Method for measuring random close packing fraction of non-spherical particles

Abstract

The present invention discloses a method for measuring the random close packing fraction of non-spherical particles, comprising the following steps: S1, constructing a non-spherical hard core-soft shell structure; S2, characterizing the percolation network of the non-spherical hard core-soft shell structure under repulsive characteristics; S3, based on the percolation phase transition that preferentially occurs before the jamming phase transition, rapidly applying pressure to the soft shell of the hard core-soft shell percolation network to densify and form a non-spherical particle percolation network; S4, mapping the continuous percolation model in three-dimensional space to a lattice percolation model; S5, introducing the non-spherical particle shape information into the mean-field cluster size to characterize the scale law of the mean-field clusters of the non-spherical particle random packing structure; S6, based on the scale theory and critical exponent, transforming the mean-field cluster back to the original three-dimensional space; S7, measuring the random packing fraction of non-spherical particles with a jamming phase transition. The present invention can measure key physical quantities such as the packing fraction and average contact number of non-spherical particle packing and the local packing configuration.

Description

Technical Field

[0001] The present invention belongs to the technical field of particle composite material processing, and particularly relates to a method for theoretically determining the random close packing fraction of non-spherical particles based on percolation-based mean field. Background Art

[0002] Finding the tightest and most superior particle packing method has always been an old and open problem in the fields of mechanics, physics, materials, etc. In 2016, the journal Science listed 125 century-old problems faced by humanity, among which the packing of granular materials and the glass transition behavior ranked among the top 50 century-old problems. Elucidating the non-local and non-equilibrium characteristics of packing from aspects such as the geometric morphology of particles, the degree of order in arrangement, and spatial correlation is a core and difficult challenge today. In addition, the jamming transition in particle packing and the percolation transition in particle systems are also important issues in the processing and preparation of particle composite materials. On the one hand, particle packing has wide applications in aspects such as nanomaterials, crystal, glass, and particulate processing, biological media, and composite material forming. On the other hand, in recent years, materials with excellent stiffness, strength, thermal conductivity, and electrical conductivity, such as particle-reinforced materials, carbon fiber materials, ceramic matrix materials, and graphene materials, have been widely used. Therefore, it is crucial to characterize the fabric characteristics and properties of materials. Quantifying the correlation between the two experimentally is expensive and time-consuming, so it is crucial to make reasonable predictions and clarifications theoretically. In recent years, many studies have revealed the problem of particle packing from experimental and numerical perspectives. Among them, random close packing, random loose packing, maximum random jamming packing, face-centered cubic packing, and the jamming transition phenomenon of packing have become open hotspots.

[0003] Since the particle blocking phase transition is the critical state of the stacking structure with rigid bearing (mechanical stability), many studies have attempted to capture the critical blocking phase transition point. Some methods give the relationship between the number of non-spherical constraints and the system's degrees of freedom based on the Maxwell mechanical stability criterion. Other studies capture the quasi-long-range correlation in the maximum random blocking structure as an important feature of the pores and particles being locked in the blocking structure. Some studies analyze marginal stability and describe it as an important sign that the unstable system is approaching the blocking phase transition. Some studies explain the energy deposition phenomenon in the metastable basin based on the glass phase transition and show the energetic manifestation of the blocking phase transition. In addition, some studies describe the process of the stacking structure from disorder to maximum random blocking based on the power-law behavior of the average contact number. Considering the appearance of excess soft modes in the vibration density, they successfully predicted the average contact number of soft and hard spheres. Through these studies, we found that different types of particle stacking and blocking phase transitions will produce completely different situations. In addition, the average contact number of particles may also show two types: isostatic and solid. However, the study of associating particle stacking with the percolation model and using the percolation network to characterize the contact network is still in its infancy. At present, there are numerical studies that have clarified that the particle percolation phase transition can serve as a precursor to the particle blocking phase transition, and on this basis, the lower limit of the average contact number of the structure close to the blocking point is evaluated. There are also numerical studies that explore the scaling law of the blocking phase transition of the frictional system within the framework of rigid percolation. The emergence of a cross-percolation rigid cluster controls the blocking phase transition of the entire system, accompanied by the critical divergence of the cluster size. In the quasi-static densification process, the percolation phase transition of the contact network is the minimum structural correlation required for the blocking phase transition. Combining particle percolation with particle stacking to explain the process from disorder to order in the system is a scientific problem that needs to be solved urgently. For a wide range of non-spherical particles, it is very important to propose an analyzable functional relationship to determine the stacking fraction and average contact number of non-spherical particles in the fields of condensed matter physics, micromechanics of granular materials, and particle-type composite material processing technology. Summary of the invention

[0004] In order to solve the technical problems mentioned in the background, the present invention proposes a method for determining the random close packing fraction of non-spherical particles.

