Three-dimensional particle medium force chain identification method

Abstract

The invention discloses a three-dimensional particle medium force chain identification method, which comprises the following steps: traversing all particles in a three-dimensional particle medium, and calculating the stress tensor of each particle to obtain the minimum principal stress of each particle; the average value of the minimum principal stress of all the particles is calculated, and the particles with the minimum principal stress larger than the average value of the minimum principal stress of all the particles in absolute value are screened out to serve as high-stress particles; any one high-stress particle is selected as an initial particle of a force chain; taking the direction vector of the minimum principal stress of the initial particles as the extension direction of a force chain; particles meeting the collimation requirement are searched from the particles adjacent to the initial particles to serve as potential force chain particles; selecting the particles with the minimum principal stress from the potential force chain particles as effective force chain particles; and taking the effective force chain particles as initial particles, and repeating the steps until the effective force chain particles do not exist, thereby obtaining a force chain with a certain length. According to the method, the three-dimensional particle medium force chain can be quickly and accurately obtained.

Description

Technical Field

[0001] The present invention relates to the field of granular computational mechanics, and particularly to a method for identifying force chains in three-dimensional granular media. Background Art

[0002] Under the action of an external load, contacts are generated between adjacent particles inside the granular medium, forming a path for stress transmission. The resulting filamentous structure with significantly different strengths is called a force chain. Force chains can be divided into strong and weak ones. The path that transmits a larger share of the load constitutes a strong force chain. Conversely, a weak force chain is formed. Force chains are not only related to the intrinsic properties of the granular medium itself but also affected by boundary conditions and the initial state. A number of force chains intersect and penetrate inside the granular medium to form a force chain network. The complex dynamic response of the force chain network largely affects the strain localization characteristics and strength characteristics of the granular medium, determining the macroscopic mechanical properties of the granular medium. Photoelastic tests and magnetic resonance elastography can identify the force chain network. The greater the brightness of a particle, the greater the stress it experiences. A number of highly bright particles form a filamentous force chain structure, and multiple force chains constitute the force chain network.

[0003] Scholars have many different understandings of force chains, and there is still no consensus on its definition so far. Therefore, it is difficult to quantitatively analyze the structure and its evolution behavior of force chains. Currently, most scholars believe that a force chain needs to meet three necessary conditions: (1) A force chain is a string of particles composed of three or more particles; (2) The particles that make up the force chain are high-stress particles; (3) The force chain meets the collinearity requirement in terms of spatial structure, that is, the acute angle between the branch vector direction of any two adjacent particles in the force chain and the direction of the minor principal stress of each particle needs to be less than or equal to 45°. This definition has practical application value for revealing the mesoscopic mechanism of granular media and has been widely used in studying the dynamic response of force chains inside two-dimensional granular media. However, when this definition is applied to three-dimensional granular media, it is difficult to meet the collinearity requirement of force chains, resulting in a chaotic force chain network and being unable to effectively reveal the internal response mechanism of three-dimensional granular media under external stress. Summary of the Invention

[0004] Aiming at the deficiencies existing when the current definition of force chains is applied to three-dimensional granular media, the present invention proposes a method for identifying force chains in three-dimensional granular media, and the specific technical solution is as follows:

[0005] A method for identifying force chains in three-dimensional granular media includes the following steps:

[0006] Step 1: Traverse the information of all particles in the three-dimensional granular medium, calculate the stress tensor of each particle, and obtain the minimum principal stress of each particle; then calculate the average value of the minimum principal stresses of all particles, and screen out the particles whose absolute value of the minimum principal stress is greater than the average value of the minimum principal stresses of all particles as high-stress particles;

[0007] Step 2: Select any high-stress particle as the starting particle of the force chain;

[0008] Step 3: Use the direction vector of the minimum principal stress of the starting particle as the extension direction of the force chain;

[0009] Step 4: Search for particles that meet the collinearity requirements from the adjacent particles of the starting particle as potential force chain particles; the collinearity requirements include:

[0010] (1) The acute angle between the branch vector directions of any two adjacent particles in the force chain and the minimum principal stress direction of each particle needs to be less than or equal to the set angle threshold;

[0011] (2) The acute angle between the branch vectors of two adjacent particles on the force chain and the branch vectors of the initial two particles on the force chain needs to be less than or equal to the set acute angle threshold;

[0012] Step 5: If the number of potential force chain particles obtained in Step 4 is one, then take this particle as the effective force chain particle; if it is greater than one, select the particle with the minimum minimum principal stress among the potential force chain particles as the effective force chain particle; and take the effective force chain particle as the starting particle, and return to Step 3 until there are no effective force chain particles, thereby obtaining a force chain of a certain length.

