particle at the i-th time step is determined and applied to the particle.

[0017] Obtain the sliding velocity of the particle at the (i+1)th time step, determine the friction coefficient of the particle at the (i+1)th time step based on the sliding velocity at the (i+1)th time step, and apply the friction coefficient at the (i+1)th time step to the particle; continue iterating until a preset time is reached to end the iteration, and determine the intermediate discrete element model based on the friction coefficient and sliding velocity obtained at the end of the iteration; where i is a positive integer greater than or equal to 0.

[0018] In one embodiment, the method further includes:

[0019] The sliding speed and preset time obtained at the end of the iteration are scaled using a time scaling algorithm to obtain the scaled sliding speed and scaled time.

[0020] In one embodiment, the above-mentioned establishment of the initial discrete element model includes:

[0021] Based on the wall location information and computational domain information obtained from the initial discrete element model, six walls are generated.

[0022] Within a cubic space surrounded by six walls, a basic discrete element model is generated based on a pre-defined porosity.

[0023] Obtain the contact mechanics parameters of the basic discrete element model;

[0024] Control the particles in the basic discrete element model to bounce off in the computational domain until the particles in the basic discrete element model move to an equilibrium state.

[0025] The initial discrete element model is obtained by setting the velocities of all particles in the basic discrete element model to preset values.

[0026] In one embodiment, the above-described calibration process for the intermediate discrete element model to obtain the target discrete element model includes:

[0027] The indenter load during the holding phase is input into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function;

[0028] Based on the pre-obtained simulation results, the creep parameters corresponding to the experimental results are corrected to obtain the target discrete element model; the creep parameters include at least activation energy, unit normal contact force, and flow unit.

[0029] Secondly, this application also provides a hydration calcium silicate gel nanoindentation creep simulation device based on a discrete element model, comprising:

[0030] The displacement change function determination module is used to input the first indentation load of the bearing stage into the target discrete element model pre-established for hydrated calcium silicate gel, and determine the displacement change function of the indentation head during the bearing stage;

[0031] The contact area function determination module is used to determine the contact area function of the nanoindentation at the end of the load based on the displacement change function;

[0032] The contact creep function determination module is used to determine the contact creep function of hydrated calcium silicate gel based on indenter load, displacement change function, and contact area function of nanoindentation.

[0033] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method of any one of the first aspects.

[0034] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method of any one of the first aspects.

[0035] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the method of any one of the first aspects. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1This is an internal structural diagram of a computer device in one embodiment;

[0038] Figure 2 This is a schematic diagram of the process for simulating nanoindentation creep of calcium silicate gel based on the discrete element model in one embodiment.

[0039] Figure 3 This is a schematic diagram of the indentation contact area corresponding to the contact area function of the nanoindentation at any time step in one embodiment.

[0040] Figure 4 This is a flowchart illustrating the simulation method for nanoindentation creep of hydrated calcium silicate gel based on the discrete element model in another embodiment.

[0041] Figure 5 This is a schematic diagram illustrating the process of developing a viscous slip creep mechanism in an initial discrete element model in one embodiment.

[0042] Figure 6 This is a flowchart illustrating the simulation method for nanoindentation creep of hydrated calcium silicate gel based on the discrete element model in another embodiment.

[0043] Figure 7 This is a flowchart illustrating the simulation method for nanoindentation creep of hydrated calcium silicate gel based on the discrete element model in another embodiment.

[0044] Figure 8 This is a schematic diagram illustrating the generation of six walls in one embodiment;

[0045] Figure 9 This is a schematic diagram of a six-sided wall with different porosities in one embodiment;

[0046] Figure 10a Visualization of the coordination number and corresponding histogram for a particle model with a bulk density of 0.74;

[0047] Figure 10b Visualization of the coordination number and corresponding histogram for a particle model with a packing density of 0.64;

[0048] Figure 10c Visualization of coordination number and corresponding histogram for a particle model with a packing density of 0.58;

[0049] Figure 11 This is a flowchart illustrating the simulation method for nanoindentation creep of hydrated calcium silicate gel based on the discrete element model in another embodiment.

[0050] Figure 12 This is a schematic diagram comparing simulation results and experimental results in one embodiment;

[0051] Figure 13This is a structural block diagram of a hydrated calcium silicate gel nanoindentation creep simulation device based on a discrete element model in one embodiment. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0053] Currently, it is generally believed that the creep properties of concrete are mainly related to calcium silicate hydrate (CSH) gel. At present, the primary method for testing CSH creep is the nanoindentation creep test. The microscopic creep parameters of CSH determined by this technique can be used as input parameters for multi-scale creep models of concrete. However, the nanoindentation creep test technique has some drawbacks, such as: 1. The nanoindentation testing equipment is expensive, usually requiring high-precision testing instruments and a special laboratory environment; 2. The preparation of CSH gel samples is relatively complex, requiring very low surface roughness and the absence of obvious defects; 3. Factors such as the sample's microstructure, humidity conditions, and loading method can significantly affect the test results, resulting in poor repeatability. In summary, although the nanoindentation test technique is an effective method for characterizing the microscopic creep properties of calcium silicate hydrate gel, its high cost and the uncertainty of test data limit its widespread application. Therefore, numerical simulation of CSH nanoindentation creep tests has scientific value.

[0054] The classic CSH gel model considers the smallest structural unit of CSH gel to be spherical particles. Based on different gel particle packing densities, CSH is classified into three types: low-density CSH, high-density CSH, and ultra-high-density CSH. This application proposes a CSH nanoindentation creep test simulation method based on a discrete element model, using micromechanical analysis software (Particle Flow Code 3D, PFC3D). This model can design different CSH gel particle packing densities and CSH cohesion to accurately simulate the indentation creep performance of CSH, thus promoting the development of multi-scale modeling methods for concrete creep.

