Three-dimensional heterogeneous material simulation method, system and equipment based on near-field dynamics

Abstract

The invention discloses a three-dimensional heterogeneous material simulation method, system and equipment based on near-field dynamics, and the method comprises the following steps: carrying out model discretization: according to a set particle size distribution requirement, gradually generating aggregate particles with different particle sizes according to the particle sizes from large to small; distance verification is carried out on each newly generated aggregate particle in the generation process, three-dimensional random deformation is carried out on the shape of the aggregate particle, and generation of the current particle size is ended when the aggregate particle meets a termination condition; marking an aggregate area and a cementing material area; configuring material attributes; carrying out heterogeneous near-field dynamics simulation; according to the method, random distribution of particles can be simulated, interaction and heterogeneous characteristics between materials can be truly represented, the authenticity and precision of simulation are effectively improved, reliable support is provided for research and optimization of a complex material system in engineering application, and particularly deep analysis of heterogeneity and material behaviors in the complex material system is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of heterogeneous materials, and particularly relates to a three-dimensional heterogeneous material simulation method, system and device based on peridynamics. Background Art

[0002] Heterogeneous materials refer to materials whose composition, structure or properties show differences at different positions or in different directions. These differences may be manifested as changes in the composition of substances, the distribution of particles, density or other physical properties. In engineering, heterogeneous materials are widely used in various fields. Common examples include consolidated bodies of grouting materials and gravel, concrete, soil improvement materials, composite materials, etc. Taking concrete as an example, concrete is composed of cement, sand, aggregates, etc. These components are not uniform at the microscale. The size, distribution of aggregates and the interfacial structure with cement paste have important effects on its overall performance; while the consolidated body of grouting materials and gravel is composed of gravel, polymers or cement paste, etc., and its structure also shows obvious heterogeneity due to different materials.

[0003] Although heterogeneous materials are widely present in engineering applications, most current numerical simulation methods still fail to effectively handle the behavior of these complex materials. Traditional simulation methods usually simplify heterogeneous materials as homogeneous materials for modeling, which ignores the internal microstructure and inhomogeneity of the materials. For example, many numerical simulations of consolidated bodies equivalent the composite body of grouting materials and gravel to a uniform solid material, simplifying the random distribution between particles and the interfacial contact problem. In addition, some methods also simplify three-dimensional problems into two-dimensional models, further reducing the reduction accuracy of the real material behavior. These simplified assumptions may lead to large deviations between the simulation results and the actual behavior in some cases, especially in high-stress or complex mechanical environments, and the prediction ability of the model is significantly limited.

[0004] In addition, existing technologies such as the rock numerical modeling method considering mineral spatial distribution characteristics and heterogeneity with the patent number CN118506929A, and some existing heterogeneous modeling methods although consider the inhomogeneity of materials, most still rely on relatively simple models and fail to fully capture the complex interactions between various different materials and their mechanical responses. For example, when simulating concrete or the consolidated body of grouting materials and gravel, existing methods often cannot truly reproduce the three-dimensional distribution of particles, particle size grading and the interfacial behavior between them and other materials. This deficiency leads to problems in the accuracy of predicting and optimizing the mechanical properties.

[0005] Therefore, there is an urgent need for a numerical simulation method that can accurately simulate the heterogeneity in a multi-material system to better reproduce the interactions between different materials, improve the authenticity and accuracy of the simulation, and further meet the precise analysis and optimization requirements of complex heterogeneous materials in engineering applications. Summary of the Invention

[0006] The object of the invention is to provide a simulation method, system and device for three-dimensional heterogeneous materials based on peridynamics, which solves the problems of insufficient heterogeneity in simulating a variety of heterogeneous materials and insufficient simulation of the complexity of material behavior in the prior art.

[0007] In the present invention, the heterogeneous materials to be simulated usually consist of two parts: aggregate and cementitious material. Aggregate refers to the particulate components in heterogeneous materials, such as sand, gravel, etc. These particles form a skeleton structure in space through a certain particle size distribution and random distribution. The distribution characteristics of the aggregate have an important impact on the mechanical properties of the material. Especially in a high-stress environment, the interaction between the aggregate particles plays a key role in the compressive, shear and other properties of the material. The cementitious material refers to the material that connects the aggregate particles together, such as cement slurry, polymer, grouting material, etc. These materials form the overall structure of the consolidated body by filling the voids between the aggregate particles and interfacial connection. The penetration behavior, interfacial characteristics and bonding strength with the aggregate of the cementitious material are important factors determining the mechanical properties of the composite material. Therefore, by accurately simulating the interaction, interfacial characteristics and their distribution between the aggregate and the cementitious material, the complex mechanical behavior of the heterogeneous material can be more realistically reproduced, and thus more accurate numerical support can be provided for engineering design and material optimization.

