Topological structure transformation-based granular material shear localization characterization method and system

Abstract

The invention discloses a granular material shearing localization characterization method based on topological structure transformation, which comprises the following steps: converting an original disordered granular system into a spatial interconnection topological network structure based on a topological space division method of granular information and Delou triangulation; identifying adjacent triangular structures with topological transformation in the topological network structure, and determining the starting time and the ending time of the topological transformation according to the time sequence evolution trend of the corresponding geometrical shape factor; and according to the starting time and the finishing time of the topological transformation, identifying an active adjacent triangular structure which is currently subjected to the topological transformation, and calculating related characteristic parameters of the topological transformation based on the active adjacent triangular structure so as to represent the shear localization behavior of the particle system under the action of the external load. On the basis, the shearing localization behavior of the particle system is finely and quantitatively represented from the perspective of meso-topological structure transformation.

Description

Technical Field

[0001] This invention relates to the field of granular material mechanics, specifically to a method and system for characterizing the shear localization of granular materials based on topological transformation. Background Technology

[0002] Particulate materials are widely present in human production and daily life, and are considered to be the most processed material on Earth besides water. The vast majority of geological bodies are granular materials, which are complex, disordered systems composed of a large number of discrete particles. When packed, they resemble solids; when flowing, they resemble liquids. However, their liquid and solid properties differ significantly from those of continuous media systems such as Newtonian fluids and elastic solids, exhibiting complex macroscopic and microscopic mechanical properties under external shear. Because granular materials are typical disordered and complex systems, they exhibit significant dynamic heterogeneity under external shear. That is, particles at different locations exhibit different motion characteristics due to significantly different local environments, leading to typical shear localization phenomena. Among these, the formation of shear bands is the most common type of strain localization and is considered closely related to the occurrence of geological disasters such as landslides. Therefore, to more accurately describe the constitutive relations and mechanical properties of granular materials, it is necessary to accurately obtain information such as the thickness of shear bands, the dip angle of shear bands, and the evolution of local microstructures.

[0003] Current methods for identifying shear localization in granular materials mostly calculate indices such as displacement increment, shear displacement, and non-affine displacement of individual particles, and then set thresholds to obtain particles with strong dynamics and identify shear localization regions. In fact, granular materials exhibit significant spatial correlation; the motion of a single particle inevitably induces the cooperative motion of surrounding particles, leading to changes in the local topology. However, current methods only consider the motion characteristics of individual particles and cannot quantitatively characterize the shear localization regions in the granular system from the perspective of topological changes. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies that only focus on the motion behavior of individual particles and cannot quantitatively characterize the shear localization of particle systems from the perspective of topological changes, this invention provides a method and system for characterizing the shear localization of particle materials based on topological transformation. By accurately identifying adjacent triangular structures of topological transformation, and then measuring them according to the relevant characteristic parameters of these adjacent triangular structures, the shear localization behavior of particle systems can be precisely and quantitatively characterized from the perspective of microscopic topological transformation.

[0005] According to one aspect of the present invention, a method for characterizing the shear localization of particulate materials based on topological transformation is provided, comprising: converting an original disordered particulate system into a spatially interconnected topological network structure based on particulate information and Delaunay triangulation; identifying adjacent triangular structures in the topological network structure that undergo topological transformation, and determining the start and end times of the topological transformation according to the temporal evolution trend of the corresponding geometric shape factors; calculating parameters such as the statistical characteristics, spatial correlation, and fractal dimension of the topological transformation to characterize the shear localization behavior of the particulate system under external loads.

[0006] Furthermore, based on particle information and Delaunay's triangulation method, the original disordered particle system is transformed into a spatially interconnected topological network structure, including: performing spatial topological partitioning on the original disordered particle system based on particle information and Delaunay's triangulation method to obtain the nearest neighbor relationship of each particle in space; constructing the topological network structure of the particle system based on the nearest neighbor relationship of each particle in space, including: treating each particle as a node in the topological network structure, adding a connecting edge between particles that are neighbors to form a spatially interconnected topological network structure.

