Quantitative analysis method, device and equipment for dynamic heterogeneity of irregular granular material

Abstract

The invention relates to the technical field of particle macro-micro mechanics, in particular to a quantitative analysis method, device and equipment for dynamic heterogeneity of an irregular particle material, and the method comprises the following steps: selecting the irregular particle material, carrying out a triaxial test based on X-ray CT, and obtaining CT slice images of the irregular particle material after deformation at different moments; carrying out image segmentation and three-dimensional reconstruction to obtain a result containing particle numbers and geometric features, and obtaining particle dynamic information through cross-strain state particle matching pursuit; active clusters are identified from the information, geometric information of the active clusters is evolved, cluster space distribution in different strain states is compared, and spatio-temporal evolution behaviors of the active clusters are tracked; and calculating the structure, dynamics and comprehensive indexes of the cluster according to the evolution behavior, determining the dynamic heterogeneity quantitative characterization by using at least one index, outputting and carrying out visual analysis on the dynamic heterogeneity quantitative characterization. Therefore, the problem that dynamic heterogeneity spatio-temporal evolution of irregular particle materials is difficult to quantitatively analyze from the micro-scale in the prior art is solved.

Description

Technical Field

[0001] This application relates to the field of particle macro- and micro-mechanical technology, and in particular to a method, apparatus and equipment for quantitative analysis of the kinetic heterogeneity of irregular particulate materials. Background Technology

[0002] In the field of particulate materials engineering and mechanics research, a deep understanding of the spatiotemporal evolution of dynamic heterogeneity during shearing of irregular particulate materials is crucial for revealing the mechanisms of macroscopic deformation and shear localization. However, related techniques are difficult to use for quantitative analysis of this evolution process, relying mostly on qualitative observations, and there is insufficient experimental data to support this for irregular particles. Summary of the Invention

[0003] This application provides a method, apparatus, and equipment for quantitative analysis of the dynamic heterogeneity of irregular particulate materials, in order to solve the problem in related technologies that it is difficult to quantitatively analyze the spatiotemporal evolution of dynamic heterogeneity of irregular particulate materials at the mesoscale.

[0004] The first aspect of this application provides a method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials, comprising the following steps: selecting irregular particulate materials from experimental data, conducting triaxial tests based on X-ray CT on the irregular particulate materials, and obtaining CT slice images of the particulate materials after deformation at different times; performing image segmentation on the CT slice images, and reconstructing a three-dimensional segmentation result containing the particle number and geometric features based on the image segmentation result; performing cross-strain state particle matching and tracking based on the three-dimensional segmentation result to obtain particle kinetic information; identifying active clusters from the particle kinetic information, evolving the geometric information of the active clusters, comparing the spatial distribution of clusters under different strain states based on the geometric information, and tracking the spatiotemporal evolution behavior of the active clusters based on the comparison result; calculating the structural index, kinetic index, and comprehensive index of the active clusters based on the spatiotemporal evolution behavior; determining the quantitative characterization of kinetic heterogeneity based on at least one of the structural index, kinetic index, and comprehensive index; outputting the quantitative characterization of kinetic heterogeneity and performing visualization analysis on the quantitative characterization of kinetic heterogeneity.

[0005] Based on the aforementioned technical means, this application takes real irregular particles as the research object, captures microscopic images of material deformation through X-ray CT triaxial experiments, and accurately obtains particle dynamics information by combining image segmentation, three-dimensional reconstruction, and transstrain particle matching technology. Furthermore, through the identification of active clusters, spatiotemporal evolution tracking, and multi-dimensional index calculation, it overcomes the limitation of related technologies in quantitatively analyzing the microscopic dynamic heterogeneity of irregular particulate materials. It not only reveals the evolution law of dynamic heterogeneity from local to global and the microscopic driving mechanism of macroscopic mechanical behavior, but also provides a scientific quantitative index system and visualization tools for the microscopic mechanical analysis of particulate materials. Finally, it provides high-fidelity physical experimental data support for in-depth research on the shear localization mechanism of irregular particulate materials, as well as for establishing constitutive models based on irregularly shaped particle systems and predicting shear localization behavior.

[0006] Optionally, cross-strain state particle matching and tracking are performed based on the 3D segmentation results to obtain particle dynamics information, including: constructing a multi-scale shape descriptor characterizing the particle shape; matching particles in adjacent strain states by minimizing the L2 norm difference of the shape descriptor vector; calculating the particle displacement vector and rotation matrix based on the particle matching results to obtain the particle's 3D motion trajectory and rotation information; selecting particles within the target range as local reference frames with the particle as the center; and solving the linear transformation tensor by least-squares fitting of the particle's 3D motion trajectory and rotation information, and calculating the non-affine displacement characterizing the degree of local irreversible plastic deformation based on the linear transformation tensor.

[0007] Based on the above-mentioned technical means, the embodiments of this application achieve accurate matching of adjacent strain state particles by constructing a multi-scale shape descriptor and minimizing its vector L2 norm difference. The three-dimensional motion trajectory and rotation information are obtained by combining particle displacement and rotation matrix calculation. Then, non-affine displacement is obtained by constructing a local reference frame and solving the linear transformation tensor by least square fitting. This overcomes the limitations of difficult matching of irregular particles across strain states and inaccurate acquisition of microscopic dynamic information such as motion, rotation, and plastic deformation. It provides reliable microscopic particle dynamic data support for subsequent identification of active clusters and quantitative characterization of dynamic heterogeneity.

[0008] Optionally, the multi-scale shape descriptor includes at least one of elongation, flatness, sphericity, convexity, and roundness. The definition and calculation formula of each shape descriptor are as follows: Elongation E and flatness F The calculation formula is:

[0009]

[0010] in, a , b ,c These are the lengths of the three main axes of the particle: long, medium, and short. The formula for calculating sphericity S is:

[0011] in, To match the actual particle volume For the same sphere, This represents the actual surface area of ​​the particles; convexity The calculation formula is:

[0012] in, Let V be the volume of the convex shell surrounding the particle. Roundness R The calculation formula is:

[0013] in, For the particle surface The area of ​​the triangular grid; The curvature corresponding to the largest inscribed sphere of the particle; Let be the average curvature of the particle.

[0014] Optionally, the formula for calculating particle matching is:

[0015] in, It is in an axial strain state. +1 is for AND The next adjacent axial strain state, Number the selected morphological feature indicators. The number of morphological feature indicators, In order to be in Under strain conditions, the first particle to be matched The values ​​of each morphological characteristic index, In order to be in Under +1 strain state, the candidate matching particle's first The numerical values ​​of each morphological characteristic index.

[0016] The formula for calculating the three-dimensional motion trajectory of a particle is:

[0017] in, Current strain state For the strain increment, Particles The corresponding matching particles are in The position of the center of mass under strain conditions. Particles The corresponding matching particles are in The position of the center of mass under strain.

[0018] The formula for calculating rotation information is:

[0019] in, Particles exist Triaxial orientation matrix under strain conditions Particles exist Triaxial orientation matrix under strain conditions for The inverse matrix.

[0020] The formula for calculating the root mean square error of the non-affine displacement of particles is:

[0021] in, Centered reference particle The best-fit affine deformation tensor For the central particle The total number of neighboring particles, Number the neighboring particles. , They are respectively and In this state, neighboring particles Relative central particles The displacement vector.

[0022] Optionally, the geometric information of the active clusters includes at least one of the following: cluster number, cluster size, centroid, and radius of gyration. The formulas for calculating the centroid and radius of gyration are as follows:

[0023]

[0024] in, This represents the total number of particles contained in the active cluster; This refers to the numbering of particles within the cluster; For the first in the cluster The volume of each particle; For the first in the cluster The location of the center of mass of each particle; It is the center of mass of the cluster.