[0008] The present invention provides a simulation method for three-dimensional heterogeneous materials based on peridynamics. The heterogeneous materials include aggregate and cementitious material, and the method includes the following steps:

[0009] S1. Model discretization: Obtain the analysis model of the heterogeneous material and discretize the analysis model into material points in space;

[0010] S2. Aggregate particle generation: According to the set particle size distribution requirements, generate aggregate particles of different particle sizes step by step from large to small; during the generation process, perform distance verification on each newly generated aggregate particle, and perform three-dimensional random deformation on the shape of the aggregate particle. When the aggregate particle meets the termination condition, end the generation of the current particle size;

[0011] S3. Aggregate region and cementitious material region marking: After generating the aggregate particles, mark the material points in the aggregate region and the cementitious material region according to the positions of the material points;

[0012] S4. Material property configuration: Assign different material properties to the material points in different regions;

[0013] S5. Heterogeneous peridynamics simulation: Based on the peridynamics method, perform mechanical simulation according to the material properties of different regions, and analyze its mechanical response behavior and failure mechanism under different conditions.

[0014] When simulating heterogeneous materials in the prior art, a multi-material system is usually simplified into a homogeneous material or a two-dimensional model, which results in the inability to accurately simulate the interaction between different materials and their behavior under complex mechanical conditions. Traditional methods fail to fully consider the heterogeneity, particle distribution, and interface characteristics of materials, leading to large deviations in the prediction of mechanical properties. To overcome these deficiencies, the present invention introduces a three-dimensional heterogeneous modeling method based on peridynamics. By obtaining an analytical model of the heterogeneous material and discretizing it into material points in space, combined with a step-by-step generation method, aggregate particles are randomly generated according to the target particle size ratio. The spatial arrangement constraint mechanism is used to ensure that there is no overlap between particles, so as to more realistically restore the distribution characteristics of the cementitious material and the aggregate solid. This method can accurately discretize complex solidification models, flexibly configure various material properties, and can output detailed simulation results. It can capture the random distribution of particles, truly reproduce the interaction between materials and heterogeneous characteristics, effectively improve the authenticity and accuracy of the simulation, provide reliable support for the research and optimization of complex material systems in engineering applications, and is applicable to the research and optimization of the performance of various heterogeneous materials in engineering applications, especially for the in-depth analysis of heterogeneity and material behavior in complex material systems.

[0015] A further technical solution of the present invention is that in step S2, the steps of generating aggregate particles of different particle sizes step by step from large to small according to the set particle size distribution requirements include:

[0016] S21. Calculation of the target volume: According to the total target volume V of the aggregate particles target , and the volume ratio of aggregate particles of different particle sizes, calculate the target volume V of aggregate particles of different particle sizes n :

[0017] V n =P n ·V target

[0018] Wherein, V n is the target volume of aggregate particles of different particle sizes, and P n represents the proportion of aggregate particles of different particle sizes; n is the number of aggregate particles of different particle sizes divided;

[0019] The target volume V n is defined as the volume occupied by the aggregate in the overall model. In actual engineering, the aggregate usually consists of particles of different particle sizes, and the proportion of particles of each particle size is different (refer to the grading of crushed stones in concrete). Therefore, it is necessary to calculate the target volume of aggregate in different particle size ranges separately.

[0020] S22. The aggregates are evenly filled step by step according to the particle size range from large to small until the target volume corresponding to the particle size range is satisfied. The current aggregates are filled in the voids between the already generated aggregate particles; optimize the overall distribution.

[0021] Precisely control the particle size distribution: Through the step-by-step generation strategy from large particle size to small particle size, the target volume and distribution ratio of each particle size can be precisely controlled, supporting the distribution simulation of complex multi-particle size particles. This strategy significantly improves the engineering applicability of the simulation, especially suitable for actual application scenarios with complex particle size distributions.

[0022] A further technical solution of the present invention is that the distance verification in step S2 includes the following steps:

[0023] S23. For a randomly generated particle, determine its center coordinates (x, y, z) and radius r, ensuring that the radius is within the set range corresponding to the particle size;

[0024] S24. Check the distance d between the newly generated particle and the already generated particles. If the distance d between the particles ≥ r i +r j , then the aggregate particle is successfully generated and this particle is accepted; if d < r i +r j , regenerate or adjust the radius until d ≥ r i +r j or if the set number of attempts to adjust still cannot meet the condition, record that the particle generation fails and continue with the generation of the next particle.

[0025] Through the aggregate generation method of the present invention, aggregate particles of different sizes are generated according to the particle size distribution requirements, and a spatial arrangement constraint mechanism is adopted to ensure that there is no overlap between the particles, which is closer to the actual engineering conditions, realizing aggregate generation and spatial arrangement constraint.