[0007] Furthermore, before transforming the original disordered particle system into a spatially interconnected topological network structure using a topological space partitioning method based on particle information and Delaunay triangulation, the method also includes: employing a visual photoelastic particle experiment to capture particle information of the particle system during the shearing process using a high-speed camera.

[0008] Furthermore, the process involves identifying adjacent triangle structures undergoing topological transformation within the network structure, and determining the start and end times of the transformation based on the temporal evolution trend of the corresponding geometric shape factors. This includes: defining adjacent triangle structures as any two triangles sharing a common edge, and identifying common and non-common nodes within these adjacent triangle structures; comparing the network structures at two adjacent time points to identify all adjacent triangle structures undergoing topological transformation; whereby a topological transformation of an adjacent triangle structure is defined as a common node at the previous time point becoming a non-common node at the next time point, and vice versa; for adjacent triangle structures undergoing topological transformation, the geometric shape factor is defined as the ratio of the distance between the original common nodes to the distance between the original non-common nodes; based on the temporal evolution trend of the geometric shape factor, identifying monotonically increasing phases before and after the topological transformation time, and using the start and end points of these monotonically increasing phases as the start and end times of the topological transformation, respectively.

[0009] Furthermore, based on the temporal evolution trend of the geometric shape factor, a monotonically increasing phase before and after the topological transition is identified. The start and end points of the monotonically increasing phase are taken as the start and end times of the topological transition, respectively. This includes: calculating the corresponding geometric shape factor at each moment in the shearing process for adjacent triangle structures undergoing the topological transition to obtain the temporal evolution trend of the geometric shape factor; performing linear asymptotic fitting using a sliding time window method based on the temporal evolution trend of the geometric shape factor, and determining whether the current window shows an increasing trend based on the sign of the fitting slope; wherein, if the fitting slope is positive, the current window is determined to show an increasing trend; otherwise, the current window is determined not to show an increasing trend; integrating windows with continuous positive slopes, including the time when the topological transition occurs, to obtain the monotonically increasing phase before and after the topological transition; wherein, the start and end points of the monotonically increasing phase correspond to the start and end times of the topological transition, respectively.

[0010] Furthermore, the relevant characteristic parameters of the topological transformation are calculated to characterize the shear localization behavior of the granular system under external loads. This includes: at each time step, identifying active adjacent triangular structures undergoing topological transformation within the current granular system based on the start and completion times of the topological transformation; calculating the relevant characteristic parameters of the topological transformation based on the active adjacent triangular structures; and quantitatively characterizing the shear localization behavior of the granular system under external loads based on the temporal evolution trend of the relevant characteristic parameters with the shear process.

[0011] Furthermore, the relevant feature parameters include statistical features, spatial correlation, and fractal dimension.

[0012] According to one aspect of the present invention, a shear localization characterization system for particulate materials based on topological transformation is provided, comprising: a topological space partitioning module for converting an original disordered particulate system into a spatially interconnected topological network structure based on particulate information and the Delaunay triangulation method; a topological transformation identification module for identifying adjacent triangular structures undergoing topological transformation in the topological network structure, and determining the start and end times of the topological transformation based on the temporal evolution trend of the corresponding geometric shape factors; and a shear localization behavior characterization module for identifying active adjacent triangular structures currently undergoing topological transformation based on the start and end times of the topological transformation, and calculating relevant characteristic parameters of the topological transformation based on the active adjacent triangular structures to characterize the shear localization behavior of the particulate system under external loads.

[0013] According to one aspect of the present invention, an electronic device is provided, including a memory and a processor, the memory storing program instructions that are executed by the processor, the processor invoking the program instructions to perform the aforementioned method for characterizing the shear localization of particulate materials based on topological transformation.

[0014] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the aforementioned method for characterizing the shear localization of particulate materials based on topological transformation.