[0025] Optionally, the spatiotemporal evolution behavior of active clusters includes merging behavior and diffusion behavior. Merging behavior: a convex hull is formed based on the centroid of the cluster particles in the next state. A search is performed on the convex hull. If the convex hull contains at least two centroids of the clusters in the previous state, the clusters in the previous state are merged into the clusters in the next state. The direction of the centroids of the clusters in the previous and next states is the merging direction. Diffusion behavior: a convex hull is formed in the clusters in the previous state. Particles in the clusters in the next state that are outside the convex hull are considered as diffused particles.

[0026] Based on the aforementioned technical means, this application embodiment clearly defines two core spatiotemporal evolution behaviors of active clusters through a convex hull retrieval method: for merging behavior, the convex hull of the subsequent state cluster contains at least two centroids of the preceding state cluster, with the merging direction also clearly defined; for diffusion behavior, the criterion is whether the particles of the subsequent state cluster are located outside the convex hull of the preceding state cluster. This solves the problem of the lack of a unified and quantifiable method for defining the merging and diffusion behaviors of active clusters, achieving accurate identification and classification of the two evolution behaviors, and providing a clear behavioral judgment basis for subsequent geometric information evolution analysis and quantitative characterization of dynamic heterogeneity of active clusters.

[0027] Optionally, the structural indices of the active clusters include cluster size and average local volume fraction of the clusters. The cluster size is the number of particles contained in the cluster, and the average volume fraction of the clusters is the average of the local volume fractions of the particles contained in the clusters. The formula for calculating the average volume fraction of the clusters is as follows:

[0028] in, For particle volume, This represents the volume of the Voronoi cell corresponding to the particle; The formula for calculating the kinetic parameters of active clusters is as follows:

[0029] in, For all particles in a cluster under the current strain state average value, For all clusters under this strain state The maximum value in; The formula for calculating the comprehensive index of active clusters is as follows:

[0030] in, For the size of the cluster, The average relative non-affine displacement of the cluster. denoted as the average local volume fraction of the cluster.

[0031] A second aspect of this application provides a device for quantitative analysis of the kinetic heterogeneity of irregular particulate materials, comprising: an acquisition module for selecting irregular particulate materials from experimental data, conducting triaxial tests based on X-ray CT on the irregular particulate materials, and acquiring CT slice images of the particulate materials after deformation at different times; a segmentation module for performing image segmentation on the CT slice images, reconstructing a three-dimensional segmentation result containing the particle number and geometric features based on the image segmentation result, and performing cross-strain state particle matching and tracking based on the three-dimensional segmentation result to obtain particle kinetic information; a comparison module for identifying active clusters from the particle kinetic information, evolving the geometric information of the active clusters, comparing the spatial distribution of clusters under different strain states based on the geometric information, and tracking the spatiotemporal evolution behavior of the active clusters based on the comparison result; and an analysis module for calculating the structural index, kinetic index, and comprehensive index of the active clusters based on the spatiotemporal evolution behavior, determining the quantitative characterization of kinetic heterogeneity based on at least one of the structural index, kinetic index, and comprehensive index, outputting the quantitative characterization of kinetic heterogeneity, and performing visual analysis on the quantitative characterization of kinetic heterogeneity.

[0032] Optionally, the segmentation module is further used for cross-strain state particle matching and tracking based on the three-dimensional segmentation results to obtain particle dynamics information, including: constructing a multi-scale shape descriptor characterizing the particle shape; matching particles in adjacent strain states by minimizing the L2 norm difference of the shape descriptor vector; calculating the particle displacement vector and rotation matrix based on the particle matching results to obtain the particle's three-dimensional motion trajectory and rotation information; selecting particles within the target range as local reference frames with the particle as the center; and solving the linear transformation tensor by least-squares fitting of the particle's three-dimensional motion trajectory and rotation information, and calculating the non-affine displacement characterizing the degree of local irreversible plastic deformation based on the linear transformation tensor.

[0033] Optionally, the multi-scale shape descriptor includes at least one of elongation, flatness, sphericity, convexity, and roundness. The definition and calculation formula of each shape descriptor are as follows: Elongation E and flatness F The calculation formula is:

[0034]

[0035] in, a , b , c These are the lengths of the three main axes of the particle: long, medium, and short. The formula for calculating sphericity S is:

[0036] in, To match the actual particle volume For the same sphere, This represents the actual surface area of ​​the particles; convexity The calculation formula is:

[0037] in, Let V be the volume of the convex shell surrounding the particle. Roundness R The calculation formula is:

[0038] in, For the particle surface The area of ​​the triangular grid; The curvature corresponding to the largest inscribed sphere of the particle; Let be the average curvature of the particle.

[0039] Optionally, the formula for calculating particle matching is:

[0040] in, It is in an axial strain state. +1 is for AND The next adjacent axial strain state, Number the selected morphological feature indicators. The number of morphological feature indicators, In order to be in Under strain conditions, the first particle to be matched The values ​​of each morphological characteristic index, In order to be in Under +1 strain state, the candidate matching particle's first The numerical values ​​of each morphological characteristic index.

[0041] The formula for calculating the three-dimensional motion trajectory of a particle is:

[0042] in, Current strain state For the strain increment, Particles The corresponding matching particles are in The position of the center of mass under strain conditions. Particles The corresponding matching particles are in The position of the center of mass under strain.

[0043] The formula for calculating rotation information is:

[0044] in, Particles exist Triaxial orientation matrix under strain conditions Particles exist Triaxial orientation matrix under strain conditions for The inverse matrix.

[0045] The formula for calculating the root mean square error of the non-affine displacement of particles is:

[0046] in, Centered reference particle The best-fit affine deformation tensor For the central particle The total number of neighboring particles, Number the neighboring particles. , They are respectively and In this state, neighboring particles Relative central particles The displacement vector.

[0047] Optionally, the geometric information of the active clusters includes at least one of the following: cluster number, cluster size, centroid, and radius of gyration. The formulas for calculating the centroid and radius of gyration are as follows:

[0048]

[0049] in, This represents the total number of particles contained in the active cluster; This refers to the numbering of particles within the cluster; For the first in the cluster The volume of each particle; For the first in the cluster The location of the center of mass of each particle; It is the center of mass of the cluster.

[0050] Optionally, the spatiotemporal evolution behavior of active clusters includes merging behavior and diffusion behavior. Merging behavior: a convex hull is formed based on the centroid of the cluster particles in the next state. The convex hull is searched, and if it contains at least two centroids of the previous state clusters, the previous state clusters are merged into the next state clusters. The direction of the centroids of the previous and next state clusters is the merging direction. Diffusion behavior: a convex hull is formed in the previous state clusters, and the particles of the next state cluster outside the convex hull are regarded as diffused particles.

[0051] Optionally, the structural indices of the active clusters include cluster size and average local volume fraction of the clusters. The cluster size is the number of particles contained in the cluster, and the average volume fraction of the clusters is the average of the local volume fractions of the particles contained in the clusters. The formula for calculating the average volume fraction of the clusters is as follows:

[0052] in, For particle volume, This represents the volume of the Voronoi cell corresponding to the particle; The formula for calculating the kinetic parameters of active clusters is as follows:

[0053] in, For all particles in a cluster under the current strain state average value, For all clusters under this strain state The maximum value in; The formula for calculating the comprehensive index of active clusters is as follows:

[0054] in, For the size of the cluster, The average relative non-affine displacement of the cluster. denoted as the average local volume fraction of the cluster.

[0055] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the program to implement the quantitative analysis method for the kinetic heterogeneity of irregular particulate materials as described in the above embodiments.

[0056] A fourth aspect of this application provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement the method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials as described in the above embodiments.

[0057] The fifth aspect of this application provides a computer program that, when executed, is used to implement the quantitative analysis method for the kinetic heterogeneity of irregular particulate materials as described in the above embodiments.