[0055] This application proposes a simulation scheme for nanoindentation creep of hydrated calcium silicate gel based on a discrete element model. The scheme includes: inputting a first indenter load during the holding phase into a pre-established target discrete element model for hydrated calcium silicate gel to determine the displacement change function of the indenter during the holding phase; determining the contact area function of the nanoindentation at the end of the holding phase based on the displacement change function; and determining the contact creep function of the hydrated calcium silicate gel based on the indenter load, the displacement change function, and the contact area function of the nanoindentation. Using this scheme, the mechanical behavior of hydrated calcium silicate gel can be simulated in a virtual environment through the established target discrete element model, thereby reducing reliance on expensive experimental equipment and significantly reducing the investment in experimental equipment and resources.

[0056] In one exemplary embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 1 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores data from the simulation process of hydrated calcium silicate gel nanoindentation creep based on a discrete element model. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for simulating hydrated calcium silicate gel nanoindentation creep based on a discrete element model.

[0057] Those skilled in the art will understand that Figure 1 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0058] In one exemplary embodiment, such as Figure 2 As shown, a method for simulating nanoindentation creep of hydrated calcium silicate gel based on discrete element model is provided, and this method is applied to... Figure 1 The following steps, 201 to 203, are used as an example of computer equipment.

[0059] Step 201: Input the first indentation load of the holding stage into the target discrete element model pre-established for hydrated calcium silicate gel to determine the displacement change function of the indentation head during the holding stage.

[0060] The first indenter load refers to the external load applied to the indenter. In nanoindentation testing, the indenter applies force to press into the particle surface inside the target discrete element model.

[0061] Calcium silicate hydrate gel is a major product formed during the cement hydration process and a key component that imparts strength to cement during the hardening process.

[0062] Discrete Element Method (DEM) is a numerical simulation method used to model the behavior of particulate matter (such as sand, powder, and granular materials). In the DEM, particles are treated as independent discrete objects, and their mechanical behavior is simulated through the interaction forces between nodes. The target DEM model refers to a DEM model specifically designed to simulate the mechanical behavior of hydrated calcium silicate gel.

[0063] Displacement refers to the amount of displacement of an object after being subjected to force, that is, the offset of the indenter under load. The displacement variation function is a mathematical function that describes how the displacement of the indenter changes with time or load increase during the loading phase; it describes the displacement change law of the indenter as the load increases. The displacement variation function is used to represent the interaction relationship between the indenter and the sample.

[0064] In this embodiment of the application, the first indentation load of the holding stage is input into the target discrete element model pre-established for hydrated calcium silicate gel to determine the displacement change function of the indentation head during the holding stage.

[0065] In some embodiments, the first indenter load is calculated by summing the forces exerted on the particles in contact with the indenter in the vertical direction.

[0066] Step 202: Based on the displacement change function, determine the contact area function of the nanoindentation at the end of the load holding period.

[0067] Nanoindentation is a precise experimental method for measuring the hardness, elastic modulus, and other mechanical properties of materials. In this test, a hard indenter is pressed into the sample surface to a very small depth, and the data on load and displacement can be used to deduce the mechanical properties of the material.

[0068] The contact area refers to the size of the region where the indenter contacts the surface of the hydrated calcium silicate gel. During nanoindentation, as the load increases, the indenter deepens, and the contact area increases accordingly. The contact area function describes how the contact area between the indenter and the material surface changes with displacement.

[0069] In the embodiments of this application, the contact area function of the nanoindentation at the end of the load can be determined based on the displacement change function.

[0070] In some embodiments, the displacement change function can be directly obtained through the embedded function of the micromechanical analysis software.

[0071] The contact area function of nanoindentation can be indirectly determined by the displacement change function and the indenter shape function. For example... Figure 3 As shown, Figure 3 In this context, h represents the indenter displacement corresponding to the displacement change function, and Ac represents the indentation contact area corresponding to the contact area function of the nanoindentation. By processing the data using micromechanical analysis software, Ac at any time step can be identified. Figure 3 The triangular region in the diagram represents the vertical projection of the contact surface between the indenter and the CSH particle, denoted as Ac. Each dot within the triangular region represents a contact point between the indenter and the particle (the larger the dot, the greater the contact force between the particle). At any time step, the Ac of the nanoindentation can be calculated using formula (1):

[0072] A c =24.49h 2 (1)

[0073] Where h is the indenter displacement corresponding to the displacement change function, and Ac is the indentation contact area corresponding to the nanoindentation contact area function.

[0074] Step 203: Determine the contact creep function of the hydrated calcium silicate gel based on the indenter load, displacement change function, and contact area function of nanoindentation.

[0075] Contact creep refers to the chronic deformation of a material over a certain period of time after a load is applied, due to the material's viscoelastic behavior. Creep typically manifests as a gradual and slow deformation of a material under prolonged load. The contact creep function is a mathematical function established by combining indentation load, displacement change function, and contact area function to describe the creep behavior of hydrated calcium silicate gel materials at the contact surface. This function can describe the deformation characteristics of the material under long-term load.

[0076] In the embodiments of this application, the contact creep function of the hydrated calcium silicate gel can be determined based on the indenter load, displacement change function, and contact area function of nanoindentation.

[0077] In some embodiments, the contact creep function [L(t)-L(0)] can be calculated using formula (2):

[0078]

[0079] Where Δh(t) is the displacement change function during the holding stage, Ac(t) is the contact area function of the nanoindentation at the end of the holding stage, P is the indenter load, and [L(t)-L(0)] is the contact creep function.

[0080] In the aforementioned method for simulating the nanoindentation creep of hydrated calcium silicate gel based on a discrete element model, the first indenter load of the holding stage is first input into a pre-established target discrete element model for hydrated calcium silicate gel to determine the displacement change function of the indenter during the holding stage. Then, based on the displacement change function, the contact area function of the nanoindentation at the end of the holding stage is determined. Finally, based on the indenter load, displacement change function, and contact area function of the nanoindentation, the contact creep function of the hydrated calcium silicate gel is determined. Traditional methods typically require high-precision experimental equipment (such as nanoindenters) that necessitates significant investment and high maintenance costs. However, this embodiment, through the established target discrete element model, can simulate the mechanical behavior of hydrated calcium silicate gel in a virtual environment, thereby reducing reliance on expensive experimental equipment and significantly lowering the investment in experimental equipment and resources.