[0015] The above technical solution performs spatial topological partitioning of the original disordered particle system based on particle information and the Delaunay triangulation method, thereby constructing a spatially interconnected particle topological network structure. Then, based on the geometric shape factors of adjacent triangular structures, the start and end times of topological transformation events can be identified. By calculating the relevant characteristic parameters of the topological transformation events, the shear localization behavior of the particle system can be finely characterized from the perspective of microscopic topological structure transformation.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0017] (1) Based on particle information and Delaunay triangulation method, the present invention transforms the original disordered particle system into a spatially interconnected topological network structure to associate each particle in the particle system, so that the present invention can consider the motion characteristics of multiple particles at the same time.

[0018] (2) This invention can accurately identify the adjacent triangular structures of topological transformation, and by calculating the relevant characteristic parameters of topological transformation events, it realizes the quantitative characterization of shear localization regions in particulate systems from the perspective of topological structure change, thus providing a new and effective way for the study of the microstructure evolution mechanism and constitutive theory of particulate matter. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 The flowchart illustrates a method for characterizing the shear localization of particulate materials based on topological transformation, as provided in an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of a photoelastic particle physics experiment provided in an embodiment of the present invention.

[0022] Figure 3 This is a schematic diagram of a topological network structure constructed using Delaunay triangulation, provided as an embodiment of the present invention.

[0023] Figure 4This is a schematic diagram illustrating the temporal evolution of topological transformation events and their corresponding geometric shape factors, provided in an embodiment of the present invention.

[0024] Figure 5 This is a schematic diagram illustrating the shear localization evolution of a particle system during the shearing process, as provided in an embodiment of the present invention. Detailed Implementation

[0025] It should be noted that:

[0026] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0027] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices. The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be decomposed, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0029] Please refer to Figure 1 This invention provides a method for characterizing the shear localization of particulate materials based on topological transformation, specifically including the following steps:

[0030] Step S101: Based on particle information and Delaunay's triangulation method, the original disordered particle system is transformed into a spatially interconnected topological network structure.

[0031] In some embodiments, before step S101, the method further includes: conducting a shear test on the particle system using a visual photoelastic particle testing method, wherein the experimental parameters are determined according to specific circumstances; during the test, a high-speed camera is used to record the evolution characteristics of the particle system under external load, as shown in the attached figure. Figure 2 The schematic diagram of the particle system shown also provides particle information, including but not limited to particle position coordinates, size, and interparticle contact force. Particle position and size can be accurately extracted using image recognition algorithms; the interparticle contact force can be calculated from the light transmittance of the photoelastic particles under an external light field (existing technology, not elaborated here). The specific steps of step S101 will be further described below:

[0032] Step S1011: Based on particle information and the Delaunay triangulation method, the original disordered particle system is spatially topologically partitioned to obtain the nearest neighbor relationships of each particle in space. Obtaining the nearest neighbor relationships of each particle in space means finding its neighboring particles for each particle in the particle system, thus providing a foundation for the next step of constructing the topological network structure.

[0033] Step S1012, based on the construction of a topological network structure of the particle system in space for each particle, includes: treating each particle as a node in the topological network structure, and adding an edge between particles that are neighbors to form a spatially interconnected topological network structure (please refer to the appendix). Figure 3 ).

[0034] Step S102: Identify adjacent triangular structures in the topological network structure that have undergone topological transformation, and determine the start and end times of the topological transformation based on the temporal evolution trend of the corresponding geometric shape factors.

[0035] Step S1021: In the topological network structure, define any two triangles sharing a common edge as adjacent triangles, and identify common and non-common nodes within the adjacent triangles. Specifically, the two nodes on the shared edge are the common nodes of the adjacent triangles, and the other two nodes not on the edge are the non-common nodes. Figure 4 For example, in the initial adjacent triangles formed by particles h, i, j, and k, particles h and j are common nodes, while particles i and k are non-common nodes.

[0036] Step S1022: Compare the topological network structures at two adjacent time points to identify all adjacent triangles that have undergone a topological transformation. A topological transformation of adjacent triangles is defined as a common node in the previous time point becoming a non-common node in the next time point, and simultaneously, a non-common node in the previous time point becoming a common node in the next time point, i.e., a nearest neighbor exchange occurs. (See attached...) Figure 4 For example, under external shear action, Figure 4 The adjacent triangles shown undergo a topological transformation, where the original common nodes h and j become non-common nodes, while the original non-common nodes i and k become common nodes, thus completing the nearest neighbor exchange.