[0005] In order to achieve the above technical objectives, the present invention provides a method for determining the random close packing fraction of non-spherical particles, comprising the following steps:

[0006] S1. Construct non-spherical particles as hard cores, construct intermediate phases of equal thickness around the particles as soft shells, introduce non-spherical hard core-soft shell parallel structure to quantify intermediate phase (soft shell) area; deduce the exclusion volume of non-spherical particles and the exclusion influence area of the surrounding intermediate phase based on geometric probability and mean curvature;

[0007] S2. Characterize the percolation network of non-spherical hard-core / soft-shell structures under repulsive characteristics based on the intermediate phase (soft shell) repulsive influence region, radial distribution function, and intermediate phase volume fraction;

[0008] S3. Based on the percolation phase transition that occurs prior to the blocking phase transition, rapidly apply pressure to the soft shell of the hard-core / soft-shell percolation network to densify and form a non-spherical particle percolation network; Based on the local conditional probability of percolation, characterize the baseline model of the average contact number in the non-spherical particle percolation network;

[0009] S4. Characterize the non-spherical particle contact network with the average contact number and average cluster size as the bridge, map the continuous percolation model in three-dimensional space to the lattice percolation model, design a mean-field model based on the analytic Bethe lattice percolation, and construct the relationship between the cluster size and the average contact number under the mean-field model;

[0010] S5. Consider the influence of anisotropy and spatial arrangement order on the random packing structure of non-spherical particles, characterize the geometric shape factor of non-spherical particles, introduce the non-spherical particle shape information into the mean-field cluster size, and characterize the scale law of the mean-field cluster of the random packing structure of non-spherical particles;

[0011] S6. Based on the scale theory and critical exponent, transform the mean-field cluster back to the original three-dimensional space, and use the intermediate phase volume fraction, non-spherical particle excluded volume, geometric shape factor, and fluid state equilibrium equation to derive the limiting form of the non-spherical particle random packing fraction function;

[0012] S7. The packing fraction covers particle shape information, repulsive short-range correlations, and long-range correlations of the percolation phase transition. Construct an implicit relationship between the non-spherical particle packing fraction and the average contact number. By regulating the average contact number, the random packing fraction of non-spherical particles with a blocking phase transition can be measured.

[0013] First, in S1, the intermediate phase repulsive influence region V of the non-spherical hard-core / soft-shell parallel structure ex ITZ is expressed as:

[0014]

[0015] where ī is the average curvature diameter of the particle, t is the intermediate phase thickness, D eq is the equivalent diameter, defined as the diameter of an equivalent sphere with the same volume as the non-spherical particle, and ss is the sphericity.

[0016] Furthermore, in S2, to characterize the percolation network of non-spherical hard-core / soft-shell structures under the influence of intermediate phase repulsion, the connectivity number n of the non-spherical hard-core / soft-shell parallel structure c is expressed as:

[0017]

[0018] Among them, is the particle volume fraction, g CS is the radial distribution function for congruent hard spheres, and the classical Carnahan - Starling (CS) model is adopted, expressed as:

[0019]

[0020] Intermediate phase volume fraction is expressed as:

[0021]

[0022] where λ = t / D eq , <·> represents the particle - number - based average treatment, and f(t) is expressed as:

[0023]

[0024] The percolation threshold of the non - spherical hard - core - soft - shell percolation network is an implicit function, expressed as:

[0025]

[0026] Among them, is the critical volume fraction of the particles as the percolation threshold of the particle packing structure, is the critical volume fraction of the non - spherical hard - core - soft - shell parallel structure as the percolation threshold of the non - spherical hard - core - soft - shell parallel - structure percolation network.

[0027] Furthermore, in S3, rapid pressure is applied to the intermediate phase of the hard - core - soft - shell percolation network, and densification forms a non - spherical particle percolation network; using the limit of t→0 (tending to 0), the average contact number Z of the hard particles is obtained, expressed as:

[0028]

[0029] where ρ is the number density of the particles, and g2 is the radial distribution function for the non - spherical hard - core - soft - shell parallel structure.