[0026] A further technical solution of the present invention is that the three-dimensional random deformation in step S2 includes at least one of proportional scaling, random eccentricity, and surface perturbation; the termination condition is when the current total volume V current of the aggregates of a certain particle size reaches the target volume Vn of the aggregates of this particle size or the number of attempts to generate the particle size exceeds the set value, end the generation process of the current particle size; the determination of the termination condition includes the following steps:

[0027] S25. Calculate the current total volume V current of the aggregates of a certain particle size:

[0028] S251. Calculate the volume of the particle after random deformation:

[0029]

[0030] where S x, S y , S z is a random scaling factor, and r is the particle radius;

[0031] S252. Calculate the volume correction of the surface perturbation:

[0032] V particle,sdjusted = V particle (1 + k)

[0033] where k is the perturbation correction coefficient;

[0034] S253. Accumulate the current volume: After each particle is generated and passes the distance check, add the adjusted volume V particle,adjusted to the total volume V of the current particle size: current :

[0035] V current = V current,n-1 + V particle,adjusted

[0036] where V current,n-1 is the total volume of the previous particle size;

[0037] If a certain particle fails the distance check, its volume will not be included in V current ; Only the volumes of successfully generated particles will be accumulated;

[0038] S26. After each particle is generated, compare the total volume V of the current particle size in real time current with the target volume V n : If the condition V current ≥ V n is satisfied, end the generation process of the current particle size.

[0039] The present invention conducts intelligent management on the aggregate generation termination condition, introduces a refined management mechanism, and dynamically adjusts the generation process according to the aggregate volume content and particle size distribution to ensure that the volume ratio of the overall model precisely meets the preset requirements.

[0040] Three-dimensional randomly deformed particles: Use a three-dimensional random deformation strategy to generate more realistic randomly shaped particles. This strategy improves the reduction degree of the model to the actual material form and avoids the errors caused by overly regular particle shapes in traditional methods.

[0041] A further technical solution of the present invention is that the method for dividing the aggregate and cementitious material regions in step S3 includes the following steps:

[0042] S31. Traverse all the material points in the model, obtain their coordinates (x, y, z), and for each material point, calculate the distance d from it to the centers of all the generated aggregate particles:

[0043]

[0044] Among them, S x , S y , S z are the scaling factors of the particles in the x, y, and z directions respectively;

[0045] S32. Region marking: If the distance d from a material point to any aggregate particle is d ≤ r, it is marked as the aggregate region with a marking value of "1"; otherwise, it is marked as the cementitious material region with a marking value of "0";

[0046] S33. Interface region identification: Analyze the markings of adjacent material points. If the two material points belong to the aggregate region and the cementitious material region respectively, mark it as the interface region.

[0047] Enhanced interface effect capture ability: By regionally marking material points and configuring material properties, the present invention can assign corresponding mechanical parameters to the aggregate region, the cementitious material region, and the interface region respectively. This feature enables the present invention to better capture the mechanical responses and interface effects of different regions, thereby simulating the interface bonding strength and failure behavior.

[0048] A further technical solution of the present invention is that the material property configuration method in the step S4 includes the following steps:

[0049] S41. Aggregate region: Configure the aggregate material properties for the aggregate region. The orthopedic material properties include density ρ1 and elastic modulus E1;

[0050] S42. Cementitious material region: Configure the cementitious material properties for the cementitious material region. The cementitious material properties include density ρ2 and elastic modulus E2.

[0051] The present invention clearly distinguishes the aggregate particle region and the cementitious material region in the model, and accurately configures the material properties of each and the contact surface properties between the two to simulate the interaction and interface response of the two materials.

[0052] A further technical solution of the present invention is that the peridynamic simulation method in the step S5 includes the following steps:

[0053] S51. Mechanical model construction: Construct peridynamic heterogeneous models for the aggregate particle region, the cementitious material region, and the interface region respectively; set the properties of three types of bonds, including "1-1" bonds within the aggregate, "0-0" bonds within the cementitious material, and "1-0" bonds at the interface;

[0054] S52. Dynamic response analysis: Under loading conditions, simulate the mechanical response behaviors of the heterogeneous material, including tensile, compressive, and shear actions; to capture the failure process and fracture behavior of the interface;

[0055] S53. Result Output: The output results include the aggregate particle distribution state, the cementitious material region, the overall mechanical properties, and the local damage characteristics.

[0056] Using the peridynamics method, three-dimensional heterogeneous simulation of non-uniform materials is achieved. This simulation technology accurately simulates the heterogeneity and complex interaction between aggregates and cementitious materials through precise physical point discretization and material property assignment.

[0057] Peridynamics method is used for heterogeneous dynamics simulation, and a detailed simulation result is provided through the output module, including the overall and local mechanical properties of the consolidated body, and the evolution of interface failure behavior.

[0058] The second aspect of the present invention provides a three-dimensional heterogeneous material simulation system based on peridynamics, and the system includes the following modules:

[0059] Model Discretization Module: Used to obtain the analysis model and discretize it into material points;

[0060] Aggregate Generation Module: Used to generate aggregate particles of different particle sizes step by step, ensure the reasonable volume distribution ratio and spatial arrangement, and avoid particle overlap through the distance verification mechanism; then mark the material points in the aggregate region and the cementitious material region respectively;

[0061] Material Configuration Module: Used to assign different material properties to the material points in the aggregate region, the cementitious material region, and the junction region, and configure the mechanical parameters of three types of bonds;

[0062] Peridynamics Solving Module: Used to simulate the response behavior of the consolidated body under different mechanical conditions based on the peridynamics method, including the mechanical interaction between particles and the interface failure mode;

[0063] Output Module: The output results include the material deformation condition, the stress distribution condition, the failure mode, etc.;

[0064] Among them, the Material Configuration Module configures the mechanical parameters of the following three types of bonds: the "1-1" bond inside the aggregate particle; the "0-0" bond inside the cementitious material region; the "1-0" bond at the junction of the aggregate particle and the cementitious material region.