[0081] In one exemplary embodiment, such as Figure 4 As shown, the process of establishing the above-mentioned target discrete element model includes the following steps 301 to 303, wherein:

[0082] Step 301: Establish an initial discrete element model for hydrated calcium silicate gel.

[0083] Step 302: Establish a viscous sliding creep mechanism in the initial discrete element model to obtain an intermediate discrete element model; the viscous sliding creep mechanism is used to change the contact relationship between particles in the initial discrete element model.

[0084] Viscous slip refers to the phenomenon of relative sliding between particles at the contact point due to the viscous properties of the material. This sliding is caused by external loads or the material's inherent fluidity and hysteresis behavior. In particle interactions, viscous slip affects the relative position and contact state of the particles. Creep refers to the slow, continuous deformation process of a material under long-term loading. Creep is usually related to the viscoelastic properties of the material, that is, after being subjected to a constant load, the material gradually undergoes plastic or elastic deformation over time. The viscous slip creep mechanism describes the long-term deformation and sliding of particles at the contact point. Introducing the viscous slip creep mechanism into the discrete element model aims to simulate the change in the contact relationship between particles under long-term loading. By introducing the effects of slip and creep, the mechanical behavior and deformation process of CSH gel under long-term loading can be described more accurately.

[0085] The intermediate discrete element model is an intermediate version of the initial discrete element model obtained by introducing a viscous slip creep mechanism. It incorporates new parameters and mechanical mechanisms related to material creep and slip behavior, enabling better simulation of the behavior of CSH gels under complex mechanical environments.

[0086] In this embodiment, an initial discrete element model is established for hydrated calcium silicate gel. Then, a viscous slip creep mechanism is established within the initial discrete element model to obtain an intermediate discrete element model.

[0087] It should be noted that the viscous slip creep mechanism is derived from the rate process theory, which is expressed by formula (3):

[0088]

[0089] Where s is the slip velocity between particles (m / s); k is the Boltzmann constant (J / K); T is the absolute temperature (K); h1 is the Planck constant (J·s); R is the ideal gas constant (kJ / mol / K); λ is the flow unit (nm); ΔF is the activation energy (kJ / mol); and n1 is the number of bonds per unit normal contact force (bonds / N). It is the ratio of the tangential force to the normal force at the particle contact point.

[0090] The relationship with the coefficient of friction is Formula (3) can be rewritten as formula (4):

[0091]

[0092] in,

[0093] Equations (3) and (4) show that the slip velocity between particles is determined by the ratio of tangential contact force to normal contact force. Under the action of external force, as the particle aggregate undergoes creep deformation, the particles continuously rearrange themselves, resulting in a decrease in the tangential component of the contact force and / or an increase in the normal component. This mechanism continuously reduces the particle slip velocity, thereby causing a decrease in the creep deformation rate of the particle model.

[0094] This application embodiment develops a "viscous slip" contact model (i.e., establishes a viscous slip creep mechanism) in PFC3D. The model is as follows: Figure 5 As shown, in Figure 5 In this context, the RPT unit is the theoretical unit for rate processes, f t f is the tangential force at the particle contact point. n k is the normal force at the particle contact point. n k is the stiffness of a linear spring.t For the stiffness of a linear spring, δ n δ represents the tangential relative distance between particles. t Let be the normal relative distance between the particles, and u be the particle friction coefficient.

[0095] exist Figure 5 In the middle, a stiffness of k is used n Linear springs are used to represent normal contact, while tangential contact uses springs with stiffness k. t The linear spring is represented by a series of velocity process theoretical units. The slip velocity of the velocity process theoretical unit is controlled by the ratio of tangential force to normal force at the contact point, i.e., formula (3). During the creep deformation process, the friction coefficient of the particles is not a fixed value, but decreases as the tangential force of the particles and the slip velocity at the contact point decrease.

[0096] Step 303: The intermediate discrete element model is calibrated to obtain the target discrete element model.

[0097] The calibration process refers to adjusting the intermediate discrete element model based on experimental and model results. The calibration process typically involves adjusting model parameters to ensure that the simulation results match the actual experimental results.

[0098] In this embodiment, the intermediate discrete element model is calibrated to obtain the target discrete element model. The target discrete element model obtained after calibration can accurately simulate the mechanical behavior of calcium silicate hydrate gel. The target discrete element model is optimized based on theory and experiments and can reflect the actual response of CSH gel under different loads and environmental conditions.

[0099] In the above embodiments, by introducing a viscous sliding creep mechanism, the mechanical behavior of hydrated calcium silicate gel can be simulated more accurately, reflecting the stress and strain response of the material under actual stress conditions, thus making the target discrete element model closer to actual behavior.

[0100] In one exemplary embodiment, such as Figure 6 As shown, the process of establishing the above intermediate discrete element model includes the following steps 401 to 403, wherein:

[0101] Step 401: Apply a second indenter load to the initial discrete element model until the second indenter load reaches the target value.

[0102] The target value can be 2 mN. The second indenter load refers to the external load applied to the indenter. In nanoindentation testing, the indenter applies force to press into the particle surface inside the target discrete element model.

[0103] In this embodiment of the application, a second indenter load is applied to the initial discrete element model until the second indenter load reaches the target value.

[0104] Step 402: Perform iterative calculations for each particle in the initial discrete element model. In each iteration, obtain the sliding velocity of the particle at the i-th time step, determine the friction coefficient of the particle at the i-th time step based on the sliding velocity at the i-th time step, and apply the friction coefficient of the i-th time step to the particle.

