Calcium silicate hydrate gel nanoindentation creep simulation method based on discrete element model

Abstract

The invention relates to a calcium silicate hydrate gel nanoindentation creep simulation method based on a discrete element model. The method comprises the following steps: inputting a first pressure head load in a loading stage into a target discrete element model pre-established for hydrated calcium silicate gel, and determining a displacement change function of a pressure head in the loading stage; based on the displacement change function, determining a contact area function of the nanoindentation at the end of loading; and determining the contact creep function of the hydrated calcium silicate gel based on the pressure head load, the displacement change function and the contact area function of the nanoindentation. By adopting the method, the test cost can be reduced.

Description

Technical Field

[0001] The present application relates to the technical field of cement-based material mechanics, and in particular to a method for simulating the nanoindentation creep of calcium silicate hydrate gel based on a discrete element model. Background Art

[0002] At present, it is generally believed that the creep performance of concrete is mainly related to calcium silicate hydrate gel (CSH). At present, the main method for testing CSH creep is nanoindentation creep test. The CSH micro creep parameters measured by this technology can be used as input parameters of the concrete multi-scale creep model.

[0003] However, there are some disadvantages in nanoindentation creep test technology, such as: 1. Nanoindentation test equipment is expensive and usually requires high-precision testing instruments and special laboratory environment; 2. CSH sample preparation is relatively complicated, and it is necessary to ensure that the surface roughness of the sample is very low and there are no obvious defects; 3. Factors such as the sample's microstructure, humidity conditions and loading method may have a significant impact on the test results, and the repeatability is relatively poor.

[0004] In summary, although nanoindentation testing technology is an effective method to characterize the micro-creep properties of calcium silicate hydrate gel, its disadvantages such as high cost and uncertainty of test data limit its wide application. Summary of the invention

[0005] Based on this, it is necessary to provide a nanoindentation creep simulation method of calcium silicate hydrate gel based on discrete element model that can reduce the experimental cost in order to address the above technical problems.

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

[0007] Inputting the first pressure head load in the loading stage into the target discrete element model established in advance for the calcium silicate hydrate gel, and determining the displacement change function of the pressure head in the loading stage;

[0008] Based on the displacement change function, determine the contact area function of the nanoindentation at the end of the loading;

[0009] The contact creep function of calcium silicate hydrate gel is determined based on the indenter load, displacement change function and contact area function of nanoindentation.

[0010] In one embodiment, the process of establishing the target discrete element model includes:

[0011] An initial discrete element model was established for hydrated 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 intermediate discrete element model includes:

[0015] Applying a second indenter load to the initial discrete element model until the second indenter load reaches a target value;

[0016] Iterative calculation is performed for each particle in the initial discrete element model. In each round of 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;

[0017] The sliding velocity of the particle at the i+1th time step is obtained, the friction coefficient of the particle at the i+1th time step is determined based on the sliding velocity at the i+1th time step, and the friction coefficient at the i+1th time step is applied to the particle; the iteration ends until a preset time is reached, and an intermediate discrete element model is determined based on the friction coefficient and sliding velocity obtained when the iteration ends; wherein i is a positive integer greater than or equal to 0.

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

[0019] The sliding speed and the preset time obtained when the iteration ends are scaled based on the time scaling algorithm to obtain the scaled sliding speed and the scaled time.

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

[0021] Based on the obtained wall position information and computational domain information of the initial discrete element model, six walls are generated;

[0022] In a cubic space surrounded by six walls, a basic discrete element model is generated based on a pre-set 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 in the computational domain until the particles in the basic discrete element model move to a balanced state;

[0025] The velocities of all particles in the basic discrete element model are set to preset values ​​to obtain an initial discrete element model.

[0026] In one embodiment, the calibrating the intermediate discrete element model to obtain the target discrete element model includes:

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

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

[0029] In a second aspect, the present application also provides a calcium silicate hydrate gel nanoindentation creep simulation device based on a discrete element model, comprising:

[0030] A displacement change function determination module is used to input the first pressure head load in the loading stage into a target discrete element model pre-established for calcium silicate hydrate gel to determine the displacement change function of the pressure head in the loading stage;

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

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

[0033] In a third aspect, the present application further provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements any one of the methods in the first aspect when executing the computer program.

[0034] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the method of any one of the first aspects is implemented.