[0058] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0059] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to an embodiment of this application; Figure 2 This is a schematic diagram of a device for quantitative analysis of the dynamic heterogeneity of irregular particulate materials based on X-ray CT, according to an embodiment of this application. Figure 3 This is a flowchart of a method for quantitative analysis of the dynamic heterogeneity of irregular particulate materials based on X-ray CT, according to an embodiment of this application. Figure 4 The macroscopic mechanical response curve provided according to the embodiments of this application; Figure 5 Figure a is a schematic diagram of CT image processing provided in an embodiment of this application; Figure 5 Figure b is a schematic diagram of the three-dimensional particle reconstruction results provided in the embodiments of this application; Figure 6 This is a schematic diagram of the spatiotemporal evolution of the non-affine displacement of particles within five strain increments according to an embodiment of this application; Figure 7 This is a schematic diagram illustrating the spatiotemporal distribution evolution of active clusters in a shear particle system under different strain states according to embodiments of this application. Figure 8 Figure a is a schematic diagram of the size evolution of the largest and second largest clusters of the shear particle system under different strain states provided in the embodiments of this application; Figure 8 Figure b is a schematic diagram of the evolution of the number of clusters in the shear particle system under different strain states provided in the embodiments of this application; Figure 9 This is a schematic diagram illustrating the merging behavior of active clusters in a shear particle system under different strain states according to embodiments of this application. Figure 10 This is a schematic diagram illustrating the diffusion behavior of active clusters in a shear particle system under different strain states according to embodiments of this application. Figure 11 Figure a shows the sizes of different evolutionary types of clusters provided in the embodiments of this application. S Schematic diagram of probability density distribution; Figure 11 Figure b is a schematic diagram of the average relative non-affine displacement (ARD) of different evolutionary types of clusters provided in the embodiments of this application; Figure 11 Figure c is a schematic diagram of the average local volume fraction of different evolutionary types of clusters provided in the embodiments of this application; Figure 11 The d-plot represents the fitness of different evolutionary cluster types provided in the embodiments of this application. AA schematic diagram of the frequency distribution; Figure 12 Figure a is a schematic diagram of the differences in fitness among different evolutionary clusters provided in the embodiments of this application; Figure 12 Figure b is a schematic diagram illustrating the relationship between the probability of cluster dominance and diffusion and its fitness provided in the embodiments of this application. Figure 13 This is a block diagram of a device for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to an embodiment of this application; Figure 14 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0060] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0061] Particulate matter is a complex system formed by the interaction of a large number of solid particles. It is widely present in nature, such as pebbles, in industrial production and daily life, such as in grains. In the field of hydraulic engineering, the mixing and filling processes of rockfill are closely related to its mechanical behavior. Therefore, in-depth research on the mechanical properties of particulate materials has important theoretical value and engineering significance for improving engineering quality and structural safety. Under external shear, particulate materials exhibit heterogeneous and irreversible plastic rearrangement at the particle scale, which is considered to be the microscopic origin of macroscopic yielding, shear band formation, and slip avalanche. Among these, the dynamic heterogeneity originating from the disordered structure of particles plays a key role in controlling the deformation and failure modes of particulate systems. Revealing the evolution characteristics of this heterogeneity in sheared particulate systems is of great scientific significance for understanding the shear band formation mechanism and macroscopic yielding behavior.

[0062] Specifically, the spatiotemporal distribution of local plastic zones determines the formation of shear bands and macroscopic yielding. These regions are called STZs (Shear Transformation Zones), which manifest as particle clusters that rearrange themselves in response to external loads, directly reflecting the dynamic heterogeneity of the granular system. Colloidal glass experiments have observed that small clusters grow and merge with increasing strain, eventually forming large clusters; similar phenomena have also been observed in granular materials. Currently, there is a consensus that the evolution of plastic zones in shear granular materials is a percolation behavior from a local to a global scale. However, related technologies can only observe the qualitative characteristics of the dynamic heterogeneous evolution; the detailed process and driving mechanism of its accumulation, development, and eventual macroscopic deformation remain unclear.

[0063] In addition, the relevant technology has two technical limitations: First, numerical simulations often assume that particles are ideal spheres or simplified geometric shapes, making it difficult to capture the key characteristics of cluster evolution in irregular granular materials, which may lead to prediction errors in macroscopic deformation and localization behavior. Although some studies have attempted to introduce irregular particle shapes, there is a lack of corresponding experimental observations to verify this.

[0064] Second, although the rapid development of X-ray CT technology has enabled the non-destructive acquisition of information on the internal structure and motion of particulate materials at the three-dimensional scale, providing a new approach for studying particle dynamics, experimental data on the spatiotemporal evolution of irregular particulate materials during shearing is still relatively scarce.

[0065] The following description, with reference to the accompanying drawings, outlines a method, apparatus, and device for quantitative analysis of the dynamic heterogeneity of irregular particulate materials according to embodiments of this application. Addressing the difficulties mentioned in the background art regarding the inability to quantitatively analyze the spatiotemporal evolution of dynamic heterogeneity of irregular particulate materials at the mesoscale, this application provides a method for quantitative analysis of the dynamic heterogeneity of irregular particulate materials based on X-ray CT. This method, by combining in-situ triaxial shear tests with X-ray CT, enables precise characterization of the dynamic heterogeneity of irregular particulate materials during shearing and quantitative analysis of the spatiotemporal evolution of clusters. It allows for in-depth research into the shear localization mechanism of irregular particulate materials and provides high-fidelity physical experimental data support for establishing constitutive models based on irregularly shaped particle systems and predicting shear localization behavior. This solves the problems in related technologies, such as the difficulty in quantitatively analyzing the mesoscale dynamic heterogeneity of irregular particulate materials, the limitation to observing only qualitative evolutionary characteristics, prediction biases in numerical simulations due to particle shape simplification, and the lack of experimental data on the spatiotemporal evolution of clusters during the shearing of irregular particles.

[0066] Specifically, Figure 1 This is a flowchart illustrating a method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials provided in an embodiment of this application.

[0067] like Figure 1 As shown, the quantitative analysis method for the kinetic heterogeneity of irregular particulate materials includes the following steps: In step S101, irregular particulate materials are selected from the experimental data, and triaxial tests based on X-ray CT are carried out on the irregular particulate materials to obtain CT slice images of the particulate materials after deformation at different times.

[0068] It is understandable that the embodiments of this application acquire key raw data during the material deformation process, namely, microscopic CT slice images of granular materials after deformation at different times. This overcomes the limitations of numerical simulations in related technologies that often use ideal spherical or simplified geometrically shaped particles, allowing the research object to highly match actual irregular granular materials such as riprap in hydraulic engineering. In addition, by utilizing the non-destructive detection characteristics of X-ray CT, penetrating observation of the internal microstructure of granular materials is achieved. The time-series data acquisition at different times fills the gap in related technologies where it is difficult to capture the dynamic deformation process of particles. At the same time, the in-situ design based on triaxial tests can simulate the stress state of granular materials in actual engineering, such as shear loads, ensuring that the acquired CT images truly reflect the microscopic characteristics of the material under stress and deformation. This provides high-quality and highly reliable raw data support for subsequent steps such as image segmentation, 3D reconstruction, and particle matching and tracking, ensuring the accuracy of subsequent quantitative analysis of dynamic heterogeneity from the source.

[0069] It should be noted that irregular granular materials refer to solid particle aggregates whose particle geometry does not follow ideal spherical, cubic, or other regular shapes, and whose particle size and contours vary significantly. A key characteristic is the natural randomness of particle morphology, such as sharp edges and asymmetrical contours. Typical examples in engineering include riprap and natural sand and gravel in the fields of water conservancy and civil engineering. This clearly distinguishes them from the ideal spherical particles commonly used in numerical simulations and is closer to real-world engineering applications.