[0013] Furthermore, the reasonable ranges of φ and θ are 40° to 50°.

[0014] Furthermore, both φ and θ are 45°.

[0015] Furthermore, the three-dimensional granular medium is a unit material or a multi-component composite material.

[0016] The beneficial effects of the present invention are as follows:

[0017] (1) The three-dimensional granular medium force chain identification method of the present invention can intuitively observe a force chain network similar to that inside a two-dimensional granular medium.

[0018] (2) The three-dimensional granular medium force chain identification method of the present invention is applicable to both single and multi-component composite materials. Brief Description of the Drawings

[0019] Figure 1 is the identification flow chart of the three-dimensional granular medium force chain identification method of the present invention.

[0020] Figure 2 is a schematic diagram of a discrete element specimen of a certain binary composite material in the standard triaxial test state in the embodiment of the present invention.

[0021] Figure 3 is the distribution state of high-stress particles at different loading stages in the embodiment of the present invention.

[0022] Figure 4 It is the morphology and spatial distribution of force chains at different loading stages in the embodiments of the present invention. Detailed implementation manners

[0023] The present invention will be described in detail below according to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become more apparent. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0024] As Figure 1 shown, the three-dimensional granular medium force chain identification method of the present invention includes the following steps:

[0025] Step 1: Traverse the information of all particles in the three-dimensional granular medium, calculate the stress tensor of each particle, and obtain the minimum principal stress of each particle; then calculate the average value of the minimum principal stresses of all particles, and screen out the particles whose absolute value of the minimum principal stress is greater than the average value of the minimum principal stresses of all particles as high-stress particles.

[0026] Under the action of an external load, the stress tensor of any particle α inside the granular medium is σ α , which is expressed in component form as:

[0027]

[0028] In the formula, V α is the volume of particle α; n c,α is the number of contacts acting on particle α; is the component of the contact point coordinate x c ; is the component of the center coordinate x α of particle α; is the component of the unit vector pointing from the geometric center of particle α to the contact point; is the component of the contact force at the contact point; R α is the radius of particle α; is the normal component f c,α of the contact force f c,n ; is the tangential component f c,α of the contact force f c,t ;

[0029] The minimum principal stress of particle α is calculated from the stress tensor σ α of particle α. Then, the high-stress particles need to satisfy the following formula:

[0030]

[0031] In the formula, N is the total number of particles, is the minimum principal stress of particle k.

[0032] Step 2: Select any high-stress particle as the starting particle of the force chain;

[0033] Step 3: Use the direction vector of the minimum principal stress of the starting particle as the extension direction of the force chain.

[0034] In this embodiment, the minimum principal stress of particle α The direction vector of is The components of can be determined by the components of the stress tensor σ α Their calculation formulas are respectively

[0035]

[0036] In the formula, σ ii (i = 1, 2, 3) are the components on the main diagonal of the stress tensor σ α τ ij (i, j = 1, 2, 3 and i ≠ j) are the components off the main diagonal of the stress tensor σ α Off the main diagonal.

[0037] Step 4: Search for particles that meet the collinearity requirement from the adjacent particles of the starting particle as potential force chain particles; the collinearity requirement includes:

[0038] (1) The acute angle between the branch vector directions of any two adjacent particles in the force chain and the direction of the minimum principal stress of each particle needs to be less than or equal to the set angle threshold;

[0039] (2) The acute angle between the branch vectors of two adjacent particles on the force chain and the branch vectors of the initial two particles on the force chain needs to be less than or equal to the set acute angle threshold.

[0040] In this embodiment, taking β and γ in contact with the starting particle α as an example, the branch vector u β,α Is the vector from the center of particle α to the center of particle β, and the branch vector u γ,α Is the vector from the center of particle α to the center of particle γ.