[0037] Step S1023: For adjacent triangles that have undergone a topological transformation, define the geometric shape factor of the adjacent triangles as the ratio of the distance between the original common nodes to the distance between the original non-common nodes. (See attached...) Figure 4 For example, Figure 4 The geometric shape factor of the adjacent triangles shown is defined as the ratio of the distance between the original common nodes h and j to the distance between the original non-common nodes i and k.

[0038] Step S1024: Based on the temporal evolution trend of the geometric shape factor, identify the monotonically increasing phases before and after the topological transition moment, and take the start point and end point of the monotonically increasing phase as the start time and completion time of the topological transition event, respectively.

[0039] In step S1024, for adjacent triangular structures undergoing topological transformation, the corresponding geometric shape factor is calculated at each moment during the shearing process to obtain the temporal evolution trend of the geometric shape factor. Based on the temporal evolution data of the geometric shape factor, a sliding time window method is used for linear asymptotic fitting. The sign of the fitting slope determines whether the current window data shows an overall increasing trend. Specifically, if the slope is positive, the current window shows an increasing trend; otherwise, the current window does not show an increasing trend. Windows with consecutive positive slopes, including the moment of topological transformation, are integrated to obtain a monotonically increasing phase before and after the moment of topological transformation. The start and end points of the obtained monotonically increasing phase are the start and end times of the corresponding topological transformation event, respectively. (See attached diagram.) Figure 4 For example, attached Figure 4 The temporal evolution trend of the geometric shape factors of adjacent triangular structures is illustrated, where the black dashed lines mark the start time, nearest neighbor exchange time, and end time of the corresponding topological transformation event, respectively.

[0040] Step S103: Identify the active adjacent triangular structures undergoing topological transformation within the current particle system based on the start and completion times of the topological transformation event, and calculate the relevant characteristic parameters of the topological transformation based on the active adjacent triangular structures to characterize the shear localization behavior of the particle system under external loads.

[0041] It should be noted that step S102 determines the start and end times of each topological transformation event individually based on the change in shape factor. Step S103, after obtaining the start and end times of each topological transformation event, studies all topological transformation events currently occurring in the system at each shear step (i.e., studies all adjacent triangular structures undergoing topological transformation at each shear step; these active adjacent triangular structures will connect in space to form clusters and complex spatial structures). Further analysis of the distribution characteristics of the spatial connectivity structures formed by these topological transformation events is then performed, thereby achieving a quantitative characterization of the shear localization behavior of the granular system under external loads. The specific steps of step S103 will be further described below:

[0042] Step S1031: At each time step, based on the start and completion times of the topological transformation, identify the active adjacent triangular structures undergoing topological transformation within the current particle system. (See attached...) Figure 5 As shown, at each time step, based on the start and end times of the topological transition event, active adjacent triangular structures undergoing topological transition within the current particle system are identified. Figure 5 The figure shows the adjacent triangular structures of the particle system undergoing topological transformation at different shear strains.

[0043] Step S1032: Calculate the relevant feature parameters of the topological transformation based on the active adjacent triangle structure; wherein, the relevant feature parameters include, but are not limited to, statistical features, spatial correlation and fractal dimension.

[0044] In step S1032, the total number and location of active adjacent triangular structures are statistically analyzed. The spatial correlation characteristics of these structures are calculated using a two-point correlation function, and the fractal dimension of the connected clusters formed by these structures is also calculated. It should be noted that active adjacent triangular structures are not randomly distributed in space. A topological shift in one location can lead to adjustments in neighboring particles, potentially causing other topological shift events. Therefore, different active adjacent triangular structures exhibit spatial correlation characteristics, which can be quantified using a two-point correlation function or other spatial correlation measurement methods. Different topological shift events are closely related in space, forming connected clusters of varying sizes. Based on the size-equivalent diameter distribution of connected clusters in the particle system, the fractal dimension of the connected clusters can be obtained. This quantity is essentially also a measure of the spatial distribution of topological shift events.