[0030] Considering the local conditions of the percolation network, a correction term is introduced. This is a conditional probability that can ensure that in the integration region V ex ITZ around the central particle, there is at least a probability of finding the existence of other particles. The baseline model of the average contact number is expressed as:

[0031]

[0032] Furthermore, in S4, the contact network of non-spherical particles is characterized by the average contact number and the average cluster size, and the continuous percolation model in three-dimensional space is mapped to the lattice percolation model. The average cluster size C of the resolvable Bethe lattice percolation BL and the average contact number Z BL The relationship can be expressed as:

[0033] C BL = 1 + Z BL T BL (9)

[0034] where T BL is the average cluster size contributed by a branch connected to the central site in the Bethe lattice percolation.

[0035] Construct the relationship between the cluster size and the average contact number under the mean field model, which is expressed as:

[0036] C MF = 1 + Z MF T MF (10)

[0037] where the subscript "MF" represents the corresponding mean field quantity. C MF characterizes the mean field cluster size, Z MF is the contact number of non-spherical particles in the mean field model, and T MF is the average cluster size contributed by a branch connecting the central particle.

[0038] Furthermore, in S5, the influence of anisotropy and spatial arrangement order on the random packing structure is considered, and the shape factor M of non-spherical particles with smooth surfaces and sharp surfaces is given f , which is expressed as:

[0039]

[0040]

[0041] where V is the particle volume, V normalized is the volume of the normalized sphere with the average curvature radius of the particle, m BL is the number of the outermost sites after the Bethe lattice site is magnified, m MF is the corresponding number of the outermost sites in the mean field model, κ is the aspect ratio, V superball is the volume of the hypersphere particle. For the Platonic regular polyhedron, E is the total number of edges of the polyhedron, f and n represent the number of faces connected to each vertex and the number of edges of each face, and b is a parameter related to the type of polyhedron and can be obtained from Table 1.

[0042] Introduce the shape information M of non-spherical particles fUsing the percolation probability p and the percolation threshold p c describe C MF 's scaling law. C BL As an intermediate quantity, it provides the critical exponent γ of C MF , and the mean-field cluster C MF is expressed as:

[0043]

[0044] Furthermore, in S6, based on the scaling theory and the critical exponent, the mean-field cluster is transformed back to the original three-dimensional space. Thus, the mean contact number Z MF of the mean-field model is expressed as:

[0045]

[0046] where C3 is the mean cluster size in three-dimensional space.

[0047] covers the geometric information of non-spherical particles, the local consideration of percolation, and the long-range correlation of the percolation cluster captured by the critical exponent γ. Based on the mean-field cluster C MF , the mean-field model derives a reasonable mean contact number Z MF for non-spherical particles, which includes the long-range correlation and local characteristics of the particle network. Further, taking the limit of t→0 to solve for Z MF . Expand the intermediate-phase volume fraction in the form given previously:

[0048]

[0049] For hard-particle contact, substitute the limit of the intermediate-phase thickness t = 0 for Taylor expansion. Through L'Hopital's rule, the final packing fraction can be obtained, covering the analytical relationship between Z MF and , which can be used to determine the random packing fraction of non-spherical particles at the jamming transition.

[0050]

[0051] where R Vn (t), is the high-order remainder of the Taylor expansion.

[0052] Furthermore, in S7, by regulating the mean contact number, the random packing fraction of non-spherical particles with a jamming transition can be measured. For the random packing structure of hard spheres, the packing fraction relationship is expressed as:

[0053]

[0054] In three-dimensional space, the critical exponent is reasonably approximated as γ = 1.7 - 1.8, at which the sphere packing is isostatic. Substituting the average contact number Z = 6, the packing fraction φ ≈ 0.638 can be measured. For the random packing structure of non-spherical particles, the packing structure is hyperstatic for solids, and the number of constraints of non-spherical particles is greater than one times the system degrees of freedom and less than two times the system degrees of freedom. The ellipsoid packing and the sphere-column packing satisfy 6 < Z < 10, the super-sphere and polyhedron random packing satisfy 6 < Z < 10, and the super-ellipsoid random packing satisfies 6 < Z < 12. The packing rate relationship of non-spherical particles is expressed as:

[0055]

[0056] The physical quantities and parameters therein can be obtained through S1 - S7.