[0105] Step 403: Obtain the sliding velocity of the particle at the (i+1)th time step, determine the friction coefficient of the particle at the (i+1)th time step based on the sliding velocity at the (i+1)th time step, and apply the friction coefficient at the (i+1)th time step to the particle; until the preset time is reached to end the iteration, determine the intermediate discrete element model based on the friction coefficient and sliding velocity obtained at the end of the iteration; where i is a positive integer greater than or equal to 0.

[0106] Iterative calculation refers to the process of gradually approximating the final result by repeatedly calculating and updating the parameters or variables in the initial discrete element model. In this method, iterative calculation means continuously calculating the slip velocity and friction coefficient of the particles according to the changes in time steps until the initial discrete element model reaches the predetermined termination condition or time step number.

[0107] Slip velocity refers to the relative speed of movement of particles when relative sliding occurs between them. Slip velocity is usually measured at the contact surface between particles and represents the rate at which particles move relative to each other under load.

[0108] The coefficient of friction is a dimensionless constant relating the frictional force to the normal force between the contact surfaces of two objects. In particle contact, the coefficient of friction determines the degree of relative sliding and viscous sliding between particles. The coefficient of friction dynamically adjusts with changes in sliding velocity, therefore it needs to be recalculated at each time step.

[0109] The slip velocity at the i-th time step refers to the relative sliding velocity between particles within the i-th time step of the discrete element simulation. As the simulation progresses, the time steps advance, and the slip velocity and relative velocity between particles are calculated at each time step.

[0110] The friction coefficient at time step i refers to the friction coefficient calculated based on time step i within the simulation. The calculation of the friction coefficient typically depends on the sliding velocity and other mechanical parameters, representing the degree of resistance to sliding between particles. The friction coefficient changes dynamically within each time step and therefore needs to be updated based on the sliding velocity at each time step.

[0111] The sliding velocity at time step i+1 refers to the relative sliding velocity between particles at time step i+1, and the friction coefficient is updated based on this velocity.

[0112] Friction coefficient at time step (i+1): The new friction coefficient is calculated based on the slip velocity at time step (i+1) and applied to the mechanical calculations between particles.

[0113] The preset time refers to the predetermined simulation time length, which is set at the beginning of the simulation to determine the time range of the simulation. This time limits the number of iterations and the scope of calculation.

[0114] Ending the iteration means that the iterative calculation stops after a preset time or number of iterations. At this point, parameters such as the friction coefficient and slip velocity obtained during the iteration process will be used to generate the final model result.

[0115] In this embodiment, iterative calculations are performed for each particle in the initial discrete element model. During each iteration, the sliding velocity of the particle at time step i is obtained, and the friction coefficient of the particle at time step i is determined based on this velocity. This friction coefficient is then applied to the particle. The sliding velocity of the particle at time step i+1 is obtained, and the friction coefficient of the particle at time step i+1 is determined based on this velocity. This friction coefficient is then applied to the particle. The iteration continues until a preset time is reached, at which point the intermediate discrete element model is determined based on the friction coefficient and sliding velocity obtained at the end of the iteration. Here, i is a positive integer greater than or equal to 0.

[0116] In some embodiments, during iterative calculations, the friction coefficient is dynamically adjusted based on the particle slip velocity and applied to the interparticle interaction until a preset iteration termination condition is met.

[0117] The key to developing a "viscous sliding" model in PFC3D is to modify the particle friction coefficient, i.e., the μ value, according to formula (4) during the PFC3D solution process. Formula (4) can be rewritten as formula (5):

[0118] μ=[ln(2s&)-ln(α)] / β (5)

[0119] At each time step, PFC3D updates the position and velocity of the particles based on the current time step increment Δt0 and the force calculated in the previous time step. After the particle velocity is updated, the relative sliding velocity s& of the particles can be obtained. The friction coefficient of each particle is calculated according to formula (5) and reassigned, and then the calculation for the next time step can be performed.

[0120] In the above embodiments, by acquiring the particle sliding velocity at each time step and adjusting the friction coefficient based on this velocity, the actual behavior of the material under dynamic loads can be captured more accurately. This time-stepping method allows the model to adjust its frictional behavior in a timely manner when subjected to load changes, simulating a more realistic material response. By iteratively calculating the friction coefficient and considering the interaction and frictional changes between particles, the model can reflect the contact and relative motion between particles in real time.

[0121] In one exemplary embodiment, the method further includes:

[0122] The sliding speed and preset time obtained at the end of the iteration are scaled using a time scaling algorithm to obtain the scaled sliding speed and scaled time.

[0123] Time scaling algorithms are used to scale or transform the time range in a simulation to adapt to different physical conditions or computational needs. In discrete element simulations, time scaling is used to accelerate the simulation process and adjust the model's response speed.

[0124] The slip velocity at the end of the iteration refers to the final velocity of interparticle slip calculated after a predetermined number of time steps (or when the simulation stops) during the iterative calculation process. Slip velocity represents the rate of relative sliding between particles and typically varies with load and time.

[0125] The preset time refers to a time range or duration of simulation set before the simulation begins. This time is usually a baseline time used for calculations and adjustments during the simulation. It can be used to determine the number of iterations, the duration of the simulation, or as a reference for time scaling. A preset time can be 180 seconds.

[0126] The scaled slip velocity is a new slip velocity obtained by adjusting the slip velocity based on a certain scaling factor after applying a time scaling algorithm. Time scaling affects the magnitude of the slip velocity, usually by compressing or expanding the time step to change the velocity variation pattern.

[0127] Scaled time refers to the simulation time adjusted using a time scaling algorithm. Scaled time is obtained by compressing or expanding a preset time, aiming to more accurately reflect the material's response characteristics or complete calculations more efficiently during the simulation. Scaled time helps in adjusting the calculation step size.

[0128] In this embodiment of the application, the sliding speed and preset time obtained at the end of the iteration are scaled based on the time scaling algorithm to obtain the scaled sliding speed and scaled time.