[0065] The third aspect of the present invention provides an electronic device, including a processor and a memory coupled to the processor, and the processor is used to read the computer program stored in the memory to execute a three-dimensional heterogeneous material simulation method based on peridynamics as described above.

[0066] The fourth aspect of the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements a three-dimensional heterogeneous material simulation method based on peridynamics as described above.

[0067] The present invention aims to provide a more efficient and accurate engineering material simulation tool, especially suitable for dealing with consolidated materials with strong heterogeneity and complex interactions.

[0068] Explanation of related terms in the present invention:

[0069] Peridynamics (PD): A mathematical theory method used to simulate long-range forces and fracture behavior in continuous media. It does not rely on traditional concepts of stress and strain, but describes the mechanical response inside materials through the interactions between material points.

[0070] Heterogeneity: Refers to the non-uniform distribution of physical or chemical properties in materials or structures. In the present invention, heterogeneity particularly refers to the physical property differences among the components in grouting materials and gravel consolidated bodies.

[0071] Aggregate generation module: The part of the computer program used to automatically create aggregate particles in the simulation. This module generates particles according to a predetermined particle size distribution and arranges them reasonably in three-dimensional space to ensure that their physical layout conforms to actual engineering conditions.

[0072] Material property configuration: Refers to the process of assigning specific material properties (such as elastic modulus, density, etc.) to each material point in the simulation. This process involves distinguishing different regions (such as aggregate regions and cementitious material regions) and setting different properties for them.

[0073] Interface property: Refers to the specific physical properties set in the interaction region between different materials, such as the strength and toughness of the interface, used to simulate the interaction and possible fracture behavior between two materials.

[0074] Dynamic solution module: The part of the program used to calculate and update the state of material points (such as displacement, velocity, stress) during the simulation. It calculates the response of the material in real time according to the loading conditions and the interaction relationships between material points.

[0075] Output module: The part of the program used to generate and display the results after the simulation is completed. It can display detailed information such as the distribution of gravel and grouting materials, stress state, damage, and fracture patterns.

[0076] Aggregate volume content: In the analysis model, the proportion of the total volume occupied by aggregate particles. This parameter is crucial for simulating the physical properties of heterogeneous materials.

[0077] Particle overlap: When generating aggregate particles, the physical space of two or more particles overlaps, which should be avoided in actual simulations to ensure the independence of each particle and the accuracy of the simulation.

[0078] By defining and explaining these terms, the object of the present invention is to use the above technical solutions to achieve high-precision, high-efficiency and practical simulation of the grouting material and the gravel consolidated body. These technical solutions jointly support a system that can simulate the complex material behavior under actual engineering conditions, especially the performance under non-homogeneous and multi-physical field conditions.

[0079] Advantages of the present invention: 1. Realistically restore the distribution characteristics: By obtaining the analysis model of the non-uniform material, discretizing it into material points in space, randomly generating aggregate particles according to the target particle size ratio by means of a step-by-step generation method, and using the spatial arrangement constraint mechanism to ensure no overlap between particles, it is possible to more realistically restore the distribution characteristics of the cementitious material and the aggregate consolidated body. This method can capture the random distribution of particles and improve the accuracy and realism of the simulation.

[0080] 2. Accurately control the particle size distribution: Through the step-by-step generation strategy from large particle size to small particle size, it is possible to accurately control the target volume and distribution ratio of each particle size, and support the simulation of the distribution of complex multi-particle sizes. This strategy significantly improves the engineering applicability of the simulation, especially suitable for actual application scenarios with complex particle size distributions.

[0081] 3. Enhance the ability to capture interface effects: By regionally marking the material points and configuring the material properties in the present invention, corresponding mechanical parameters can be assigned to the aggregate region, the cementitious material region and the interface region respectively. This feature enables the present invention to better capture the mechanical responses and interface effects in different regions, thereby simulating the interface bonding strength and failure behavior.

[0082] 4. Three-dimensional randomly deformed particles: Adopting a three-dimensional random deformation strategy to generate more realistic randomly shaped particles. This strategy improves the restoration degree of the model to the actual material form and avoids the errors caused by overly regular particle shapes in traditional methods.

[0083] 5. Comprehensive mechanical behavior simulation: Combining the non-homogeneous mechanics simulation based on peridynamics, the present invention supports the response of the consolidated body under different mechanical conditions, including tensile, compressive and shear behaviors. By dynamically analyzing local damage and interface failure, the present invention can provide a more accurate assessment of the mechanical properties of the consolidated body.

[0084] 6. Improving simulation accuracy and reliability: Compared with traditional methods, the present invention can more realistically simulate the mechanical properties of the cementitious material and the aggregate solidified body, significantly improving the simulation accuracy and reliability. Through this method, the mechanical properties of complex solidified bodies can be evaluated more comprehensively and accurately, thus providing more reliable theoretical support and technical means for engineering design and optimization.