[0035] In a fifth aspect, the present application further provides a computer program product, comprising a computer program, which implements any one of the methods in the first aspect when the computer program is executed by a processor. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments of the present application or related technical descriptions will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

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

[0038] Figure 2 Schematic diagram of a process of a nanoindentation creep simulation method of calcium silicate hydrate gel based on a discrete element model in one embodiment;

[0039] Figure 3 A schematic diagram of the indentation contact area corresponding to the contact area function of nanoindentation at any time step in one embodiment;

[0040] Figure 4 A schematic diagram of a process flow of a method for simulating nanoindentation creep of calcium silicate hydrate gel based on a discrete element model in another embodiment;

[0041] Figure 5 A schematic diagram of a process for developing a viscous sliding creep mechanism in an initial discrete element model in one embodiment;

[0042] Figure 6 A schematic diagram of a process flow of a method for simulating nanoindentation creep of calcium silicate hydrate gel based on a discrete element model in another embodiment;

[0043] Figure 7 A schematic diagram of a process flow of a method for simulating nanoindentation creep of calcium silicate hydrate gel based on a discrete element model in another embodiment;

[0044] Figure 8 A schematic diagram of generating six walls in one embodiment;

[0045] Fig. 9 A schematic diagram of six walls corresponding to different porosities in one embodiment;

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

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

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

[0049] Fig.11 A schematic diagram of a process flow of a method for simulating nanoindentation creep of calcium silicate hydrate gel based on a discrete element model in another embodiment;

[0050] Fig.12 A schematic diagram showing the comparison between simulation results and experimental results in one embodiment;

[0051] Fig.13It is a structural block diagram of a calcium silicate hydrate gel nanoindentation creep simulation device based on a discrete element model in one embodiment. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0053] At present, it is generally believed that the creep performance of concrete is mainly related to calcium silicate hydrate gel (CSH). At present, the main means of testing CSH creep is nanoindentation creep test. The CSH micro creep parameters measured by this technology can be used as input parameters of the multi-scale creep model of concrete. However, there are some disadvantages in the nanoindentation creep test technology, such as: 1. Nanoindentation test equipment is expensive, usually requiring high-precision testing instruments and special laboratory environment; 2. The sample preparation of CSH gel is relatively complicated, and it is necessary to ensure that the surface roughness of the sample is very low and there are no obvious defects; 3. The microstructure, humidity conditions and loading method of the sample may have a significant impact on the test results, and the repeatability is relatively poor. In summary, although the nanoindentation test technology is an effective method to characterize the micro creep performance of calcium silicate hydrate gel, its high cost and uncertainty of test data limit its wide application. Therefore, it is of scientific value to perform numerical simulation of CSH nanoindentation creep test.

[0054] The classic CSH gel model assumes that the smallest structural unit of CSH gel is a spherical particle. According to the different packing densities of gel particles, CSH is divided into three types: low-density CSH, high-density CSH, and ultra-high-density CSH. The embodiment of the present application proposes a CSH nanoindentation creep test simulation method based on a discrete element model, which is modeled by micromechanical analysis (Particle Flow Code 3D, PFC3D) software. The model can design different CSH gel particle packing densities and CSH cohesion, accurately simulate the indentation creep performance of CSH, and promote the development of multi-scale modeling methods for concrete creep.

[0055] The present application proposes a nanoindentation creep simulation scheme for calcium silicate hydrate gel based on a discrete element model, which includes: inputting the first indenter load in the loading stage into the target discrete element model pre-established for the calcium silicate hydrate gel, determining the displacement change function of the indenter in the loading stage; determining the contact area function of the nanoindentation at the end of the loading based on the displacement change function; determining the contact creep function of the calcium silicate hydrate gel based on the indenter load, the displacement change function and the contact area function of the nanoindentation. With this scheme, the mechanical behavior of the calcium silicate hydrate gel can be simulated in a virtual environment through the established target discrete element model, thereby reducing the dependence on expensive experimental equipment and significantly reducing the investment in experimental equipment and resources.

[0056] In an exemplary embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as shown in FIG. Figure 1 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. Among them, the processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store data in the process of nanoindentation creep simulation of hydrated calcium silicate gel based on a discrete element model. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for simulating nanoindentation creep of hydrated calcium silicate gel based on a discrete element model is implemented.

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

[0058] In an exemplary embodiment, Figure 2 As shown in the figure, a method for simulating the nanoindentation creep of calcium silicate hydrate gel based on discrete element model is provided. Figure 1 The computer device in the example is used to illustrate, including the following steps 201 to 203. Among them:

[0059] Step 201 : inputting the first pressure head load in the loading stage into the target discrete element model established in advance for the calcium silicate hydrate gel, and determining the displacement variation function of the pressure head in the loading stage.

[0060] The first indenter load refers to the external load applied to the indenter. In the nanoindentation test, the indenter presses into the particle surface inside the target discrete element model by applying force.

[0061] Hydrated calcium silicate gel is a major product formed during cement hydration and is the key component that gives cement strength during cement hardening.

[0062] Discrete element method is a numerical simulation method used to simulate the behavior of granular materials (such as sand, powder, granular materials, etc.). In the discrete element method, particles are regarded as independent discrete objects, and the mechanical behavior of objects is simulated by the interaction force between nodes. The target discrete element model refers to a discrete element model established for simulating the mechanical behavior of hydrated calcium silicate gel based on its characteristics.