[0041] If particle β is a force chain particle, then it needs to simultaneously meet the following conditions of the collinearity requirement (1):

[0042]

[0043] If and particle γ are force chain particles, then the following conditions need to be simultaneously met:

[0044]

[0045] The collinearity requirement (2) is specifically expressed as:

[0046]

[0047] In the formula, u k,k-1 is the branch vector of two adjacent particles on a single force chain, and u 1,0 is the branch vector of the starting two particles on a single force chain, and n is the number of particles on a single force chain.

[0048] The values of the angle φ and the angle θ have a great influence on the configuration of the force chain and need to be reasonably selected. The reasonable ranges of φ and θ are 40° to 50°, and more preferably 45°.

[0049] Step Five: If the potential force chain particles obtained in Step Four are one, then take this particle as the effective force chain particle; if there are more than one, then select the particle with the minimum minimum principal stress among the potential force chain particles as the effective force chain particle; and take the effective force chain particle as the starting particle, and return to Step Three until there are no effective force chain particles, thereby obtaining a force chain of a certain length.

[0050] When there are more than one potential force chain particles, that is, if the identified force chain structure has a branch structure, at this time, select the particle with a relatively small minimum principal stress among the potential force chain particles as the effective force chain particle.

[0051] This embodiment takes the standard triaxial test of a certain binary mixed granular medium as an example. As Figure 2 shown, the upper and lower ends of the specimen are subjected to deviatoric stress, and the side is subjected to confining pressure. During the loading process, when the specimen is in a certain stress state, traverse the contact forces and contact point information of all particles, calculate the stress tensor of the particles, and then calculate the minimum principal stress of the particles. According to the judgment formula of high-stress particles, screen out the high-stress particles. Select at least the particles adjacent to two high-stress particles from these high-stress particles as the search range of force chain particles.

[0052] Figure 3 Shows the distribution state of high-stress particles in the specimen at different loading stages. Among them, the high-stress particles are in a highlighted state, and the remaining particles are treated transparently. In this embodiment, both φ and θ are taken as 45°. Figure 4 Shows the morphology and spatial distribution of the force chain at different loading stages. Under the static stress state before loading, the force chains are randomly distributed in all directions in three-dimensional space. After loading, the force chains quickly concentrate in the loading direction, and the distribution density of the force chains is relatively large. As the loading progresses, the direction of the force chains deflects, and the distribution density of the force chains becomes smaller and smaller. This dynamic characteristic is consistent with the general understanding of the evolution of internal force chains in the specimen during the standard triaxial test.

[0053] Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not used to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims

1. A three-dimensional granular medium force chain identification method, characterized in that: The steps include: Step 1: Traverse the information of all particles in the three-dimensional granular medium, calculate the stress tensor of each particle, and obtain the minimum principal stress of each particle; then calculate the average value of the minimum principal stress of all particles, and screen out particles whose minimum principal stress is greater than the average value of the minimum principal stress of all particles in absolute value as high stress particles; Step 2: Select any high stress particle as the starting particle of the force chain; Step 3: Take the direction vector of the minimum principal stress of the starting particle as the extension direction of the force chain; Step 4: Find particles that meet the collimation requirements from the adjacent particles of the starting particle as potential force chain particles; the collimation requirements include: (1) The acute angle between the branch vector direction of any two adjacent particles in the force chain and the minimum principal stress direction of each particle needs to be less than or equal to the set angle threshold; (2) The acute angle between the branch vectors of two adjacent particles on the force chain and the branch vectors of the initial two particles on the force chain needs to be less than or equal to the set acute angle threshold; Step 5: If there is only one potential force chain particle obtained in step 4, then this particle is used as the effective force chain particle; if there is more than one, then the particle with the smallest minimum principal stress among the potential force chain particles is selected as the effective force chain particle; and the effective force chain particle is used as the starting particle, and the process returns to step 3 until there are no effective force chain particles, thereby obtaining a force chain of a certain length.

2. The three-dimensional granular medium force chain identification method according to claim 1, characterized in that: The reasonable range of φ and θ is 40° to 50°.

3. The three-dimensional granular medium force chain identification method according to claim 1, characterized in that: The φ and θ are both 45°.

4. The three-dimensional granular medium force chain identification method according to claim 1, characterized in that: The three-dimensional granular medium is a unit material or a multi-component mixed material.

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