[0085] In summary, the present invention not only improves the simulation accuracy of the mechanical properties of the solidified body, but also provides a strong technical guarantee for solving complex engineering problems, especially having broad application prospects in fields such as grouting reinforcement, subgrade stability enhancement, and foundation improvement. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 Schematic diagram of the overall process of a three-dimensional heterogeneous material simulation method based on peridynamics provided by an embodiment of the present invention;

[0087] Figure 2 Schematic diagram of the process of randomly generating aggregate particles in the present invention;

[0088] Figure 3 Schematic diagram of the process of marking the aggregate area and assigning attributes in the present invention;

[0089] Figure 4 Schematic diagram of the dynamic evolution process of the local damage degree provided by an embodiment of the present invention;

[0090] Figure 5 Schematic diagram of the heterogeneous model generation and mechanical response process provided by an embodiment of the present invention;

[0091] Figure 6 Block diagram of a three-dimensional heterogeneous material simulation system based on peridynamics provided by an embodiment of the present invention;

[0092] Figure 7 Internal structure schematic diagram of an electronic device provided by an embodiment of the present invention;

[0093] Figure 8 Physical diagram of a high polymer (cementitious material) - crushed stone (aggregate) solidified body provided by Embodiment 2 of the present invention;

[0094] Figure 9 Schematic diagram of the quantity and volume proportion of crushed stones with different particle sizes in the model provided by the present invention in Embodiment 2;

[0095] Figure 10 Practical application scenario diagram taken in Embodiment 2 of the present invention;

[0096] Figure 11 Failure mode of the model in Embodiment 2 of the present invention;

[0097] Figure 12 The failure mode of the model in Embodiment 2 predicted by the method of the present invention. Specific implementation manners

[0098] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0099] Embodiment 1:

[0100] This embodiment proposes a three-dimensional heterogeneous material simulation method and system based on peridynamics. The specific steps include:

[0101] S1. Model discretization: First, obtain the analysis model of the heterogeneous material and discretize the analysis model into material points in space.

[0102] S2. Aggregate particle generation: According to the set particle size distribution requirements, generate aggregate particles of different particle sizes step by step in descending order. Larger particle size particles are preferably generated first to ensure their uniform distribution. For each newly generated aggregate particle, the distance verification rule is used to avoid overlap between particles, and three-dimensional random deformation is performed on the particle shape during the generation process to more realistically simulate the irregularity of actual aggregates.

[0103] S3. Aggregate area and cementitious material area marking: After generating the aggregate particles, mark the material points in the aggregate area and the cementitious material area according to the positions of the material points. The material points in the aggregate area are marked as "1", and the material points in the cementitious material area are marked as "0".

[0104] S4. Material property configuration: Different material properties are assigned to the material points in different regions. Specifically, the material points in the aggregate particle area (marked as "1") are configured with aggregate material properties; the material points in the cementitious material area (marked as "0") are configured with cementitious material properties; at the junction of the aggregate particle area and the cementitious material area, the interfacial bonding strength and interfacial fracture criterion of the "1-0" bond are set.

[0105] S5. Heterogeneous peridynamics simulation: Based on the peridynamics method, a heterogeneous dynamics model of the heterogeneous material is constructed. According to the material properties of different regions, mechanical simulations are performed to analyze the response behaviors of the heterogeneous material under mechanical conditions such as tension, compression, and shear. Under the loading condition, the interface parameters are dynamically adjusted to simulate the interfacial bonding strength and failure behavior of the "1-0" bond, and simulation results including the overall deformation situation, local damage characteristics, and interfacial failure evolution behavior are output.

[0106] In this embodiment, step S2 adopts a method of gradually generating aggregate particles, including the following steps:

[0107] Gradual generation and volume allocation:

[0108] S21. Calculation of target volume:

[0109] According to the total target volume V of the aggregate particles target , and the volume ratios of aggregates with different particle sizes, calculate the target volumes V of aggregates with different particle sizes respectively n :

[0110] V n = P n ·V target

[0111] where V n is the target volume of aggregates with different particle sizes, and P n represents the proportion of aggregates with different particle sizes; n is the number of aggregates with different particle sizes divided.

[0112] S22. Gradual generation:

[0113] Preferentially generate the largest particle size aggregates to ensure their uniform filling; after meeting the target volume, switch to generating medium particle size aggregates and fill the voids between the large particle size particles; finally, generate small particle size aggregates to further fill the voids between the medium and large particles and optimize the overall distribution.

[0114] In this embodiment, the distance verification in step S2 includes the following steps: random generation and position verification:

[0115] S23. Random generation: Each time, randomly generate a particle, determine its center coordinates (x, y, z) and radius r, and ensure that the radius is within the specified range (such as the large particle size range [0.004, 0.005]).

[0116] S24. Position verification: Check the distance between the newly generated particle and the already generated particles; if the distance d between the particles ≥ r i + r j , then the aggregate particle is successfully generated and this particle is accepted; if d < r i + r j , regenerate or adjust the radius until the non-overlap condition is met; if the condition still cannot be met after multiple adjustments, record that the particle generation fails and continue to generate the next particle.