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

[0064] In the embodiment of the present application, the first pressure head load in the loading stage is input into the target discrete element model pre-established for the calcium silicate hydrate gel to determine the displacement change function of the pressure head in the loading stage.

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

[0066] Step 202, based on the displacement change function, determine the contact area function of the nanoindentation at the end of the loading.

[0067] Among them, nanoindentation is an accurate 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 at a very small depth, and the load and displacement data can be used to deduce the mechanical properties of the material.

[0068] The contact area refers to the area of ​​contact between the indenter and the surface of the calcium silicate hydrate gel. During the nanoindentation process, as the load increases, the indenter will become deeper and deeper, and the contact area will increase accordingly. The contact area function describes the law of change of the contact area between the indenter and the material surface with displacement.

[0069] In the embodiment of the present application, based on the displacement change function, the contact area function of the nanoindentation at the end of the loading can be determined.

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

[0071] The calculation of the contact area function of nanoindentation can be indirectly determined by the displacement change function and the indenter shape function. Figure 3 As shown, Figure 3 In the figure, h is the displacement of the indenter corresponding to the displacement change function, and Ac is the contact area of ​​the nanoindentation corresponding to the contact area function. Ac at any time step can be identified by processing the micromechanical analysis software. Figure 3 The triangular area in represents the vertical projection of the contact surface between the indenter and the CSH particle, i.e., Ac. Each dot in the triangular area 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] Among them, h is the indenter displacement corresponding to the displacement change function, and Ac is the indentation contact area corresponding to the contact area function of nanoindentation.

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

[0075] Among them, contact creep refers to the chronic deformation of the material due to the viscoelastic behavior of the material within a certain period of time after the load is applied. Creep usually manifests itself as a gradual and slow deformation of the material under long-term load. The contact creep function is a mathematical function that describes the creep behavior of calcium silicate hydrate gel material at the contact surface by combining the indenter load, displacement change function and contact area function. This function can describe the deformation characteristics of the material under long-term load.

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

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

[0078]

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

[0080] In the above-mentioned discrete element model-based calcium silicate hydrate gel nanoindentation creep simulation method, the first indenter load in the loading stage is first input into the target discrete element model pre-established for the calcium silicate hydrate gel to determine the displacement change function of the indenter in the loading stage; then based on the displacement change function, the contact area function of the nanoindentation at the end of the loading is determined; finally, based on the indenter load, the displacement change function and the contact area function of the nanoindentation, the contact creep function of the calcium silicate hydrate gel is determined. In traditional methods, high-precision experimental equipment (such as nanoindenters) usually require a large amount of equipment investment and high maintenance costs, while the embodiment of the present application can simulate the mechanical behavior of calcium silicate hydrate gel in a virtual environment through the established target discrete element model, thereby reducing the dependence on expensive experimental equipment and significantly reducing the investment in experimental equipment and resources.

[0081] In an exemplary embodiment, Figure 4 As shown, the process of establishing the target discrete element model includes the following steps 301 to 303, wherein:

[0082] Step 301: Establish an initial discrete element model for calcium silicate hydrate 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] Among them, viscous sliding refers to the phenomenon that at the contact point between particles, due to the viscous properties of the material, there will be relative sliding between particles. This sliding is caused by external loads or the fluidity and hysteresis behavior of the material itself. In particle interactions, viscous sliding affects the relative position and contact state of the particles. The creep mechanism refers to the slow and continuous deformation process of the material under long-term loading. Creep is usually related to the viscoelastic properties of the material, that is, the material gradually undergoes plastic or elastic deformation over time after being subjected to a constant load. The viscous sliding creep mechanism is a mechanism that describes the long-term deformation and sliding of particles at the contact point. The viscous sliding creep mechanism is introduced in the discrete element model to simulate the changes in the contact relationship between particles under the action of long-term loads. By introducing the effects of sliding and creep, the mechanical behavior and deformation process of CSH gel under long-term loading can be more accurately described.

[0085] The intermediate discrete element model is an intermediate version of the discrete element model obtained by introducing the viscous sliding creep mechanism based on the initial discrete element model. It is based on the initial discrete element model and adds new parameters and mechanical mechanisms of material creep and sliding behavior, which can better simulate the behavior of CSH gel in complex mechanical environments.

[0086] In the embodiment of the present application, an initial discrete element model is established for calcium silicate hydrate gel. Then, a viscous sliding creep mechanism is established in the initial discrete element model to obtain an intermediate discrete element model.

[0087] It should be noted that the viscous sliding creep mechanism is based on the rate process theory, which is expressed in 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); n1 is the number of bonds corresponding to the unit normal contact force (bonds / N); is the ratio of the tangential force to the normal force at the particle contact point.