[0070] X-ray CT technology utilizes the penetrating power of X-rays to perform non-destructive scanning of particulate material samples during testing. A detector receives the penetrating X-ray signals, generating tomographic images reflecting the internal structure of the sample, enabling microstructural observation at the particle level. Triaxial testing involves applying confining pressure and axial pressure to the sample using testing equipment, simulating the stress environment of particulate materials in actual engineering. CT slice images are two-dimensional tomographic images generated along the sample's axial direction or a specified direction during X-ray CT scanning, reflecting the internal structure of the sample at a certain depth.

[0071] In step S102, the CT slice image is segmented, and a three-dimensional segmentation result containing the particle number and geometric features is obtained based on the image segmentation result. Based on the three-dimensional segmentation result, cross-strain state particle matching and tracking are performed to obtain particle dynamics information.

[0072] Understandably, this embodiment of the application accurately separates particles from the background in CT slices through image segmentation, laying the foundation for subsequent identification of individual particles; then, based on the segmentation results, it performs three-dimensional reconstruction to generate a three-dimensional segmentation result containing the unique number and geometric features of each particle; finally, it uses this three-dimensional result to perform cross-strain state particle matching and tracking, that is, to associate the same particle under different strains, thereby obtaining key particle dynamics information such as particle displacement and rotation. This solves the problem of the difficulty in accurately identifying and locating irregular particles due to their complex shapes, and overcomes the technical difficulty of matching the same particle under cross-strain states by binding particle numbers with geometric features. The resulting particle dynamics information provides data support for subsequent identification of active clusters and analysis of dynamic heterogeneity, providing a structured and traceable data foundation for quantifying the deformation behavior of particulate materials at the microscopic level.

[0073] In this embodiment, cross-strain state particle matching and tracking are performed based on the three-dimensional segmentation results to obtain particle dynamics information, including: constructing a multi-scale shape descriptor characterizing the particle shape; matching particles in adjacent strain states by minimizing the L2 norm difference of the shape descriptor vector; calculating the particle displacement vector and rotation matrix based on the particle matching results to obtain the particle's three-dimensional motion trajectory and rotation information; selecting particles within the target range as local reference frames with the particle as the center; and solving the linear transformation tensor by least-squares fitting of the particle's three-dimensional motion trajectory and rotation information, and calculating the non-affine displacement characterizing the degree of local irreversible plastic deformation based on the linear transformation tensor.

[0074] It is understood that the embodiments of this application achieve accurate matching of adjacent strain state particles by constructing a multi-scale shape descriptor and minimizing its vector L2 norm difference. The three-dimensional motion trajectory and rotation information are obtained by combining particle displacement and rotation matrix calculations. Then, non-affine displacement is obtained by constructing a local reference frame and solving the linear transformation tensor by least squares fitting. This overcomes the limitations of difficult matching of irregular particles across strain states and inaccurate acquisition of microscopic dynamic information such as motion, rotation, and plastic deformation. It provides reliable microscopic particle dynamic data support for subsequent identification of active clusters and quantitative characterization of dynamic heterogeneity.

[0075] It should be noted that the target range refers to the spatial range artificially defined around a single particle to be analyzed, used to select the necessary neighboring particles for the local reference frame. Its purpose is to construct a statistically significant set of particles that reflects local deformation characteristics for subsequent least-squares fitting to solve the linear transformation tensor and calculate non-affine displacements. This application does not specify the exact data for the target range.

[0076] In this embodiment, the multi-scale shape descriptor includes at least one of elongation, flatness, sphericity, convexity, and roundness. The definition and calculation formula of each shape descriptor are as follows: ElongationE and flatness F The calculation formula is:

[0077]

[0078] in, a , b , c These are the lengths of the three main axes of the particle: long, medium, and short. The formula for calculating sphericity S is:

[0079] in, To match the actual particle volume For the same sphere, This represents the actual surface area of ​​the particles; convexity The calculation formula is:

[0080] in, Let V be the volume of the convex shell surrounding the particle. Roundness R The calculation formula is:

[0081] in, For the particle surface The area of ​​the triangular grid; The curvature corresponding to the largest inscribed sphere of the particle; Let be the average curvature of the particle.

[0082] In this embodiment of the application, the formula for calculating particle matching is:

[0083] in, It is in an axial strain state. +1 is for AND The next adjacent axial strain state, Number the selected morphological feature indicators. The number of morphological feature indicators, In order to be in Under strain conditions, the first particle to be matched The values ​​of each morphological characteristic index, In order to be in Under +1 strain state, the candidate matching particle's first The numerical values ​​of each morphological characteristic index.

[0084] The formula for calculating the three-dimensional motion trajectory of a particle is:

[0085] in, Current strain state For the strain increment, Particles The corresponding matching particles are in The position of the center of mass under strain conditions. Particles The corresponding matching particles are in The position of the center of mass under strain.

[0086] The formula for calculating rotation information is:

[0087] in, Particles exist Triaxial orientation matrix under strain conditions Particles exist Triaxial orientation matrix under strain conditions for The inverse matrix.

[0088] The formula for calculating the root mean square error of the non-affine displacement of particles is:

[0089] in, Centered reference particle The best-fit affine deformation tensor For the central particle The total number of neighboring particles, Number the neighboring particles. , They are respectively and In this state, neighboring particles Relative central particles The displacement vector.

[0090] In step S103, active clusters are identified from particle dynamics information, the geometric information of active clusters is evolved, the spatial distribution of clusters under different strain states is compared based on the geometric information, and the spatiotemporal evolution behavior of active clusters is tracked based on the comparison results.

[0091] It is understood that the embodiments of this application identify active clusters with cooperative rearrangement characteristics from particle dynamics information, corresponding to shear transition regions, and then dynamically evolve the geometric information of these clusters under different strain states, such as cluster size, centroid, and radius of gyration. Subsequently, by comparing the spatial distribution differences of clusters under different strain states, the spatiotemporal evolution behavior of active clusters, such as merging and diffusion, is finally tracked. This solves the problem in related technologies that clusters can only be observed qualitatively and it is difficult to accurately capture their dynamic changes. Furthermore, by using the method of "geometric information evolution and spatial distribution comparison," a quantifiable dynamic tracking path is provided for the cluster analysis of irregular particulate materials. At the same time, the obtained spatiotemporal evolution behavior of clusters also lays the behavioral analysis foundation for subsequent calculation of the structural and dynamic indices of active clusters, and thus quantitatively characterizes the dynamic heterogeneity.

[0092] In this embodiment, the geometric information of the active clusters includes at least one of the following: cluster number, cluster size, centroid, and radius of gyration. The formulas for calculating the centroid and radius of gyration are as follows:

[0093]

[0094] in, This represents the total number of particles contained in the active cluster; This refers to the numbering of particles within the cluster; For the first in the cluster The volume of each particle; For the first in the cluster The location of the center of mass of each particle; It is the center of mass of the cluster.

[0095] In step S104, the structural, kinetic, and comprehensive indices of the active clusters are calculated based on the spatiotemporal evolution behavior. Based on at least one of the structural, kinetic, and comprehensive indices, a quantitative characterization of kinetic heterogeneity is determined, and the quantitative characterization of kinetic heterogeneity is output and visualized.

[0096] It is understood that the embodiments of this application complete a closed-loop analysis of the spatiotemporal evolution behavior, quantitative indicators, heterogeneity characterization, and result output of active clusters: First, based on the spatiotemporal evolution behavior of active clusters obtained in step S103, the corresponding structural indicators, kinetic indicators, and comprehensive indicators are calculated; then, based on at least one of these three types of indicators, the quantitative characterization results of kinetic heterogeneity are clarified, overcoming the limitations of qualitative descriptions in related technologies; finally, the quantitative characterization results are output and visualized. This solves the problem of the lack of a quantitative indicator system for the kinetic heterogeneity of irregular particulate materials in related technologies, and makes the abstract quantitative results more intuitive through visualization analysis. It not only provides a quantifiable analytical basis for subsequent in-depth research on shear localization mechanisms, but also provides a clear way to present results for intuitively judging the mechanical response characteristics of particulate materials in the engineering field.