[0117] In this embodiment, the shape randomization in step S2 includes scale scaling, random eccentricity, and surface perturbation; specifically:

[0118] Scale scaling: Introduce a random scaling factor S for each particlex , S y , S z , Scale in the x, y, and z directions respectively to simulate the three-dimensional shape of ellipsoidal particles.

[0119] Random eccentricity: Add an eccentricity parameter at the center of the particle to cause a random offset of the particle center, simulating the asymmetric distribution in actual engineering.

[0120] Surface perturbation: Superimpose small random perturbations on the particle surface to enhance the roughness of the particle and reflect the irregular boundary characteristics of actual aggregates.

[0121] In this embodiment, the termination condition in step S2: When the current total volume V of an aggregate with a certain particle size current reaches the target volume V of the aggregate with this particle size n or the number of attempts to generate particle sizes exceeds the set value, end the generation process of the current particle size;

[0122] The specific steps include:

[0123] S25. The calculation method of the current total volume V of a certain particle size current includes:

[0124] S251. The formula for calculating the volume of the particle after random deformation:

[0125]

[0126] where S x , S y , S z is the random scaling factor and r is the particle radius.

[0127] S252. Volume correction for surface perturbation:

[0128] V paeticle,sdjusted = V particle (1 + k)

[0129] where k is the perturbation correction coefficient.

[0130] S253. Accumulate the current volume:

[0131] After generating each particle and passing the overlap check, add the adjusted volume V particle,adjusted to the total volume V of the current particle size current :

[0132] V current = V current,n-1 + V particle,adjusted

[0133] where V current,n-1 is the total volume of the previous particle size;

[0134] S26. Judgment of termination condition:

[0135] After each particle is generated, the total current particle size volume V is compared in real time current with the target volume V n : If the condition V current ≥V n is satisfied, the generation process of the current particle size is ended.

[0136] As other embodiments: As an alternative to aggregate generation and spatial arrangement constraints: Geometric modeling technology: Using computational geometry algorithms such as Voronoi diagrams or Delaunay triangulations to generate more complex aggregate particle shapes and arrangements to more realistically simulate the actual situation. Particle flow software: Using specialized particle flow simulation software such as PFC (Particle Flow Code) to simulate the generation and arrangement of aggregates.

[0137] Among them, the processing of particles that fail the verification:

[0138] If a certain particle fails the overlap verification, its volume is not included in V current ; Only the volumes of successfully generated particles are accumulated.

[0139] In this embodiment, the method for dividing the aggregate and cementitious material regions in step S3 includes the following steps:

[0140] S31. Traversal of material points and distance calculation:

[0141] Traverse all the material points in the model to obtain their coordinates (x, y, z). For each material point, calculate its distance d to the centers of all the generated aggregate particles:

[0142]

[0143] where S x , S y , S z is the scaling factor of the particle.

[0144] S32. Region marking:

[0145] If the distance d of the material point to any aggregate particle is d ≤ r, it is marked as the aggregate region (marking value "1"); otherwise, it is marked as the cementitious material region (marking value "0").

[0146] S33. Identification of the interface region:

[0147] Analyze the markings of adjacent material points. If the two material points belong to the aggregate region and the cementitious material region respectively, mark it as the interface region; set interface characteristics in the interface region to describe the bonding behavior between the cementitious material and the aggregate.

[0148] In this embodiment, the material property configuration method in step S4 includes the following steps:

[0149] S41. Aggregate area: For the material points marked as "1", configure the material properties of the aggregate, including density ρ1, elastic modulus E1, etc.

[0150] S42. Cementitious material area: For the material points marked as "0", configure the material properties of the cementitious material, including density ρ2, elastic modulus E2, etc.

[0151] As other embodiments, alternative solutions for configuring material properties and interface properties: Intelligent material configuration: Automatically adjust material properties according to the loading history and environmental conditions through machine learning algorithms to adapt to complex application environments.

[0152] In this embodiment, the peridynamic simulation method in step S5 includes the following steps:

[0153] S51. Mechanical model construction:

[0154] For the aggregate particle area, cementitious material area, and junction area, construct peridynamic heterogeneous models respectively; set the properties of three types of bonds, including "1-1" bonds (inside the aggregate), "0-0" bonds (inside the cementitious material), and "1-0" bonds (at the junction).

[0155] S52. Dynamic response analysis:

[0156] Under loading conditions, simulate the mechanical response behaviors of inhomogeneous materials, including tensile, compressive, and shear actions; to capture the failure process and fracture behavior of the interface; the schematic diagram of the dynamic evolution process of the local damage degree is as Figure 4 shown.

[0157] S53. Result output:

[0158] The output results include the aggregate particle distribution state, cementitious material area, overall mechanical properties, and local damage characteristics.

[0159] As other embodiments, in addition to peridynamics, multi-scale simulation methods, such as the method of coupling molecular dynamics and continuum mechanics, can be used to simulate the inhomogeneity of the cementitious material and aggregate solid.