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

[0091]

[0092] in,

[0093] Formulas (3) and (4) show that the slip velocity between particles is determined by the ratio of the tangential contact force to the normal contact force. Under the action of external forces, as the creep deformation of the particle aggregate proceeds, the particles continue to rearrange, 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, which in turn leads to a decrease in the creep deformation rate of the particle model.

[0094] The present application embodiment develops a "viscous sliding" contact model in PFC3D (i.e., establishes a viscous sliding creep mechanism). Figure 5 As shown, in Figure 5 In the example, RPT unit is the rate process theory unit, f t is the tangential force at the particle contact point, f n is the normal force at the particle contact point, k n is the stiffness of the linear spring, kt is the stiffness of the linear spring, δ n is the tangential relative distance between particles, δ t is the normal relative distance between particles, and u is the particle friction coefficient.

[0095] exist Figure 5 In the example, we use a stiffness k n The normal contact is represented by a linear spring with stiffness k. t The linear spring is represented by a rate process theory unit in series. The sliding speed of the rate process theory unit is controlled by the ratio of the tangential force to the normal force at the contact point, that is, formula (3). In the process of creep deformation, the friction coefficient of the particle is not a fixed value, but decreases with the decrease of the particle tangential force and the slip rate at the contact point.

[0096] Step 303: calibrate the intermediate discrete element model to obtain a target discrete element model.

[0097] The calibration process refers to the process of adjusting the intermediate discrete element model through experimental results and model results. The calibration process usually includes adjusting the model parameters so that the simulation results are consistent with the actual experimental results.

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

[0099] In the above embodiment, by introducing the viscous sliding creep mechanism, the mechanical behavior of calcium silicate hydrate gel can be simulated more accurately, and the stress and strain response of the material under actual stress conditions can be reflected, so that the target discrete element model is closer to the actual behavior.

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

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

[0102] The target value may be 2 mN. The second indenter load refers to an external load applied to the indenter. In the nanoindentation test, the indenter presses into the particle surface inside the target discrete element model by applying force.

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

[0104] Step 402, performing iterative calculation for each particle in the initial discrete element model, in each round of iteration, obtaining the slip velocity of the particle at the i-th time step, determining the friction coefficient of the particle at the i-th time step based on the slip velocity at the i-th time step, and applying the friction coefficient at the i-th time step to the particle.

[0105] Step 403, obtaining the slip velocity of the particle at the i+1th time step, determining the friction coefficient of the particle at the i+1th time step based on the slip velocity at the i+1th time step, and applying the friction coefficient at the i+1th time step to the particle; until the iteration ends at a preset time, determining the intermediate discrete element model based on the friction coefficient and slip velocity obtained when the iteration ends; wherein i is a positive integer greater than or equal to 0.

[0106] Among them, iterative calculation refers to the process of gradually approaching the final result by repeatedly calculating and updating the parameters or variables in the initial discrete element model. In this method, iterative calculation refers to continuously calculating the sliding velocity and friction coefficient of the particles according to the change of the time step until the initial discrete element model reaches the predetermined end condition or time step number.

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

[0108] The coefficient of friction is a dimensionless constant that describes the relationship between the friction force and 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 is dynamically adjusted as the sliding velocity changes, so 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 in the i-th time step of the discrete element simulation. As the simulation progresses, the time step will advance, and the slip and relative velocity between particles will be calculated at each time step.

[0110] The friction coefficient at the i-th time step refers to the friction coefficient calculated based on the i-th time step in the simulation. The calculation of the friction coefficient usually depends on the slip velocity and other mechanical parameters, indicating the degree of resistance to sliding between particles. In each time step, the friction coefficient changes dynamically, so it needs to be updated according to the slip velocity at each time step.

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

[0112] Friction coefficient at the i+1th time step: Based on the slip velocity at the i+1th time step, a new friction coefficient is calculated and applied to the mechanical calculation between particles.

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

[0114] Ending iteration means that the iterative calculation stops after reaching the preset time or number of times. At this time, the friction coefficient and sliding speed in the iterative process will be used to generate the final model results.

[0115] In the embodiment of the present application, an iterative calculation is performed for each particle in the initial discrete element model. In each round of iteration, the sliding speed 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 speed of the i-th time step, and the friction coefficient of the i-th time step is applied to the particle. The sliding speed 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 speed of the i+1-th time step, and the friction coefficient of the i+1-th time step is applied to the particle; until the preset time is reached, the iteration ends, and the intermediate discrete element model is determined based on the friction coefficient and sliding speed obtained when the iteration ends; wherein i is a positive integer greater than or equal to 0.

[0116] In some embodiments, in iterative calculations, the friction coefficient is dynamically adjusted based on the sliding velocity of the particles and applied to the interaction between the particles until a preset iteration end condition is reached.