[0129] In some embodiments, since PFC3D uses explicit solving, the stability of the solution can only be guaranteed when the time step is less than a critical time step. Typically, the time step for PFC3D calculations is a fixed value and must not exceed the critical time step. The critical time step is related to the minimum intrinsic period of the particle model and can be simply estimated using formula (6) for a PFC3D model. crit :

[0130]

[0131] Where, m p k is the mass of the smallest or lightest particle among all particles. max Where Δt is the maximum contact stiffness of the particles, K is a stability factor less than 1, typically taken as 0.5. crit This represents the critical time step.

[0132] In some embodiments, the CSH particle density is 2600 kg / m³. 3 The particle diameter is 100 nm, and the particle mass is 1.36 × 10⁻⁶. -8 kg, particle normal contact stiffness is 1.3×10 4 N / m, from which the critical time step is calculated to be on the order of 1×10 -11 Clearly, using such a small time step results in very low computational efficiency.

[0133] Using the calculation principle of PFC3D, the simulation time of PFC can be accelerated by multiplying the particle velocity and a fixed time step (Δt0) by the same scaling factor (Γ). That is, the particle velocity is amplified by formula (7), and the time step is amplified by formula (8):

[0134] s&=Γαsinh(βμ) (7)

[0135] Δt pseudo =ΓΔt0 (8)

[0136] Where Γ is the scaling factor, Δt0 is the original time step, and Δt pseudo This represents the time step for scaling up.

[0137] When the scaling factor Γ is set to 1×10⁸, the calculation of the target discrete element model (packing density = 0.74, 0.64, 0.58) requires more than 100,000 steps to match the physical time (200 s) of the nanoindentation creep test. Therefore, setting Γ to 1×10⁸ achieves a good balance between computational efficiency and accuracy.

[0138] In the above embodiments, the time scaling algorithm modifies the relationship between the slip velocity and time by adjusting the time scale in the simulation. This can be used to improve simulation accuracy, optimize computational efficiency, or adjust the time resolution according to different physical conditions. By scaling the slip velocity at the end of the iteration, a new slip velocity can be obtained. At the same time, scaling the time allows the simulation to better adapt to preset computational requirements or real-world physical processes.

[0139] In one exemplary embodiment, such as Figure 7 As shown, the establishment of the initial discrete element model includes the following steps 501 to 505, wherein:

[0140] Step 501: Based on the wall location information and computational domain information of the obtained initial discrete element model, generate six walls.

[0141] In this context, wall location information refers to the position and shape of the physical or mathematical boundary walls in the initial discrete element model. Walls are typically used to define the computational space or the physical container of the simulation, limiting the movement range of particles and ensuring that particles do not exceed the preset space during the simulation process. Wall location information is used to generate and control the boundaries of the computational domain.

[0142] Computational domain information refers to the spatial extent and region involved in the simulation. It typically describes the physical space in the initial discrete element model and defines the geometry, size, and particle motion constraints of the simulation. The computational domain can include the physical parameters, boundary conditions, and initial conditions required for the simulation.

[0143] A six-sided wall is a cube-shaped physical or mathematical boundary composed of six planes that surrounds the computational domain and defines the space for particle movement. In discrete element simulations, the six-sided wall can serve as the boundary of the simulation, preventing particles from crossing the boundary or interacting with external objects; it is the geometric limit of the simulation space.

[0144] In this embodiment of the application, six walls are generated based on the wall location information and computational domain information of the obtained initial discrete element model. For example... Figure 8 As shown, Figure 8 This diagram illustrates the generation of a six-sided wall. The Berkovich indenter is a triangular pyramid shape with a sharp tip, used for high-precision indentation measurements. Wall servoing is an application that uses the wall as a boundary or constraint, equipped with servo control to precisely control the wall's position, speed, or force.

[0145] The initial particle model was generated using PFC3D software. First, the boundary of the initial discrete element model was defined (e.g., 5200×5200×5200 nm). 3Generate 6 boundary walls with the following IDs: left wall = 1, right wall = 2, front wall = 3, back wall = 4, top wall = 5, bottom wall = 6.

[0146] Step 502: Within the cubic space surrounded by six walls, generate a basic discrete element model based on a pre-defined porosity.

[0147] Porosity refers to the ratio of the volume of pores within a material to its total volume, representing the spatial distribution between particles. Porosity determines the size and distribution of the gaps between particles. A preset porosity can influence the initial arrangement and density of particles in a basic discrete element model.

[0148] In this embodiment of the application, a basic discrete element model is generated based on a pre-set porosity within a cubic space surrounded by six walls.

[0149] like Figure 9 As shown, Figure 9 This diagram illustrates a six-sided wall with different porosities (e.g., 26%, 36%, 42%). Within the cubic space enclosed by the six walls, a basic discrete element model with a particle diameter of 100 nm is generated according to the specified porosity. The packing density is defined as 1 minus the porosity; when the porosity is 26%, 36%, and 42%, the packing densities are 0.74, 0.64, and 0.58, respectively.

[0150] Step 503: Obtain the contact mechanics parameters of the basic discrete element model.

[0151] Contact mechanics parameters describe the physical and mechanical properties of particles in contact with each other. Common contact mechanics parameters include elastic modulus, coefficient of friction, contact stiffness, and viscous force. These parameters determine the strength and nature of the interaction between particles. Contact mechanics parameters affect the mechanical response between particles, such as collision, compression, and slippage.

[0152] In this embodiment, the contact mechanical parameters of the basic discrete element model are obtained. The contact mechanical parameters of the basic discrete element model are assigned values, which can be: the effective modulus of the particle model is 65 GPa, the normal contact stiffness of the particle is 1.3 × 10⁴ N / m, the tangential contact stiffness of the particle is 3.71 × 10³ N / m, the initial friction coefficient between particles is 0.8, the friction coefficient between particles and the wall is 0.33, and the particle density (ρ) is 2600 kg / m³.

[0153] Step 504: Control the particles in the basic discrete element model to bounce off in the computational domain until the particles in the basic discrete element model move to an equilibrium state.