[0045] Step S1033: Based on the temporal evolution trend of relevant characteristic parameters with the shear process, a quantitative characterization of the shear localization behavior of the particle system under external load is achieved.

[0046] In step S1033, Figure 5The figure presents the characterization effect on the shear localization behavior of granular systems. The black quadrilaterals in the figure represent adjacent triangular structures undergoing topological transformation. As shearing proceeds, clearly visible local shear bands form in the granular system, demonstrating the good implementation effect of this invention and its ability to accurately characterize the shear localization behavior of granular systems. It should be noted that traditional studies can only observe some areas of strong local shearing, but these observations are mostly qualitative. This invention, however, can accurately identify active adjacent triangular structures undergoing topological transformation, and then measure them based on relevant characteristic parameters such as the spatial distribution or statistical characteristics of these active adjacent triangular structures. Essentially, this quantitatively characterizes the shear localization behavior of granular systems.

[0047] Based on the same technical concept as the foregoing embodiments, this invention also provides a shear localization characterization system for particulate materials based on topological transformation. The system includes a topological space partitioning module for converting the original disordered particulate system into a spatially interconnected topological network structure based on particulate information and the Delaunay triangulation method; a topological transformation identification module for identifying adjacent triangular structures undergoing topological transformation within the topological network structure, and determining the start and end times of the topological transformation based on the temporal evolution trend of the corresponding geometric shape factors; and a shear localization behavior characterization module for identifying active adjacent triangular structures currently undergoing topological transformation based on the start and end times of the topological transformation, and calculating relevant characteristic parameters of the topological transformation based on the active adjacent triangular structures to characterize the shear localization behavior of the particulate system under external loads.

[0048] Based on the same technical concept as the foregoing embodiments, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute the aforementioned method for characterizing the shear localization of particulate materials based on topological transformation.

[0049] Based on the same technical concept as the foregoing embodiments, the present invention also provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the above-described method for characterizing the shear localization of particulate materials based on topological transformation.

[0050] In summary, this invention performs spatial topological partitioning of the original disordered particle system based on particle information and the Delaunay triangulation method, thereby constructing a spatially interconnected particle topological network structure. Furthermore, based on the geometric shape factors of adjacent triangular structures, the start and end times of topological transition events can be identified. By calculating the relevant characteristic parameters of the topological transition events, the shear localization behavior of the particle system can be precisely characterized from the perspective of mesoscopic topological structure transformation. This provides a novel and effective approach for the study of the mesoscopic structural evolution mechanism and theory of particulate matter.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for characterizing the shear localization of particulate materials based on topological transformation, characterized in that, include: Based on particle information and Delaunay's triangulation method, the original disordered particle system is transformed into a spatially interconnected topological network structure. Identify adjacent triangular structures in the topological network structure that undergo topological transformation, and determine the start and end times of the topological transformation based on the temporal evolution trend of the corresponding geometric shape factors. Based on the start and completion times of the topological transformation, active adjacent triangular structures currently undergoing topological transformation are identified. Based on the active adjacent triangular structures, relevant characteristic parameters of the topological transformation are calculated to characterize the shear localization behavior of the particle system under external loads.

2. The method for characterizing the shear localization of particulate materials based on topological transformation as described in claim 1, characterized in that, Based on particle information and Delaunay's triangulation method, the original disordered particle system is transformed into a spatially interconnected topological network structure, including: Based on particle information and Delaunay's triangulation method, the original disordered particle system is spatially topologically partitioned to obtain the nearest neighbor relationship of each particle in space. The topological network structure of the particle system is constructed based on the proximity relationship of each particle in space, including: treating each particle as a node in the topological network structure, and adding a connecting edge between particles that are close neighbors to form a spatially interconnected topological network structure.

3. The method for characterizing the shear localization of particulate materials based on topological transformation as described in claim 1, characterized in that, Before the topological space partitioning method based on granular information and Delaunay triangulation transforms the original disordered granular system into a spatially interconnected topological network structure, it also includes: A visual photoelastic particle experiment was conducted, using a high-speed camera to capture particle information during the shearing process of the particle system.