[0117] The key to developing a "sticky sliding" model in PFC3D is to modify the particle friction coefficient, i.e., the μ value, according to formula (4) during the solution process of PFC3D. 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 particle based on the current time step increment Δt0 and the force calculated at the previous time step. After the particle velocity is updated, the relative slip velocity s& of the particle can be obtained. The friction coefficient of each particle is calculated and reassigned according to formula (5), and then the calculation of the next time step can be performed.

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

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

[0122] The sliding speed and the preset time obtained when the iteration ends are scaled based on the time scaling algorithm to obtain the scaled sliding speed and the scaled time.

[0123] Among them, the time scaling algorithm is used to scale or convert the time range in the simulation to adapt to different physical conditions or computing requirements. In discrete element simulation, time scaling is used to speed up the simulation process and adjust the model response speed.

[0124] The slip velocity at the end of the iteration refers to the final velocity of the inter-particle slip calculated after a predetermined number of time steps (or when the simulation stops) during the iterative calculation process. The slip velocity indicates the relative sliding rate between particles, which usually changes with the load and time.

[0125] The preset time refers to a time range or simulation duration set before starting the simulation. This time is usually the benchmark time used for calculation and adjustment during the simulation process. It can be used to determine the number of iterations, the duration of the simulation, or as a reference for time scaling. The preset time can be 180 seconds.

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

[0127] The scaled time is the simulation time adjusted by the time scaling algorithm. The scaled time is obtained by compressing or expanding the preset time in order to more accurately reflect the response characteristics of the material during the simulation or to complete the calculation more efficiently. The scaled time helps to adjust the calculation step size.

[0128] In the embodiment of the present application, the sliding speed and the preset time obtained when the iteration ends are scaled based on the time scaling algorithm to obtain the scaled sliding speed and the 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. Usually, the time step of PFC3D calculation is a fixed value and must not exceed the critical time step. The critical time step is related to the minimum natural period of the particle model. Formula (6) can be used to simply estimate the critical time step Δt of a PFC3D model. crit :

[0130]

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

[0132] In some embodiments, the CSH particle density is 2600 kg / m 3 , the particle diameter is 100nm, and the particle mass is 1.36×10 -8 kg, and the particle normal contact stiffness is 1.3×10 4 N / m, from which the critical time step is calculated to be of the order of 1×10 -11 s. Obviously, using such a small time step is computationally inefficient.

[0133] Using the calculation principle of PFC3D, the particle velocity and a fixed time step (Δt0) can be multiplied by the same scaling factor (Γ) to accelerate the simulation time of PFC, 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 is the magnification time step.

[0137] When the scaling factor Γ is 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 (200s) of the nanoindentation creep test. Therefore, Γ is set to 1×108, which achieves a good balance between model calculation efficiency and accuracy.

[0138] In the above embodiment, the time scaling algorithm modifies the relationship between the slip velocity and time by adjusting the time scale in the simulation, which can be used to improve simulation accuracy, optimize calculation 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, and scaling the time enables the simulation to better adapt to the preset calculation requirements or the physical process in reality.

[0139] In an exemplary embodiment, Figure 7 As shown, the above-mentioned establishment of the initial discrete element model includes the following steps 501 to 505, wherein:

[0140] Step 501: Generate six walls based on the acquired wall position information and calculation domain information of the initial discrete element model.

[0141] The wall position information refers to the position and shape of the physical or mathematical boundary wall in the initial discrete element model. Walls are usually used to define the computational space or the physical container of the simulation, limit the movement range of particles, and ensure that the particles do not exceed the preset space during the simulation. The wall position information is used to generate and control the boundary of the computational domain.

[0142] The computational domain information refers to the spatial range and area involved in the simulation, which usually describes the physical space in the initial discrete element model and defines the geometry, size, and restrictions on particle motion of the simulation. The computational domain can include the physical parameters, boundary conditions, and initial conditions required for the simulation.

[0143] The six-sided wall is a physical or mathematical boundary in the shape of a cube composed of six planes. They surround the computational domain and limit the movement space of particles. In discrete element simulation, the six-sided wall can be used as the boundary of the simulation to prevent particles from crossing the boundary or interacting with external objects. It is the geometric limit of the simulation space.

[0144] In the embodiment of the present application, six walls are generated based on the wall position information and calculation domain information of the acquired initial discrete element model. Figure 8 As shown, Figure 8 The schematic diagram of the generation of six walls, where the Berkovich indenter is a Berkovich indenter, which is in the shape of a triangular pyramid with a sharp tip and is used for high-precision indentation measurement. Wall servo is an application that uses a wall as a boundary or constraint and is equipped with servo control to accurately control the wall position, velocity 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 3), generate 6 boundary walls, the wall ids are: left wall = 1, right wall = 2, front wall = 3, back wall = 4, top wall = 5, bottom wall = 6.

[0146] Step 502: Generate a basic discrete element model based on a preset porosity in a cubic space surrounded by six walls.