[0097] In this embodiment, the spatiotemporal evolution behavior of active clusters includes merging behavior and diffusion behavior. Merging behavior: a convex hull is formed based on the centroid of the cluster particles in the next state. The convex hull is searched, and if it contains at least two centroids of the previous state clusters, the previous state clusters are merged into the next state clusters. The direction of the centroids of the previous and next state clusters is the merging direction. Diffusion behavior: a convex hull is formed in the previous state clusters, and the particles of the next state cluster outside the convex hull are regarded as diffused particles.

[0098] It is understood that the embodiments of this application clearly define two core spatiotemporal evolution behaviors of active clusters through the convex hull retrieval method: for merging behavior, the convex hull of the subsequent state cluster contains at least two centroids of the preceding state cluster, with the merging direction clearly defined; for diffusion behavior, the criterion is whether the particles of the subsequent state cluster are located outside the convex hull of the preceding state cluster. This solves the problem of the lack of a unified and quantifiable method for defining the merging and diffusion behaviors of active clusters, achieving accurate identification and classification of the two evolution behaviors, and providing a clear behavioral judgment basis for subsequent geometric information evolution analysis and quantitative characterization of dynamic heterogeneity of active clusters.

[0099] In this embodiment, the structural indices of the active clusters include cluster size and average local volume fraction of the cluster. The cluster size is the number of particles contained in the cluster, and the average volume fraction of the cluster is the average of the local volume fractions of the particles contained in the cluster. The formula for calculating the average volume fraction of the cluster is as follows:

[0100] in, For particle volume, This represents the volume of the Voronoi cell corresponding to the particle; The formula for calculating the kinetic parameters of active clusters is as follows:

[0101] in, For all particles in a cluster under the current strain state average value, For all clusters under this strain state The maximum value in; The formula for calculating the comprehensive index of active clusters is as follows:

[0102] in, For the size of the cluster, The average relative non-affine displacement of the cluster. denoted as the average local volume fraction of the cluster.

[0103] It should be noted that Voronoi is a mathematical method for spatial partitioning. Using the center of mass of each particle in the particle system as the reference center point, by drawing the perpendicular bisectors connecting the centers of mass of adjacent particles, in a three-dimensional space, these perpendicular bisectors will collectively enclose non-overlapping, closed regions that completely cover the entire particle system space. Each closed region is the Voronoi cell of the corresponding particle, and its volume is... .

[0104] The quantitative analysis method for the dynamic heterogeneity of irregular particulate materials proposed in this application takes real irregular particles as the research object. It captures microscopic images of material deformation through X-ray CT triaxial experiments, and combines image segmentation, three-dimensional reconstruction, and transstrain particle matching technology to accurately obtain particle dynamic information. Furthermore, through the identification of active clusters, spatiotemporal evolution tracking, and multi-dimensional index calculation, it overcomes the limitations of related technologies in quantitatively analyzing the microscopic dynamic heterogeneity of irregular particulate materials. This method not only reveals the evolutionary law of dynamic heterogeneity from local to global and the microscopic driving mechanism of macroscopic mechanical behavior, but also provides a scientifically quantitative index system and visualization tools for the microscopic mechanical analysis of particulate materials. Ultimately, it provides high-fidelity physical experimental data support for in-depth research on the shear localization mechanism of irregular particulate materials, as well as for establishing constitutive models based on irregularly shaped particle systems and predicting shear localization behavior.

[0105] Figure 2 This is a schematic diagram of the structure of a quantitative analysis device for the dynamic heterogeneity of irregular particulate materials based on X-ray CT provided in an embodiment of this application. The device includes an axial pressure control system, a confining pressure control system, a scanning control system, a data acquisition and control terminal, and a data quantitative analysis and processing system.

[0106] The axial pressure control system includes: 2. An axial displacement controller (for receiving terminal commands and adjusting the displacement parameters of the axial load); 3. A stepper motor (for providing power for the axial load); 4. An axial loading device (for directly applying axial pressure to the specimen); 5. A force-displacement sensor (for real-time monitoring of axial pressure and displacement data); and 6. A data acquisition unit (for collecting monitoring data from the force-displacement sensor and transmitting it back to the terminal). This system controls the axial loading process, precisely controlling and recording axial pressure and displacement. The confining pressure control system includes: 7. A confining pressure controller (for receiving terminal commands and adjusting the confining pressure parameters); and 8. A standard volume pressure controller (for providing a stable confining pressure environment for the specimen). This system controls and records the confining pressure during the triaxial test, ensuring the confining pressure conditions of the test. The scanning control... The control system includes an X-ray source (labeled 9) for emitting X-rays to penetrate the sample and an X-ray detector (labeled 10) for receiving the penetrated X-rays and generating CT scan data. This system is used to perform CT scans on irregular particulate material samples during loading, acquiring microstructural data under different loading states. The data acquisition and control terminal (labeled 1) centrally controls the coordinated operation of the axial pressure control system, confining pressure control system, and scanning control system, synchronously collecting axial pressure, displacement, confining pressure, and CT scan data output by each system. The quantitative data analysis and processing system, based on the multi-source data collected by the data acquisition and control terminal, performs data processing and analysis to achieve quantitative characterization of the dynamic heterogeneity evolution of irregular particulate materials, and outputs visualization and statistical analysis results. This is a functional module, and the hardware is not shown separately in the figure. The sample (labeled 11) is the test object being scanned and belongs to the loading object of the axial pressure control system.

[0107] The workflow of this quantitative analysis equipment is as follows: First, the sample and equipment are placed in the CT cabinet. Then, the data acquisition and control terminal controls the confining pressure control system to apply a confining pressure of 300 kPa to the sample and maintain the confining pressure stable. Next, the data acquisition and control terminal controls the axial pressure control system to perform axial loading, setting the loading speed to 0.025 mm / min to ensure that the test is in a quasi-static loading state. Loading is paused every 1% or 2% of axial strain. The data acquisition and control terminal controls the scanning control system to scan and collect data, and then continues loading. This cycle is repeated 13 times to obtain the macroscopic mechanical response curve and 13 sets of CT slice images under different conditions. Finally, the data quantitative analysis and processing system processes the acquired data, quantitatively analyzes the evolution of the dynamic heterogeneity of irregular particulate materials, and outputs visualization and statistical results.

[0108] The following section will elaborate on the quantitative analysis method for the dynamic heterogeneity of irregular particulate materials based on X-ray CT provided in the embodiments of this application, using the aforementioned quantitative analysis equipment. Figure 3 As shown, the specific steps are as follows: In step one, experimental data is acquired, and representative irregular particulate materials are selected to conduct micro triaxial tests based on X-ray CT. During the test, the coordinated operation of the axial pressure control system, confining pressure control system, and scanning control system is centrally controlled through a data acquisition and control terminal. The axial pressure control system, including an axial displacement controller, a stepper motor, and an axial loading device, is responsible for controlling axial loading and recording axial pressure and displacement. The confining pressure control system, including a confining pressure controller and a standard volume pressure controller, is responsible for controlling and recording confining pressure. The scanning control system, including an X-ray source and an X-ray detector, is responsible for performing CT scans on the sample during the loading process. Simultaneously, the data acquisition and control terminal collects the raw data of axial pressure, displacement, confining pressure, and CT scan output from the three systems, and finally integrates them to obtain the macroscopic mechanical response curve and CT slice images of the particulate material after deformation at different times.

[0109] Specifically, the irregular particulate material was Ottawa sand. Cylindrical samples with a height of 25 mm and a base diameter of 12 mm were prepared. The obtained macroscopic data are as follows: Figure 4 As shown, the sample was scanned 13 times to quantitatively analyze the evolution of dynamic heterogeneity of the sample during shearing.