4. The method for characterizing shear localization of particulate materials based on topological transformation as described in claim 1, characterized in that, Identify adjacent triangular structures undergoing topological transformations in a network structure, and determine the start and end times of the topological transformations based on the temporal evolution trends of the corresponding geometric shape factors, including: In the aforementioned topological network structure, every two triangles sharing a common edge are defined as adjacent triangle structures, and common nodes and non-common nodes in the adjacent triangle structures are identified. By comparing the topological network structures at two adjacent time points, all adjacent triangle structures that have undergone topological transformation are identified. The topological transformation of adjacent triangle structures is defined as a common node in the previous time point becoming a non-common node in the next time point, and at the same time, a non-common node in the previous time point becoming a common node in the next time point. For adjacent triangle structures that undergo topological transformation, the geometric shape factor of the adjacent triangle structure is defined as the ratio of the distance between the original common nodes to the distance between the original non-common nodes. Based on the temporal evolution trend of the geometric shape factor, the monotonically increasing phases before and after the topological transition are identified, and the starting point and ending point of the monotonically increasing phase are respectively taken as the start time and completion time of the topological transition.

5. The method for characterizing the shear localization of particulate materials based on topological transformation as described in claim 4, characterized in that, Based on the temporal evolution trend of the geometric shape factor, a monotonically increasing phase is identified before and after the topological transition. The start and end points of the monotonically increasing phase are respectively taken as the start and end times of the topological transition, including: For adjacent triangular structures that undergo topological transformation, the corresponding geometric shape factor is calculated at each moment in the shearing process to obtain the temporal evolution trend of the geometric shape factor. Based on the temporal evolution trend of the geometric shape factor, a linear asymptotic fitting is performed using the sliding time window method. The sign of the fitting slope determines whether the current window shows an increasing trend. If the fitting slope is positive, the current window is determined to show an increasing trend; otherwise, the current window is determined not to show an increasing trend. By integrating windows with continuously positive slopes, including the time when the topology transition occurs, a monotonically increasing phase before and after the time of the topology transition is obtained; wherein the starting point and the ending point of the monotonically increasing phase correspond to the start time and the completion time of the topology transition, respectively.

6. The method for characterizing shear localization of particulate materials based on topological transformation as described in claim 1, characterized in that, Based on the start and completion times of the topological transformation, active adjacent triangular structures undergoing the transformation are identified. Relevant characteristic parameters of the topological transformation are calculated based on these active adjacent triangular structures to characterize the shear localization behavior of the granular system under external loads, including: At each moment, based on the start and completion times of the topological transformation, identify the active adjacent triangular structures undergoing topological transformation within the current particle system; Calculate the relevant characteristic parameters of the topological transformation based on the active adjacent triangle structure; Based on the temporal evolution trend of the relevant characteristic parameters with the shear process, a quantitative characterization of the shear localization behavior of the granular system under external load is achieved.

7. The method for characterizing shear localization of particulate materials based on topological transformation as described in claim 6, characterized in that, The relevant feature parameters include statistical features, spatial correlation, and fractal dimension.

8. A shear localization characterization system for particulate materials based on topological transformation, characterized in that, include: The topology space partitioning module is used to transform the original disordered particle system into a spatially interconnected topology network structure based on particle information and Delaunay's triangulation method. The topology transformation identification module is used to identify adjacent triangular structures in the topological network structure that have undergone topological transformation, and to determine the start and end times of the topology transformation based on the temporal evolution trend of the corresponding geometric shape factors. The shear localization behavior characterization module is used to identify active adjacent triangular structures undergoing topological transformation based on the start and completion times of the topological transformation, and to calculate relevant characteristic parameters of the topological transformation based on the active adjacent triangular structures to characterize the shear localization behavior of the particle system under external loads.

9. An electronic device, characterized in that, The device includes a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute a method for characterizing the shear localization of particulate materials based on topological transformation as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to execute the shear localization characterization method for particulate materials based on topological transformation as described in any one of claims 1 to 7.

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