[0147] Porosity refers to the ratio of the void volume inside the material to the overall volume, indicating the spatial distribution between particles. Porosity determines the size and distribution of gaps between particles. The preset porosity can affect the initial arrangement and density of particles in the basic discrete element model.

[0148] In the embodiment of the present application, a basic discrete element model is generated based on a preset porosity in a cubic space surrounded by six walls.

[0149] like Fig. 9 As shown, Fig. 9 Schematic diagram of six walls corresponding to different porosities, considering different porosities (e.g. 26%, 36%, 42%). In the cubic space surrounded by the six walls, a basic discrete element model with a particle diameter of 100nm 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 density is 0.74, 0.64, and 0.58, respectively.

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

[0151] Among them, contact mechanics parameters refer to the physical and mechanical properties that describe the contact between particles. Common contact mechanics parameters include elastic modulus, friction coefficient, contact stiffness, viscosity, etc. 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, slip, etc.

[0152] In the embodiment of the present application, the contact mechanics parameters of the basic discrete element model are obtained. The contact mechanics parameters of the basic discrete element model are assigned values, wherein the contact mechanics parameters may 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 the particle and the particle is 0.8, the friction coefficient between the particle 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 in the computational domain until the particles in the basic discrete element model move to a balanced state.

[0154] Among them, bouncing particles means that in discrete element simulation, particles are separated from each other by applying force or adjusting the interaction between particles. Usually, bouncing is to eliminate excessive overlap or unreasonable initial contact between particles to ensure a more natural and reasonable distribution of particles.

[0155] The equilibrium state means that during the simulation, the movement of particles reaches a stable state, that is, the relative movement of all particles tends to zero, and the mechanical interaction between particles reaches equilibrium. The equilibrium state usually means that the interaction force between particles no longer changes significantly, enters a stable state, and no longer has rapid movement or large changes.

[0156] In an embodiment of the present application, particles in the basic discrete element model are controlled to bounce in the computational domain until the particles in the basic discrete element model move to a balanced state.

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

[0158] Step 505: Set the velocities of all particles in the basic discrete element model to preset values ​​to obtain an initial discrete element model.

[0159] Among them, the preset value can be 0.

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

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

[0162]

[0163] Among them, Nc is the total number of contacts in the particle model (particle aggregate); Np is the total number of particles.

[0164] The method to control the CN value is to move the six boundary walls to generate servo (constraint) stress on the particle model, change the size of the space surrounded by the wall, and thus change the overlap between particles, so as to adjust the distribution of CN. The CN target 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 particle; ρ packing is the bulk density.

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

[0168] Simulate nanoindentation creep test. Generate a Berkovich indenter (wall id = 7), and realize the loading, holding, and unloading processes of the nanoindentation creep test by moving the indenter. Since the PFC calculation adopts a dynamic method, stress waves will be generated inside the particle model in the initial stage of the indenter descent, and the wall-particle contact force curve will oscillate. In order to solve this problem, a constant pressure gradient loading mode is adopted, in which the indenter speed gradually increases from 0 to the specified loading rate. When the specified loading rate is reached, the indenter moves at a constant speed until the indenter force reaches 2mN. Then the servo control mode of the indenter is started, that is, the holding stage. When the holding time (after time scaling) reaches 180s, the servo control mode of the indenter can be turned off, and the indenter is unloaded by moving upward.

[0169] During the loading, holding and unloading process, the servo mechanism keeps the 6 walls (id=1~6) of the model at a fixed confining pressure. However, during the process of the pressure head dropping and rising, the contact area between the top wall (id=5) and the particle model will change continuously, so it is necessary to monitor this contact area in real time in the PFC to ensure that the servo stress is kept constant on the actual contact surface. To this end, two independent servo mechanisms are used for walls 1 to 6 and wall 7 (pressure head), so that the above process can be realized accurately and efficiently.

[0170] In the above embodiment, by optimizing the construction of the initial discrete element model, the physical reality and mechanical accuracy of the initial discrete element model can be significantly improved, thereby helping to reduce dependence on experimental equipment and reduce research and development costs.

[0171] In an exemplary embodiment, Fig.11 As shown, the above-mentioned calibration process of 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 indenter load in the holding stage into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function.

[0173] The experimental results refer to the data or measurement results obtained by experimental methods. The experimental results are mainly used to compare with the simulation results and to correct the creep parameters.

[0174] In the embodiment of the present application, the indenter load in 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 simulation results obtained in advance, the creep parameters corresponding to the experimental results are corrected to obtain a target discrete element model; the creep parameters at least include activation energy, unit normal contact force and flow unit.

[0176] Among them, creep parameters are physical quantities that describe how calcium silicate hydrate gel deforms over time or responds to external loads during stress. In this method, creep parameters refer to specific parameters that affect contact creep behavior. Creep parameters usually include the viscoelastic characteristics of materials, which are used to characterize how materials deform or relax stress over a long period of time in response to external forces.