[0154] In discrete element method (DEM) simulations, particle separation refers to the process of applying forces or adjusting the interactions between particles to separate them from their contact state. Typically, particle separation is used to eliminate excessive overlap or unreasonable initial contact states between particles, ensuring a more natural and reasonable particle distribution.

[0155] Equilibrium state refers to a stable state in which the motion of particles reaches a equilibrium during the simulation process. This means that the relative motion of all particles tends to zero, and the mechanical interactions between particles are in balance. Equilibrium state typically implies that the interaction forces between particles no longer change significantly, entering a stable state where rapid motion or large-amplitude changes cease.

[0156] In this embodiment, the particles in the basic discrete element model are controlled to bounce off the computational domain until the particles in the basic discrete element model move to an equilibrium state.

[0157] In some embodiments, the particles are allowed to bounce freely within the computational domain until the ratio of the average unbalanced force to the average total force of all particles is less than 1 × 10⁻⁶. -4 .

[0158] Step 505: Set the velocity of all particles in the basic discrete element model to a preset value to obtain the initial discrete element model.

[0159] The preset value can be 0.

[0160] In this embodiment of the application, the velocities of all particles in the basic discrete element model are set to preset values ​​to obtain the initial discrete element model.

[0161] In some embodiments, the wall servo stress can be adjusted to bring the coordination number (CN) of the particle model to a target value. The coordination number reflects the contact density between particles and is calculated using formula (9):

[0162]

[0163] Where Nc is the total number of contacts in the particle model (particle assembly); Np is the total number of particles.

[0164] The method to control the CN value is to move the six boundary walls, generating servo (constraint) stress on the particle model, changing the size of the space enclosed by the walls, thereby changing the overlap between particles and adjusting the CN distribution. The target CN value mainly depends on the cohesion between CSH particles, and the calculation formula is formula (10):

[0165]

[0166] Where CNtarget is the target value of CN; Fn is the cohesive force between CSH particles; σc is the servo (constraint) stress of the boundary wall; Dp is the diameter of the CSH particles; ρ packing This refers to the bulk density.

[0167] For CSH particle models with porosities of 26%, 36%, and 42%, experimental studies showed that the cohesive forces between CSH particles were 100.5 nN, 43 nN, and 31.5 nN, respectively, and the CN values ​​were 7.39, 5.71, and 4.21, respectively. According to formula (10), the applied wall servo stresses could be calculated to be 105 MPa, 30 MPa, and 15 MPa, respectively. After applying the above wall servo stresses to the CSH particle model, the CN value of each particle was monitored and visualized. The final CN distribution is shown below. Figures 10a-10c As shown, where, Figure 10a Visualization of the coordination number and corresponding histogram for a particle model with a bulk density of 0.74; Figure 10b Visualization of the coordination number and corresponding histogram for a particle model with a packing density of 0.64; Figure 10c Visualization of the coordination number and corresponding histogram for a particle model with a packing density of 0.58. From Figures 10a-10c It can be seen that the method provided in the embodiments of this application can achieve accurate control of the CN value.

[0168] A nanoindentation creep test was simulated. A Berkovich indenter (wall id=7) was generated, and the loading, holding, and unloading processes of the nanoindentation creep test were realized by moving the indenter. Since the PFC calculation uses a kinetic method, stress waves are generated inside the particle model during the initial stage of indenter descent, resulting in oscillations in the contact force curve between the wall and particles. To address this issue, a constant pressure gradient loading mode was adopted, in which the indenter speed gradually increases from 0 to a specified loading rate. Once the specified loading rate is reached, the indenter moves at a constant speed until the indenter force reaches 2 mN. Then, the servo control mode of the indenter is activated, i.e., the holding phase. When the (time-scaled) holding time reaches 180 s, the servo control mode of the indenter is deactivated, and unloading is achieved by moving the indenter upwards.

[0169] During loading, holding, and unloading, a servo mechanism maintains a constant confining pressure for all six walls (id=1-6) of the model. However, as the pressure head descends and rises, the contact area between the top wall (id=5) and the particle model continuously changes. Therefore, it is necessary to monitor this contact area in real time within the PFC to ensure that the servo stress remains constant on the actual contact surface. To this end, walls 1-6 and wall 7 (pressure head) employ two independent servo mechanisms, enabling the above process to be implemented accurately and efficiently.

[0170] In the above embodiments, by optimizing the construction of the initial discrete element model, the physical realism and mechanical accuracy of the initial discrete element model can be significantly improved, thereby helping to reduce dependence on experimental equipment and reduce R&D costs.

[0171] In one exemplary embodiment, such as Figure 11 As shown, the above calibration process for the intermediate discrete element model to obtain the target discrete element model includes the following steps 601 to 602, wherein:

[0172] Step 601: Input the head load of the bearing stage into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function.

[0173] Experimental results refer to data or measurement results obtained through experimental methods. These results are primarily used to compare with simulation results and to correct creep parameters.

[0174] In this embodiment of the application, the head load during the holding stage is input into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function.

[0175] Step 602: Based on the pre-acquired simulation results, the creep parameters corresponding to the experimental results are corrected to obtain the target discrete element model; the creep parameters include at least activation energy, unit normal contact force, and flow unit.

[0176] Creep parameters are physical quantities that describe how hydrated calcium silicate gel deforms over time or responds to external loads during stress. In this method, creep parameters refer to specific parameters that influence contact creep behavior. Creep parameters typically include the viscoelastic characteristics of the material, used to characterize how the material undergoes long-term deformation or stress relaxation in response to external forces.

[0177] Activation energy refers to the energy threshold that a particle must overcome to undergo a series of mechanical or thermal processes. In creep models, activation energy reflects the energy required for hydrated calcium silicate gels to transition from one state to another, and it is typically related to interparticle interactions, deformability, or reaction rate.

[0178] Unit normal contact force refers to a unit measure of the normal (perpendicular to the contact plane) contact force between particles in a discrete element model. In the simulation, the normal force between particles is generated by their interactions (such as elastic forces, viscous forces, or frictional forces). Unit normal contact force is used to describe the strength of the contact between particles.