[0110] In step two, image segmentation and 3D particle reconstruction are performed. The acquired CT slice images are sequentially binarized, segmented into particles, labeled with particles, and reconstructed into 3D particles to obtain a 3D segmentation result containing the particle number and geometric features. The geometric features of the particles include the centroid, volume, and surface area, and principal component analysis is used to determine the length and direction of the three principal axes of the particles (long, medium, and short).

[0111] Specifically, in this embodiment, a total of 9510 particles were segmented and labeled. A schematic diagram of the image processing process and the three-dimensional particle reconstruction results are shown below. Figure 5 As shown.

[0112] In step three, cross-strain state particle matching and tracking are performed.

[0113] First, a multi-scale shape descriptor is constructed to characterize particle shape, including elongation. Flatness sphericity convexity, roundness The definitions and calculation formulas for each descriptor are as follows: elongation With flatness Based on particle length ,middle ,short Calculation of the length of the three spindles, corresponding formula , ; Sphericity The similarity between a particle and a sphere is measured by the ratio of the surface area of ​​an equivalent sphere with the same volume as the particle to the actual surface area of ​​the particle. The corresponding formula is... Convexity: Characterizes the surface undulation of a particle, defined as the ratio of the particle volume to the volume of the convex hull surrounding the particle, where the convex hull is the smallest convex surface surrounding all the vertices of the particle. The corresponding formula is... Roundness Defined as the ratio of the average radius of curvature of the particle profile angle to the radius of the largest inscribed sphere. Calculation requires the first... The area of ​​each triangular mesh, the curvature corresponding to the largest inscribed sphere, and the average curvature of the particles, and their corresponding formulas. .

[0114] Then, particle matching: particle matching between adjacent strain states is achieved by minimizing the L2 norm difference of the shape descriptor vector, corresponding to the formula... .

[0115] Next, the particle motion information is calculated: three-dimensional displacement: determined by the difference in the position of the particle's center of mass under two loading conditions, corresponding to the formula. Rotation information: A rotation matrix is ​​constructed by comparing the triaxial orientations of the particles under two loading conditions, i.e., the unit vectors along the major, middle, and minor axes. The corresponding formula is... Then, based on the rotation matrix components (Reflecting changes in particle orientation) Calculate the direction of the rotation axis, corresponding to the formula. Corresponding formula with rotation angle and Ultimately, the three-dimensional motion trajectory and rotation information of the particles are obtained.

[0116] Finally, the non-affine displacement is calculated: Neighboring particles are selected as the local reference frame, and the best-fit affine deformation tensor of the central reference particle is obtained through least-squares fitting, i.e., by minimizing the sum of squared displacement deviations of the neighboring particles. The corresponding formula is... ,in For the central particle Neighborhood particles The number is used to calculate the non-affine displacement. , For strain increment The root mean square error of the best-fit affine deformation between the inner center reference particle and its neighboring particles, corresponding to the formula. It is used to characterize the degree of local irreversible plastic deformation.

[0117] Specifically, the spatiotemporal evolution of the non-affine displacement of particles within five strain increments during the shearing process in this embodiment of the application is as follows: Figure 6 As shown, the color of the particle represents the magnitude of the particle's non-affine displacement.

[0118] In step four, the identification and evolution tracking of active clusters are defined using a ranking method. A certain proportion of the particles are identified as active particles. The Voronoi subdivision algorithm is used to find the neighboring particles of each active particle, and a density clustering algorithm is used to identify the active clusters formed by these particles. Then, the geometric information of the clusters is calculated, including the number of clusters, cluster size (i.e., the number of particles contained in the cluster), centroid, and radius of gyration. The cluster centroid passes through the centroids of all particles within the cluster. With volume The weighted summation and average calculation are given by the following formula: The radius of gyration is calculated based on the deviation between the centroid of the particles within the cluster and the cluster centroid, weighted by particle volume, and the corresponding formula is... Finally, the spatial distribution of clusters under different strain states was compared to track their spatiotemporal evolution. Cluster evolution includes two behaviors: merging and diffusion. Merging is based on the formation of a convex hull by the centroid of the particles in the subsequent state cluster. If the convex hull contains at least two centroids of the preceding state clusters, then the preceding state clusters are determined to merge into the subsequent state clusters, and the direction of the centroids of the preceding and following state clusters is the merging direction. Diffusion is based on the formation of a convex hull by the preceding state clusters, and particles in the subsequent state cluster located outside the convex hull are considered diffusion particles.

[0119] Specifically, define The top 10% of particles are considered as active particles. The spatiotemporal distribution evolution of active clusters in the shear particle system under different strain states is as follows: Figure 7 As shown, particles within a cluster are colored according to the cluster's radius of gyration, while other particles are rendered transparent for clarity. The size evolution and cluster number evolution of the largest and second-largest clusters under different strain states in the shear particle system are shown below. Figure 8 As shown, after peak strain, the size of the largest cluster increases rapidly, becoming much larger than the second largest cluster, while the number of clusters decreases sharply after peak strain, corresponding to the cluster evolution behavior. The merging behavior of active clusters in the shear particle system under different strain states is shown in the figure. Figure 9 As shown, for clarity, cluster particles that did not participate in the merging behavior, as well as other particles, have been made transparent. The red arrows indicate the direction of cluster merging. The diffusion behavior of active clusters under different strain states is as follows: Figure 10 As shown, the colored parts represent particles that have diffused from the previous state compared to the previous state, and the color of the particles is determined by the radius of gyration of the cluster to which they belong. White particles represent particles that existed in the previous state.

[0120] In step five, kinetic heterogeneity is quantitatively characterized by calculating the structure and kinetic indices of the clusters. Considering multiple parameters, a comprehensive index is defined to quantify the stability and persistence of the clusters under external shear. The structural indices include cluster size (the number of particles contained in the cluster) and average local volume fraction (the average local volume fraction of all particles within the cluster), where the local volume fraction is the particle volume. Voronoi cell volume corresponding to the particle The ratio, corresponding to the formula Kinetic parameters include ARD (Average Relative) (cluster average relative non-affine displacement), corresponding formula The comprehensive indicators include fitness indicators and integrated cluster size. ARD, mean local volume fraction This is used to describe the stability and persistence of clusters under shear stress, and the corresponding formula is... .

[0121] Specifically, the size of clusters of different evolutionary types Probability density distribution, average relative non-affine displacement Average local volume fraction and fitness The frequency distribution results are as follows Figure 11 As shown, there are differences in the quantitative indicators of clusters of different evolutionary types.

[0122] In step six, the results are output and visualized. Through the data quantitative analysis and processing system, the particle displacement field, rotation field, non-affine deformation field, and cluster evolution data are output. The microscopic dynamics of particles and the spatiotemporal evolution process of clusters are visualized by using three-dimensional particle reconstruction and color mapping. Finally, the cluster size, average local volume fraction, ARD, fitness, and other quantitative indicators are statistically analyzed to reveal the intrinsic driving mechanism of shear band formation.

[0123] Specifically, embodiments of this application analyze the inter-group differences in fitness of clusters of different evolutionary types and the relationship between cluster dominance, the probability of diffusion, and their fitness. The results are as follows: Figure 12 As shown, fitness varies significantly among different types of clusters, and the higher the fitness, the greater the probability of the cluster becoming dominant and diffusing. The results indicate that fitness dominates the merging and diffusing behavior of clusters, and high-fitness clusters drive the shear localization process through a self-reinforcing process.

[0124] In summary, the embodiments of this application have at least the following beneficial effects: (1) This application combines in-situ triaxial shearing tests with X-ray CT and utilizes image segmentation and three-dimensional particle matching tracking technology to reconstruct high-resolution particle-scale dynamics, thereby enabling accurate characterization of the dynamic heterogeneity of irregular particle materials during shearing.