[0177] Activation energy refers to the energy threshold that particles need to overcome when undergoing a series of mechanical or thermal processes. In the creep model, activation energy reflects the energy required for the transition of calcium silicate hydrate gel from one state to another, which is usually related to the interaction force between particles, deformation ability or reaction rate.

[0178] Unit normal contact force refers to the 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). The unit normal contact force is used to describe the strength of the contact between particles.

[0179] Flow units refer to physical quantities that describe the flow or slip behavior between particles. Flow units usually involve the flow characteristics of materials or particles in the contact area, such as rheological parameters, deformation rate, etc. Flow units can help describe the changes of materials under long-term load, including fluidity, viscosity and other characteristics.

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

[0181] In some embodiments, the contact creep function [L(t)-L(0)] simulation results of CSH particle models with different packing densities can be obtained. Taking the CSH particle model with packing density = 0.64 as an example, when the flow unit λ = 0.28nm, 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 simulation curve of [L(t)-L(0)] is consistent with the experimental results. Fig.12 As shown in Figure 2, the load time of the PFC simulation is 1.8×10 -6 s, and after time scaling (scaling factor Γ = 1×108), the holding time is 180 s, which completely matches the experimental holding time.

[0182] In some embodiments, the parameters involved in the "viscous sliding" creep mechanism are shown in formula (3) and formula (4), which include 7 parameters in total, among which k, R, h, and T are constants, and their values ​​are: Boltzmann constant k = 1.381×10-23J / K, absolute temperature T = 295.15K; Planck constant h = 6.626×10-34J·s, ideal gas constant R = 8.314×10-3kJ / mol / K. The remaining λ, n1, and ΔF are unknown variables that need to be calibrated, among which λ, n1, and ΔF are the number of bonds corresponding to the flow unit, unit normal contact force, and activation energy, respectively.

[0183] The calibration process is to simulate the nanoindentation creep test through PFC3D, record the indenter load (P), the indenter displacement (h) corresponding to the displacement change function, and the indentation contact area (Ac, that is, the vertical projection area of ​​the contact surface between the indenter and the CSH particle) corresponding to the nanoindentation contact area function at each time step, and calculate the contact creep function [L(t)-L(0)] 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 the trial and error method, the values ​​of λ, n1, and ΔF are adjusted many times, and finally, the calculated contact creep function [L(t)-L(0)] is consistent with the experimental results, and the calibration is completed.

[0184] In the above embodiment, the indenter load in the holding stage is input into the intermediate discrete element model, and the corresponding contact creep function is determined. After the simulation results are compared with the actual experimental data, the experimental data is corrected based on the pre-acquired simulation results. This correction method can effectively eliminate the deviation in the simulation process, make the creep parameters more consistent with the actual material behavior, and improve the accuracy and reliability of the simulation.

[0185] According to some embodiments of the present application, a method for simulating the nanoindentation creep of calcium silicate hydrate gel based on a discrete element model is provided. The method is described by taking the application of the method to a computer device as an example, and the method may include the following steps:

[0186] Step 1: Generate six walls based on the wall position information and calculation domain information of the acquired initial discrete element model.

[0187] Step 2: Generate a basic discrete element model based on a preset porosity in a cubic space surrounded by six walls.

[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 in the computational domain until the particles in the basic discrete element model move to a balanced state.

[0190] Step 5: Set the velocities of all particles in the basic discrete element model to preset values ​​to obtain an initial discrete element model.

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

[0192] Step 7, performing iterative calculation for each particle in the initial discrete element model. In each round of iteration, the slip 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 slip velocity at the i-th time step, and the friction coefficient at the i-th time step is applied to the particle.

[0193] Step 8, obtain the sliding velocity of the particle at the i+1th time step, determine the friction coefficient of the particle at the i+1th time step based on the sliding velocity at the i+1th time step, and apply the friction coefficient at the i+1th time step to the particle. The iteration ends until the preset time is reached, and the intermediate discrete element model is determined based on the friction coefficient and sliding velocity obtained when the iteration ends. Wherein, i is a positive integer greater than or equal to 0.

[0194] Step 9: Scaling the sliding speed and the preset time obtained when the iteration ends based on the time scaling algorithm to obtain the scaled sliding speed and the scaled time.

[0195] Step 10, input the indenter load in the holding stage into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function.

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

[0197] Step 12: input the first pressure head load in the loading stage into the target discrete element model pre-established for the calcium silicate hydrate gel, and determine the displacement change function of the pressure head in the loading stage.

[0198] Step 13, based on the displacement change function, determine the contact area function of the nanoindentation at the end of the loading.