[0160] Embodiment 2:

[0161] Taking the track bed repair in a certain engineering project as an example, Figure 8 as shown, consider a polymer (cementitious material)-crushed stone (aggregate) solid with a size of 5 cm in diameter and 10 cm in height, and the volume ratio of crushed stone is about 50%. The elastic modulus of the grouting material of this solid is 350 MPa, and the density is 1230 kg / m3 , Poisson's ratio is 0.25, and the critical elongation rate is 0.05457; the modulus of the gravel part is 55.4 GPa, and the density is 1220 kg / m 3 , Poisson's ratio is 0.2, and the critical elongation rate is 0.00093. Under the action of uniaxial compression load, the displacement is controlled at a loading rate of 1 mm / min, and the mechanical failure behavior is analyzed by using the modeling method of Embodiment 1 of the present invention.

[0162] Figure 9 The number and volume ratio of gravel with different particle sizes (unit: m) in the present model are as follows:

[0163] Gravel with particle size range [0.008, 0.010]: number = 7, volume ratio = 10.62%

[0164] Gravel with particle size range [0.006, 0.008]: number = 27, volume ratio = 17.71% Gravel with particle size range [0.004, 0.006]: number = 104, volume ratio = 21.46% Total volume ratio occupied by gravel: 49.79%

[0165] As Figures 8 - 12 can be seen, through model analysis, the interaction between the grouting material and the gravel and its non - homogeneity effect can be accurately simulated, and the failure mode of the material under different loading conditions can be revealed. The simulation results show that the consolidated body exhibits obvious non - homogeneity behavior during the stress process, and the interaction at the interface between the gravel and the grouting material has an important influence on the failure mode. Through this peridynamic model, detailed mechanical response predictions can be provided for projects such as ballast bed reinforcement and subgrade repair, providing reliable theoretical support for engineering design.

[0166] This application scenario verifies the advantages of the present invention in simulating the behavior of complex heterogeneous materials, and can provide more accurate material property analysis for the reinforcement and repair work of various civil engineering projects.

[0167] Embodiment 3:

[0168] The embodiment of the present invention provides a three - dimensional heterogeneous material simulation system based on peridynamics, and the system includes the following modules:

[0169] Model discretization module: used to obtain the analysis model and discretize it into material points;

[0170] Aggregate generation module: used to generate aggregate particles with different particle sizes step by step, ensure the rationality of their volume distribution ratio and spatial arrangement, and avoid particle overlap through a distance verification mechanism; then mark the material points in the aggregate area and the cementitious material area respectively;

[0171] Material configuration module: used to assign different material properties to the material points in the aggregate area, cementitious material area, and the junction area, and configure the mechanical parameters of the following three types of bonds:

[0172] "1-1" bond inside the aggregate particle;

[0173] "0-0" bond inside the cementitious material area;

[0174] "1-0" bond at the junction of the aggregate particle and the cementitious material area;

[0175] Peridynamics solution module: used to simulate the response behavior of the consolidated body under different mechanical conditions based on the peridynamics method, including the mechanical interaction between particles and the interface failure mode;

[0176] Output module: The output results include the material deformation condition, stress distribution condition, and failure mode.

[0177] Example 4:

[0178] An embodiment of the present invention provides an electronic device, including a memory, a processor, and

[0179] a computer program stored on the memory and executable on the processor, and when the processor executes the computer program, the method described in Example 1 is implemented.

[0180] Example 5:

[0181] An embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the method described in Example 1 is implemented.

[0182] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A three-dimensional heterogeneous material simulation method based on peridynamics, wherein the heterogeneous material comprises aggregate and binder, characterized in that: The method comprises the following steps: S1. Model discretization: Obtain the analytical model of heterogeneous materials and discretize the analytical model into material points in space; S2. Aggregate particle generation: According to the set particle size distribution requirements, aggregate particles of different particle sizes are generated step by step from large to small. During the generation process, the distance of each newly generated aggregate particle is verified, and the shape of the aggregate particle is subjected to three-dimensional random deformation. When the aggregate particle meets the termination condition, the generation of the current particle size ends. S3. Aggregate area and cementing material area marking: after the aggregate particles are generated, the material points of the aggregate area and the cementing material area are marked according to the positions of the material points; S4. Material property configuration: assign different material properties to material points in different areas; S5. Heterogeneous peridynamic simulation: Based on the peridynamic method, mechanical simulation is performed according to the material properties of different regions to analyze their mechanical response behavior and failure mechanism under different conditions.

2. The three-dimensional heterogeneous material simulation method based on peridynamics according to claim 1, characterized in that: In S2, according to the set particle size distribution requirements, the step of generating aggregate particles of different particle sizes step by step from large to small particle sizes includes: S21. Calculation of target volume: Based on the total target volume V of aggregate particles target , and the volume ratio of aggregates of different particle sizes, and calculate the target volume V of aggregates of different particle sizes respectively. n : V n =P n ·V target Among them, V n is the target volume of aggregates with different particle sizes, P n Indicates the proportion of aggregates with different particle sizes; n is the number of aggregates with different particle sizes; S22. Aggregates are filled evenly step by step according to the particle size range from large to small to the target volume that meets the corresponding particle size range. The current aggregates are filled in the gaps between the aggregate particles that have been generated; optimize the overall distribution.