[0125] (2) This application quantitatively describes the stability and persistence of clusters by calculating the structure and dynamics of clusters and comprehensively considering the introduction of fitness as a new index. The method can realize the transformation of cluster spatiotemporal evolution from qualitative analysis to quantitative analysis. Combined with result visualization, it can quantitatively study the shear localization mechanism in irregular particulate materials.

[0126] (3) The analysis method and equipment proposed in this invention can realize the organic combination of shear loading, X-ray CT imaging and data processing, and can output multi-source information such as particle motion field, plastic deformation field and cluster evolution characteristics, providing high-fidelity physical test data support for establishing constitutive models based on irregularly shaped particle systems and predicting shear localization behavior.

[0127] Secondly, referring to the accompanying drawings, a quantitative analysis device for the kinetic heterogeneity of irregular particulate materials according to an embodiment of this application is described. Figure 13 This is a block diagram of a device for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to an embodiment of this application.

[0128] like Figure 13 As shown, the device 130 for quantitative analysis of the kinetic heterogeneity of irregular particulate materials includes: an acquisition module 1301, a segmentation module 1302, a comparison module 1303, and an analysis module 1304.

[0129] The acquisition module 1301 is used to select irregular particulate materials from experimental data, conduct triaxial tests based on X-ray CT on the irregular particulate materials, and acquire CT slice images of the particulate materials after deformation at different times; the segmentation module 1302 is used to perform image segmentation on the CT slice images, and obtain a three-dimensional segmentation result containing the particle number and geometric features based on the image segmentation result, and perform cross-strain state particle matching and tracking based on the three-dimensional segmentation result to obtain particle dynamic information; the comparison module 1303 is used to identify active clusters from the particle dynamic information, evolve the geometric information of the active clusters, compare the spatial distribution of clusters under different strain states based on the geometric information, and track the spatiotemporal evolution behavior of the active clusters based on the comparison results; the analysis module 1304 is used to calculate the structural index, dynamic index and comprehensive index of the active clusters based on the spatiotemporal evolution behavior, determine the quantitative characterization of dynamic heterogeneity based on at least one of the structural index, dynamic index and comprehensive index, output the quantitative characterization of dynamic heterogeneity and perform visualization analysis on the quantitative characterization of dynamic heterogeneity.

[0130] In this embodiment, the segmentation module 1302 is further used to perform cross-strain state particle matching and tracking based on the three-dimensional segmentation results to obtain particle dynamics information, including: constructing a multi-scale shape descriptor characterizing the particle shape; matching particles in adjacent strain states by minimizing the L2 norm difference of the shape descriptor vector; calculating the particle displacement vector and rotation matrix based on the particle matching results to obtain the particle's three-dimensional motion trajectory and rotation information; selecting particles within the target range as local reference frames with the particle as the center; and solving the linear transformation tensor by least-squares fitting of the particle's three-dimensional motion trajectory and rotation information, and calculating the non-affine displacement characterizing the degree of local irreversible plastic deformation based on the linear transformation tensor.

[0131] In this embodiment, the multi-scale shape descriptor includes at least one of elongation, flatness, sphericity, convexity, and roundness. The definition and calculation formula of each shape descriptor are as follows: Elongation E and flatness F The calculation formula is:

[0132]

[0133] in, a , b , c These are the lengths of the three main axes of the particle: long, medium, and short. The formula for calculating sphericity S is:

[0134] in, To match the actual particle volume For the same sphere, This represents the actual surface area of ​​the particles; convexity The calculation formula is:

[0135] in, Let V be the volume of the convex shell surrounding the particle. Roundness R The calculation formula is:

[0136] in, For the particle surface The area of ​​the triangular grid; The curvature corresponding to the largest inscribed sphere of the particle; Let be the average curvature of the particle.

[0137] In this embodiment of the application, the formula for calculating particle matching is:

[0138] in, It is in an axial strain state. +1 is for AND The next adjacent axial strain state, Number the selected morphological feature indicators. The number of morphological feature indicators, In order to be in Under strain conditions, the first particle to be matched The values ​​of each morphological characteristic index, In order to be in Under +1 strain state, the candidate matching particle's first The numerical values ​​of each morphological characteristic index.

[0139] The formula for calculating the three-dimensional motion trajectory of a particle is:

[0140] in, Current strain state For the strain increment, Particles The corresponding matching particles are in The position of the center of mass under strain conditions. Particles The corresponding matching particles are in The position of the center of mass under strain.

[0141] The formula for calculating rotation information is:

[0142] in, Particles exist Triaxial orientation matrix under strain conditions Particles exist Triaxial orientation matrix under strain conditions for The inverse matrix.

[0143] The formula for calculating the root mean square error of the non-affine displacement of particles is:

[0144] in, Centered reference particle The best-fit affine deformation tensor For the central particle The total number of neighboring particles, Number the neighboring particles. , They are respectively and In this state, neighboring particles Relative central particles The displacement vector.

[0145] In this embodiment, the geometric information of the active clusters includes at least one of the following: cluster number, cluster size, centroid, and radius of gyration. The formulas for calculating the centroid and radius of gyration are as follows:

[0146]

[0147] in, This represents the total number of particles contained in the active cluster; This refers to the numbering of particles within the cluster; For the first in the cluster The volume of each particle; For the first in the cluster The location of the center of mass of each particle; It is the center of mass of the cluster.

[0148] In the embodiments of this application, the spatiotemporal evolution behavior of active clusters includes merging behavior and diffusion behavior. Merging behavior: a convex hull is formed based on the centroid of the cluster particles in the next state. The convex hull is searched. If the convex hull contains at least two centroids of the previous state clusters, the previous state clusters are merged into the next state clusters. The direction of the centroids of the previous and next state clusters is the merging direction. Diffusion behavior: a convex hull is formed in the previous state clusters. Particles of the next state cluster outside the convex hull are considered as diffused particles.

[0149] In this embodiment, the structural indices of the active clusters include cluster size and average local volume fraction of the cluster. The cluster size is the number of particles contained in the cluster, and the average volume fraction of the cluster is the average of the local volume fractions of the particles contained in the cluster. The formula for calculating the average volume fraction of the cluster is as follows:

[0150] in, For particle volume, This represents the volume of the Voronoi cell corresponding to the particle; The formula for calculating the kinetic parameters of active clusters is as follows:

[0151] in, For all particles in a cluster under the current strain state average value, For all clusters under this strain state The maximum value in; The formula for calculating the comprehensive index of active clusters is as follows:

[0152] in, For the size of the cluster, The average relative non-affine displacement of the cluster. denoted as the average local volume fraction of the cluster.

[0153] It should be noted that the foregoing explanation of the embodiment of the method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials also applies to the device for quantitative analysis of the kinetic heterogeneity of irregular particulate materials in this embodiment, and will not be repeated here.

[0154] The quantitative analysis device for the dynamic heterogeneity of irregular particulate materials proposed in this application uses real irregular particles as the research object. It captures microscopic images of material deformation through X-ray CT triaxial experiments and combines image segmentation, three-dimensional reconstruction, and transstrain particle matching technology to accurately obtain particle dynamic information. Furthermore, through the identification of active clusters, spatiotemporal evolution tracking, and multidimensional index calculation, it overcomes the limitations of related technologies in quantitatively analyzing the microscopic dynamic heterogeneity of irregular particulate materials. It not only reveals the evolution law of dynamic heterogeneity from local to global and the microscopic driving mechanism of macroscopic mechanical behavior, but also provides a scientific quantitative index system and visualization tool for the microscopic mechanical analysis of particulate materials. Finally, it provides high-fidelity physical experimental data support for in-depth research on the shear localization mechanism of irregular particulate materials, as well as for establishing constitutive models based on irregularly shaped particle systems and predicting shear localization behavior.

[0155] Figure 14 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: The memory 1401, the processor 1402, and the computer program stored on the memory 1401 and executable on the processor 1402.