[0179] A flow unit is a physical quantity that describes the flow or slip behavior between particles. Flow units typically relate to the flow characteristics of materials or particles in the contact region, such as rheological parameters and deformation rates. Flow units help describe changes in materials under long-term loading, including characteristics such as fluidity and viscosity.

[0180] In this embodiment of the application, the creep parameters corresponding to the experimental results are corrected based on the pre-acquired simulation results to obtain the target discrete element model.

[0181] In some embodiments, simulation results of the contact creep function [L(t)-L(0)] for CSH particle models with different packing densities can be obtained. Taking a CSH particle model with a packing density of 0.64 as an example, when the flow element λ = 0.28 nm, the number of bonds corresponding to the unit normal contact force n1 = 1 × 10 9 When the activation energy ΔF = 123.8 kJ / mol, the simulated curve of [L(t) - L(0)] is in excellent agreement with the experimental results, such as... Figure 12 As shown in the figure, the duration of the PFC simulation is 1.8 × 10⁻⁶. -6 After time scaling (scaling factor Γ = 1 × 10⁸), the duration is 180 s, which perfectly matches the duration of the experiment.

[0182] In some embodiments, the parameters involved in the "viscous slip" creep mechanism are shown in formulas (3) and (4), comprising a total of 7 parameters. Among them, k, R, h, and T are constants with the following values: Boltzmann constant k = 1.381 × 10⁻²³ J / K, absolute temperature T = 295.15 K; Planck constant h = 6.626 × 10⁻³⁴ J·s, ideal gas constant R = 8.314 × 10⁻³ kJ / mol / K. The remaining λ, n₁, and ΔF are unknown variables that require calibration. λ, n₁, and ΔF represent the number of bonds and activation energy corresponding to the unit flow unit and unit normal contact force, respectively.

[0183] The calibration process involves simulating nanoindentation creep tests using PFC3D. At each time step, the indenter load (P), the indenter displacement (h) corresponding to the displacement change function h, and the indentation contact area (Ac, which is the vertical projection area of ​​the contact surface between the indenter and the CSH particles) corresponding to the contact area function of the nanoindentation are recorded. The contact creep function [L(t)-L(0)] can be calculated based on P, h, and Ac. By changing the values ​​of λ, n1, and ΔF, the parameters α and β in formula (4) change accordingly, and the simulated contact creep function [L(t)-L(0)] also changes accordingly. Through trial and error, the values ​​of λ, n1, and ΔF are adjusted multiple times until the calculated contact creep function [L(t)-L(0)] matches the experimental results, thus completing the calibration.

[0184] In the above embodiments, by inputting the indenter load of the bearing stage into the intermediate discrete element model and determining the corresponding contact creep function, the simulation results are compared with the actual experimental data, and the experimental data are corrected based on the pre-acquired simulation results. This correction method can effectively eliminate the deviation in the simulation process, making the creep parameters more consistent with the actual material behavior and improving the accuracy and reliability of the simulation.

[0185] According to some embodiments of this application, a method for simulating nanoindentation creep of hydrated calcium silicate gel based on a discrete element model is provided. Taking the application of this method to a computer device as an example, it may include the following steps:

[0186] Step 1: Based on the wall location information and computational domain information obtained from the initial discrete element model, generate six walls.

[0187] Step 2: Within the cubic space surrounded by six walls, generate a basic discrete element model based on a pre-defined porosity.

[0188] Step 3: Obtain the contact mechanics parameters of the basic discrete element model.

[0189] Step 4: Control the particles in the basic discrete element model to bounce off in the computational domain until the particles in the basic discrete element model move to an equilibrium state.

[0190] Step 5: Set the velocity of all particles in the basic discrete element model to a preset value to obtain the initial discrete element model.

[0191] Step 6: Apply a second indenter load to the initial discrete element model until the second indenter load reaches the target value.

[0192] Step 7: Perform iterative calculations for each particle in the initial discrete element model. In each iteration, obtain the sliding velocity of the particle at the i-th time step, determine the friction coefficient of the particle at the i-th time step based on the sliding velocity at the i-th time step, and apply the friction coefficient of the i-th time step to the particle.

[0193] Step 8: Obtain the sliding velocity of the particle at time step i+1. Determine the friction coefficient of the particle at time step i+1 based on the sliding velocity at time step i+1, and apply the friction coefficient of time step i+1 to the particle. Continue iterating until a preset time is reached to end the iteration. Determine the intermediate discrete element model based on the friction coefficient and sliding velocity obtained at the end of the iteration. Here, i is a positive integer greater than or equal to 0.

[0194] Step 9: Based on the time scaling algorithm, scale the sliding speed and preset time obtained at the end of the iteration to obtain the scaled sliding speed and scaled time.

[0195] Step 10: Input the head load of the bearing stage into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function.

[0196] Step 11: Based on the pre-acquired simulation results, the creep parameters corresponding to the experimental results are corrected to obtain the target discrete element model. The creep parameters include at least the activation energy, unit normal contact force, and flow unit.

[0197] Step 12: Input the first indentation load of the holding stage into the target discrete element model pre-established for hydrated calcium silicate gel to determine the displacement change function of the indentation head during the holding stage.

[0198] Step 13: Based on the displacement change function, determine the contact area function of the nanoindentation at the end of the load holding period.

[0199] Step 14: Determine the contact creep function of the hydrated calcium silicate gel based on the indenter load, displacement change function, and contact area function of nanoindentation.

[0200] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0201] Based on the same inventive concept, this application also provides a discrete element model-based device for simulating the nanoindentation creep of hydrated calcium silicate gel based on the discrete element model, for implementing the aforementioned method. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the discrete element model-based device for simulating nanoindentation creep of hydrated calcium silicate gel provided below can be found in the limitations of the discrete element model-based method for simulating nanoindentation creep of hydrated calcium silicate gel described above, and will not be repeated here.