3. The three-dimensional heterogeneous material simulation method based on peridynamics according to claim 2, characterized in that: The distance verification in step S2 comprises the following steps: S23. For a randomly generated particle, determine its center coordinates (x, y, z) and radius r, and ensure that the radius is within the corresponding particle size setting range; S24. Check the distance d between the newly generated particles and the generated particles. If the distance d between the particles is ≥ r i +r j , then the aggregate particle is generated successfully and the particle is accepted; if d<r i +r j , regenerate or adjust the radius until d ≥ r is satisfied i +r j Or if the condition cannot be met after adjusting the set number of times, the particle generation failure is recorded and the next particle generation continues.

4. The method for simulating three-dimensional heterogeneous materials based on peridynamics according to claim 3, characterized in that: The three-dimensional random deformation in step S2 includes at least one of scaling, random eccentricity and surface disturbance; the termination condition is when the current total volume V of aggregate of a certain particle size is current To achieve the target volume V of aggregate of this size n Or when the number of attempts to generate the particle size exceeds the set value, the generation process of the current particle size is terminated; The specific steps include: S25. Calculate the current total volume V of aggregate of a certain particle size current : S251. Calculate the volume of particles after random deformation: Where S x , S y , S z is the random scaling factor, r is the particle radius; S252. Calculate volume corrections for surface disturbances: V particle,sdjusted =V particle (1+k) Where k is the disturbance correction coefficient; S253. Accumulate the current volume: After each particle is generated and passes the distance check, the adjusted volume V particle,adjusted Add to the total volume V of the current particle size current : V current =V current,n-1 +V particle,adjusted Where V current,n-1 is the total volume of the previous particle size; If a particle fails the distance check, its volume is not included in V current ;Only the volume of successfully generated particles will be accumulated; S26. After each particle is generated, compare the total volume V of the current particle size in real time current With the target volume V n :If V is satisfied current ≥V n If the condition is met, the generation process of the current particle size ends.

5. A three-dimensional heterogeneous material simulation method based on peridynamics according to any one of claims 1 to 4, characterized in that: The method for dividing the aggregate and cementing material regions in step S3 comprises the following steps: S31. Traverse all material points in the model, obtain their coordinates (x, y, z), and for each material point, calculate the distance d from it to the center of all generated aggregate particles: Among them, S x , S y , S z are the scaling factors of the particles in the x, y, and z directions respectively; S32. Area marking: If the distance d≤r between the material point and any aggregate particle, it is marked as an aggregate area with a marking value of "1"; otherwise, it is marked as a cementing material area with a marking value of "0"; S33. Boundary area identification: Analyze the adjacent material point marks. If two material points belong to the aggregate area and the cementing material area respectively, mark them as the boundary area.

6. A three-dimensional heterogeneous material simulation method based on peridynamics according to any one of claims 1 to 4, characterized in that: The material property configuration method in step S4 comprises the following steps: S41. Aggregate area: configure aggregate material properties for the aggregate area, wherein the orthopedic material properties include density ρ1 and elastic modulus E1; S42. Binder material area: configure binder material properties for the binder material area, wherein the binder material properties include density ρ2 and elastic modulus E2.

7. A three-dimensional heterogeneous material simulation method based on peridynamics according to any one of claims 1 to 4, characterized in that: The peridynamic simulation method in step S5 comprises the following steps: S51. Mechanical model construction: Peridynamic heterogeneous models are constructed for the aggregate particle region, the cementing material region, and the interface region. The properties of three types of bonds are set, including "1-1" bonds in the aggregate, "0-0" bonds in the cementing material, and "1-0" bonds at the interface. S52. Dynamic response analysis: Simulate the mechanical response behavior of heterogeneous materials under loading conditions, including tension, compression, and shear, to capture the failure process and fracture behavior of the interface; S53. Result output: The output results include aggregate particle distribution, cementing material area, overall mechanical properties and local damage characteristics.

8. A three-dimensional heterogeneous material simulation system based on peridynamics, characterized by: The system includes the following modules: Model discretization module: used to obtain the analysis model and discretize it into material points; Aggregate generation module: used to generate aggregate particles of different particle sizes step by step, ensure their volume distribution ratio and spatial arrangement are reasonable, and avoid particle overlap through distance verification mechanism; then mark the material points in the aggregate area and cementing material area respectively; Material configuration module: used to assign different material properties to material points in the aggregate area, cementing material area and boundary area, and configure the mechanical parameters of the following three types of bonds: "1-1" bonds inside the aggregate particles; "0-0" bonds inside the cementing material area; "1-0" bonds at the boundary between the aggregate particles and the cementing material area; Peridynamics solution module: used to simulate the response behavior of the consolidated body under different mechanical conditions based on the peridynamic method, including the mechanical interaction between particles and interface failure mode; Output module: The output results include material deformation, stress distribution and failure mode.

9. An electronic device, characterized in that: The method comprises a processor and a memory coupled to the processor, wherein the processor is used to read a computer program stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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