[0156] When the processor 1402 executes the program, it implements the quantitative analysis method for the dynamic heterogeneity of irregular particulate materials provided in the above embodiments.

[0157] Furthermore, electronic devices also include: Communication interface 1403 is used for communication between memory 1401 and processor 1402.

[0158] The memory 1401 is used to store computer programs that can run on the processor 1402.

[0159] The memory 1401 may include high-speed RAM (Random Access Memory) memory, and may also include non-volatile memory, such as at least one disk storage.

[0160] If the memory 1401, processor 1402, and communication interface 1403 are implemented independently, then the communication interface 1403, memory 1401, and processor 1402 can be interconnected via a bus to complete communication between them. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 14 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0161] Optionally, in a specific implementation, if the memory 1401, processor 1402, and communication interface 1403 are integrated on a single chip, then the memory 1401, processor 1402, and communication interface 1403 can communicate with each other through an internal interface.

[0162] The processor 1402 may be a CPU (Central Processing Unit), an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of this application.

[0163] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials.

[0164] This application also provides a computer program, which, when executed, is used to implement the above-described method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials.

[0165] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0166] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0167] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0168] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any of the following techniques known in the art, or a combination thereof: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (FPGAs), field-programmable gate arrays (FPGAs), etc.

[0169] Those skilled in the art will understand that all or part of the steps of the methods implementing the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0170] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials, characterized in that, Includes the following steps: Irregular particulate materials were selected from the experimental data, and triaxial tests based on X-ray CT were carried out on the irregular particulate materials to obtain CT slice images of the particulate materials after deformation at different times. The CT slice image is segmented, and a three-dimensional segmentation result containing the particle number and geometric features is obtained based on the image segmentation result. Based on the three-dimensional segmentation result, cross-strain state particle matching and tracking are performed to obtain particle dynamics information. Active clusters are identified from the particle dynamics information, the geometric information of the active clusters is evolved, the spatial distribution of the clusters under different strain states is compared based on the geometric information, and the spatiotemporal evolution behavior of the active clusters is tracked based on the comparison results. The structural, kinetic, and comprehensive indices of the active clusters are calculated based on the spatiotemporal evolution behavior. A quantitative characterization of kinetic heterogeneity is determined based on at least one of the structural, kinetic, and comprehensive indices. The quantitative characterization of kinetic heterogeneity is output and visualized.

2. The method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to claim 1, characterized in that, The process of performing cross-strain state particle matching and tracking based on the three-dimensional segmentation results to obtain particle dynamics information includes: Construct a multi-scale shape descriptor to characterize particle shape; Particle matching of adjacent strain states is achieved by minimizing the L2 norm difference of the shape descriptor vector; The displacement vector and rotation matrix of the particles are calculated based on the particle matching results to obtain the three-dimensional motion trajectory and rotation information of the particles. With the particles as the center, the particles within the target range are selected as the local reference frame. The three-dimensional motion trajectory of the particle and the rotation information are fitted by least squares to solve the linear transformation tensor. Based on the linear transformation tensor, the non-affine displacement characterizing the degree of local irreversible plastic deformation is calculated.

3. The method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to claim 2, characterized in that, The multi-scale shape descriptor includes at least one of elongation, flatness, sphericity, convexity, and roundness. The definition and calculation formula of each shape descriptor are as follows: The elongation E and the flatness F The calculation formula is: in, a , b , c These are the lengths of the three main axes of the particle: long, medium, and short. The formula for calculating sphericity S is: in, To match the actual particle volume For the same sphere, This represents the actual surface area of ​​the particle; convexity The calculation formula is: in, Let V be the volume of the convex shell surrounding the particle. Roundness R The calculation formula is: in, For the particle surface The area of ​​the triangular grid; The curvature corresponding to the largest inscribed sphere of the particle; Let be the average curvature of the particle.

4. The method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to claim 2, characterized in that, The formula for calculating particle matching is: in, It is in an axial strain state. +1 is for AND The next adjacent axial strain state, Number the selected morphological feature indicators. The number of morphological feature indicators, In order to be in Under strain conditions, the first particle to be matched The values ​​of each morphological characteristic index, In order to be in Under +1 strain state, the candidate matching particle's first The values ​​of each morphological characteristic index; The formula for calculating the three-dimensional motion trajectory of the particle is: in, Current strain state For the strain increment, Particles The corresponding matching particles are in The position of the center of mass under strain conditions. Particles The corresponding matching particles are in The position of the center of mass under strain conditions; The formula for calculating the rotation information is: in, Particles exist Triaxial orientation matrix under strain conditions Particles exist Triaxial orientation matrix under strain conditions for The inverse matrix; The formula for calculating the root mean square error of the non-affine displacement of the particles is as follows: in, Centered reference particle The best-fit affine deformation tensor For the central particle The total number of neighboring particles, Number the neighboring particles. , They are respectively and In this state, neighboring particles Relative central particles The displacement vector.

5. The method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to claim 1, characterized in that, The geometric information of the active clusters includes at least one of the following: cluster number, cluster size, centroid, and radius of gyration. The formulas for calculating the centroid and radius of gyration are as follows: in, This represents the total number of particles contained in the active cluster; This refers to the numbering of particles within the cluster; For the first in the cluster The volume of each particle; For the first in the cluster The location of the center of mass of each particle; It is the center of mass of the cluster.

6. The method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to claim 1, characterized in that, The spatiotemporal evolution behavior of the active clusters includes merging behavior and diffusion behavior. The merging behavior is as follows: a convex hull is formed based on the centroid of the cluster particles in the next state. The convex hull is searched, and if it contains at least two centroids of the previous state clusters, the previous state clusters are merged into the next state clusters. The direction of the centroids of the previous and next state clusters is the merging direction. The diffusion behavior is as follows: a convex hull is formed in the previous state clusters, and the particles of the next state cluster outside the convex hull are regarded as diffused particles.

7. The method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to claim 1, characterized in that, The structural indices of the active clusters include cluster size and average local volume fraction. The cluster size is the number of particles contained in the cluster, and the average volume fraction is the average local volume fraction of the particles contained in the cluster. The formula for calculating the average volume fraction is as follows: in, For particle volume, This represents the volume of the Voronoi cell corresponding to the particle; The formula for calculating the kinetic parameters of the active clusters is as follows: in, For all particles in a cluster under the current strain state average value, For all clusters under this strain state The maximum value in; The formula for calculating the comprehensive index of the active clusters is as follows: in, For the size of the cluster, The average relative non-affine displacement of the cluster. denoted as the average local volume fraction of the cluster.

8. A device for quantitative analysis of the kinetic heterogeneity of irregular particulate materials, characterized in that, include: The acquisition module is used to select irregular particulate materials from the experimental data, conduct triaxial tests based on X-ray CT on the irregular particulate materials, and acquire CT slice images of the particulate materials after deformation at different times. The segmentation module is used to segment the CT slice image, reconstruct a three-dimensional segmentation result containing the particle number and geometric features based on the image segmentation result, and perform cross-strain state particle matching and tracking based on the three-dimensional segmentation result to obtain particle dynamics information. The comparison module is used to identify active clusters from the particle dynamics information, evolve the geometric information of the active clusters, compare the spatial distribution of the clusters under different strain states based on the geometric information, and track the spatiotemporal evolution behavior of the active clusters based on the comparison results. The analysis module is used to calculate the structural, kinetic, and comprehensive indices of the active clusters based on the spatiotemporal evolution behavior, determine a quantitative characterization of kinetic heterogeneity based on at least one of the structural, kinetic, and comprehensive indices, output the quantitative characterization of kinetic heterogeneity, and perform visual analysis on the quantitative characterization of kinetic heterogeneity.

9. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials according to any one of claims 1-7.

10. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed, they implement the method for quantitative analysis of the kinetic heterogeneity of irregular particulate materials as described in any one of claims 1-7.

Images