[0202] In one exemplary embodiment, such as Figure 13As shown, a hydration calcium silicate gel nanoindentation creep simulation device based on a discrete element model is provided, comprising: a displacement change function determination module 701, a contact area function determination module 702, and a contact creep function determination module 703, wherein:

[0203] The displacement change function determination module 701 is used to input the first indentation load of the holding stage into the target discrete element model pre-established for hydrated calcium silicate gel to determine the displacement change function of the indentation during the holding stage.

[0204] The contact area function determination module 702 is used to determine the contact area function of the nanoindentation at the end of the load based on the displacement change function;

[0205] The contact creep function determination module 703 is used to determine the contact creep function of hydrated calcium silicate gel based on indenter load, displacement change function and contact area function of nanoindentation.

[0206] The modules in the aforementioned discrete element model-based hydrated calcium silicate gel nanoindentation creep simulation device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0207] According to some embodiments of this application, a computer device is also provided, including a memory and a processor. The memory stores a computer program, which, when executed by the processor, can implement the methods described above. The computer program product includes one or more computer instructions. When these computer instructions are loaded and executed on a computer, some or all of the methods described above can be implemented, wholly or partially, according to the processes or functions described in the embodiments of this application.

[0208] According to some embodiments of this application, a non-transitory computer-readable storage medium including instructions is also provided, such as a memory including instructions that can be executed by a processor of an electronic device to perform the above-described method. For example, the non-transitory computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device, etc.

[0209] According to some embodiments of this application, a computer program product is also provided, which, when executed by a processor, can implement the above-described methods. The computer program product includes one or more computer instructions. When these computer instructions are loaded and executed on a computer, some or all of the above-described methods can be implemented, wholly or partially, according to the processes or functions described in the embodiments of this application.

[0210] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0211] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0212] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for simulating nanoindentation creep of hydrated calcium silicate gel based on discrete element model, characterized in that, The method includes: The first indentation load of the holding stage is input into the target discrete element model pre-established for hydrated calcium silicate gel to determine the displacement change function of the indentation during the holding stage; Based on the displacement change function, the contact area function of the nanoindentation at the end of the load holding period is determined; The contact creep function of the hydrated calcium silicate gel is determined based on the indenter load, the displacement change function, and the contact area function of the nanoindentation. The process of establishing the target discrete element model includes: An initial discrete element model was established for the hydrated calcium silicate gel; A viscous sliding creep mechanism is established in the initial discrete element model to obtain an intermediate discrete element model; the viscous sliding creep mechanism is used to change the contact relationship between particles in the initial discrete element model. The intermediate discrete element model is calibrated to obtain the target discrete element model; The establishment of the initial discrete element model includes: Based on the wall location information and computational domain information of the obtained initial discrete element model, six walls are generated; Within the cubic space enclosed by the six walls, a basic discrete element model is generated based on a pre-defined porosity. Obtain the contact mechanics parameters of the basic discrete element model; The particles in the basic discrete element model are controlled to bounce off in the computational domain until the particles in the basic discrete element model move to an equilibrium state. The initial discrete element model is obtained by setting the velocities of all particles in the basic discrete element model to preset values.

2. The method according to claim 1, characterized in that, The process of establishing the intermediate discrete element model includes: A second indentation load is applied to the initial discrete element model until the second indentation load reaches the target value; For each particle in the initial discrete element model, iterative calculations are performed. In each iteration, the sliding velocity of the particle at the i-th time step is obtained. The friction coefficient of the particle at the i-th time step is determined based on the sliding velocity at the i-th time step, and the friction coefficient at the i-th time step is applied to the particle. The sliding velocity of the particle at the (i+1)th time step is obtained, the friction coefficient of the particle at the (i+1)th time step is determined based on the sliding velocity at the (i+1)th time step, and the friction coefficient at the (i+1)th time step is applied to the particle; the iteration ends when a preset time is reached, and the intermediate discrete element model is determined based on the friction coefficient and sliding velocity obtained at the end of the iteration; where i is a positive integer greater than or equal to 0.

3. The method according to claim 2, characterized in that, The method further includes: The sliding speed and the preset time obtained at the end of the iteration are scaled based on the time scaling algorithm to obtain the scaled sliding speed and the scaled time.

4. The method according to claim 1, characterized in that, The calibration process for the intermediate discrete element model to obtain the target discrete element model includes: The indentation load during the bearing stage is input into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function; Based on the pre-acquired simulation results, the creep parameters corresponding to the experimental results are corrected to obtain the target discrete element model; the creep parameters include at least the activation energy, the number of bonds corresponding to the unit normal contact force, and the flow unit.

5. A device for simulating nanoindentation creep of hydrated calcium silicate gel based on a discrete element model, characterized in that, The device includes: The displacement change function determination module is used to input the first indentation load of the bearing stage into the target discrete element model pre-established for hydrated calcium silicate gel, and determine the displacement change function of the indentation head during the bearing stage; The contact area function determination module is used to determine the contact area function of the nanoindentation at the end of the load holding based on the displacement change function. The contact creep function determination module is used to determine the contact creep function of the hydrated calcium silicate gel based on the indenter load, the displacement change function, and the contact area function of the nanoindentation. The displacement change function determination module is used to establish an initial discrete element model for the hydrated calcium silicate gel. A viscous sliding creep mechanism is established in the initial discrete element model to obtain an intermediate discrete element model; the viscous sliding creep mechanism is used to change the contact relationship between particles in the initial discrete element model. The intermediate discrete element model is calibrated to obtain the target discrete element model; Based on the wall location information and computational domain information of the obtained initial discrete element model, six walls are generated; Within the cubic space enclosed by the six walls, a basic discrete element model is generated based on a pre-defined porosity. Obtain the contact mechanics parameters of the basic discrete element model; The particles in the basic discrete element model are controlled to bounce off in the computational domain until the particles in the basic discrete element model move to an equilibrium state. The initial discrete element model is obtained by setting the velocities of all particles in the basic discrete element model to preset values.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.

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