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

[0200] It should be understood that, although the steps in the flowcharts involved in the above embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above embodiments may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0201] Based on the same inventive concept, the embodiment of the present application also provides a calcium silicate hydrate gel nanoindentation creep simulation device based on a discrete element model for realizing the calcium silicate hydrate gel nanoindentation creep simulation method based on a discrete element model. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in one or more embodiments of the calcium silicate hydrate gel nanoindentation creep simulation device based on a discrete element model provided below can be referred to the limitations of the calcium silicate hydrate gel nanoindentation creep simulation method based on a discrete element model above, and will not be repeated here.

[0202] In an exemplary embodiment, Fig.13As shown, a calcium silicate hydrate 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 pressure head load in the loading stage into the target discrete element model pre-established for the calcium silicate hydrate gel, and determine the displacement change function of the pressure head in the loading stage;

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

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

[0206] Each module in the above discrete element model-based calcium silicate hydrate gel nanoindentation creep simulation device can be implemented in whole or in part by software, hardware, and a combination thereof. Each of the above modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute operations corresponding to each of the above modules.

[0207] According to some embodiments of the present application, a computer device is also provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the above method can be implemented. The computer program product includes one or more computer instructions. When these computer instructions are loaded and executed on a computer, part or all of the above method can be implemented in whole or in part according to the process or function described in the embodiment of the present application.

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

[0209] According to some embodiments of the present application, a computer program product is also provided, and when the computer program is executed by a processor, the above method can be implemented. The computer program product includes one or more computer instructions. When these computer instructions are loaded and executed on a computer, part or all of the above method can be implemented in whole or in part according to the process or function described in the embodiment of the present application.

[0210] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present 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. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, an artificial intelligence (AI) processor, etc., but are not limited to this.

[0211] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, 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 above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for simulating the nanoindentation creep of calcium silicate hydrate gel based on discrete element model, characterized in that: The method comprises: Inputting the first pressure head load in the loading stage into the target discrete element model established in advance for the calcium silicate hydrate gel, and determining the displacement change function of the pressure head in the loading stage; Based on the displacement change function, determining the contact area function of the nanoindentation at the end of the loading; The contact creep function of the calcium silicate hydrate gel is determined based on the indenter load, the displacement variation function and the contact area function of the nanoindentation.

2. The method according to claim 1, characterized in that The process of establishing the target discrete element model includes: Establishing an initial discrete element model for the calcium silicate hydrate gel; Establishing 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; The intermediate discrete element model is calibrated to obtain the target discrete element model.

3. The method according to claim 2, characterized in that The process of establishing the intermediate discrete element model includes: Applying a second indenter load to the initial discrete element model until the second indenter load reaches a target value; Iterative calculation is performed for each particle in the initial discrete element model, and in each round of iteration, a slip velocity of the particle at the i-th time step is obtained, a friction coefficient of the particle at the i-th time step is determined based on the slip 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+1th time step is obtained, the friction coefficient of the particle at the i+1th time step is determined based on the sliding velocity at the i+1th time step, and the friction coefficient at the i+1th time step is applied to the particle; the iteration is terminated until a preset time is reached, and the intermediate discrete element model is determined based on the friction coefficient and the sliding velocity obtained when the iteration is terminated; wherein i is a positive integer greater than or equal to 0.

4. The method according to claim 3, characterized in that The method further comprises: The sliding speed and the preset time obtained when the iteration ends are scaled based on the time scaling algorithm to obtain the scaled sliding speed and the scaled time.

5. The method according to claim 2, characterized in that: The establishing of the initial discrete element model comprises: Generate six walls based on the acquired wall position information and calculation domain information of the initial discrete element model; In the cubic space surrounded by the six walls, a basic discrete element model is generated based on a preset porosity; Acquiring contact mechanics parameters of the basic discrete element model; Controlling particles in the basic discrete element model to bounce in the calculation domain until the particles in the basic discrete element model move to a balanced state; The velocities of all particles in the basic discrete element model are set to preset values ​​to obtain the initial discrete element model.

6. The method according to claim 2, characterized in that The calibrating the intermediate discrete element model to obtain the target discrete element model includes: Inputting the indenter load in the holding stage into the intermediate discrete element model to determine the experimental results corresponding to the contact creep function; The creep parameters corresponding to the experimental results are corrected based on the simulation results obtained in advance to obtain the target discrete element model; the creep parameters at least include activation energy, the number of bonds corresponding to the unit normal contact force, and the flow unit.

7. A nanoindentation creep simulation device for calcium silicate hydrate gel based on discrete element model, characterized in that: The device comprises: A displacement change function determination module is used to input the first pressure head load in the loading stage into a target discrete element model pre-established for calcium silicate hydrate gel to determine the displacement change function of the pressure head in the loading stage; A contact area function determination module, used to determine the contact area function of the nanoindentation at the end of the loading based on the displacement change function; The contact creep function determination module is used to determine the contact creep function of the calcium silicate hydrate gel based on the indenter load, the displacement change function and the contact area function of the nanoindentation.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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