[0057] The beneficial effects of the present invention are:

[0058] (1) Existing theoretical techniques cannot measure the local packing configuration of non-spherical particle packing, and cannot measure key physical quantities such as the packing fraction and average contact number of the random packing structure of non-spherical particles;

[0059] (2) A quantitative relationship between the packing fraction and average contact number of non-spherical particles is established, covering the shape information of non-spherical particles and the long-range spatial correlation controlled by the critical exponent. The random close packing fraction, average contact number, and radial distribution function of non-spherical particles are measured, enabling the effective measurement and characterization of random packing structures of different types of non-spherical particles, including smooth and sharp ones;

[0060] (3) Overcoming the technical bottlenecks of low numerical simulation efficiency and difficult-to-guarantee accuracy helps to reveal the intrinsic and interaction mechanisms of the particle system and optimize the design of particle-based composite materials. Description of the Drawings

[0061] Figure 1 is the flowchart of the method of the present invention;

[0062] Figure 2 is the design flowchart of the mean field model;

[0063] Figure 3 Determination diagram of the random close packing rate of hard spheres;

[0064] Figure 4 is the determination diagram of the packing fraction and aspect ratio of the random packing of non-spherical particles;

[0065] Figure 5 is the determination diagram of the average contact number and aspect ratio of the random packing of non-spherical particles;

[0066] Figure 6 is the determination diagram of the packing fraction and deformation parameter of the random jammed packing of super-sphere particles;

[0067] Figure 7 It is a graph for measuring the packing fraction and average number of contacts of random blocked packing of polyhedra. Specific implementation mode

[0068] The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0069] The present invention designs a method for measuring the random packing fraction of non-spherical particles, as Figure 1 shown, including the following steps:

[0070] S1. Construct non-spherical particles as hard cores, construct an intermediate phase with equal thickness around the particles as a soft shell, and introduce a non-spherical hard core-soft shell parallel structure to quantify the intermediate phase (soft shell) region; based on geometric probability, the average curvature is used to derive the excluded volume of non-spherical particles and the excluded influence region of the surrounding intermediate phase.

[0071] S2. Based on the excluded influence region of the intermediate phase (soft shell), the radial distribution function, and the volume fraction of the intermediate phase, characterize the percolation network of the non-spherical hard core-soft shell structure under the exclusion characteristics.

[0072] S3. Based on the percolation phase transition that preferentially occurs before the blocking phase transition, quickly apply pressure to the soft shell of the hard core-soft shell percolation network to densify and form a non-spherical particle percolation network; based on the local conditional probability of percolation, characterize the baseline model of the average number of contacts in the non-spherical particle percolation network.

[0073] S4. Use the average number of contacts and the average cluster size as a bridge to characterize the non-spherical particle contact network, map the continuous percolation model in three-dimensional space to the lattice percolation model, design an average field model based on the analytic Bethe lattice percolation, and construct the relationship between the cluster size and the average number of contacts under the average field model, as Figure 2 shown.

[0074] S5. Consider the influence of anisotropy and spatial arrangement order on the random packing structure of non-spherical particles, characterize the geometric shape factor of non-spherical particles, introduce the non-spherical particle shape information into the average field cluster size, and characterize the scale law of the average field cluster of the non-spherical particle random packing structure, as Figure 2 shown.

[0075] S6. Based on the scale theory and critical exponent, transform the average field cluster back to the original three-dimensional space, and use the volume fraction of the intermediate phase, the excluded volume of non-spherical particles, the geometric shape factor, and the fluid state equilibrium equation to derive the limiting form of the non-spherical particle random packing rate function.

[0076] S7. The packing fraction encompasses particle shape information, short-range repulsive correlations, and long-range correlations of percolation phase transitions, constructs an implicit relationship between the packing fraction of non-spherical particles and the average number of contacts, regulates the average number of contacts, and measures the random packing fraction of non-spherical particles with a jamming phase transition.

[0077] In this embodiment, the above S1 is implemented by the following preferred scheme: In S1, the intermediate-phase repulsive influence region V of the non-spherical hard-core-soft-shell parallel structure ex ITZ is expressed as:

[0078]

[0079] In this embodiment, the above S2 is implemented by the following preferred scheme: In S2, the percolation network of the non-spherical hard-core-soft-shell structure under the influence of intermediate-phase repulsion is characterized. The number of connected components n of the non-spherical hard-core-soft-shell parallel structure c is expressed as:

[0080]

[0081] Intermediate-phase volume fraction is expressed as:

[0082]

[0083] where f(t) is expressed as:

[0084]

[0085] The percolation threshold of the non-spherical hard-core-soft-shell percolation network is derived as an implicit function, expressed as:

[0086]

[0087] In this embodiment, the above S3 is implemented by the following preferred scheme: In S3, rapid pressure is applied to the intermediate phase of the hard-core-soft-shell percolation network to densify and form a non-spherical particle percolation network. Using the limit of t→0 (tending to 0), the average number of contacts Z of the hard particles is obtained, expressed as:

[0088]

[0089] Considering the local conditions of the percolation network, a correction term is introduced The baseline model of the average number of contacts is expressed as:

[0090]

[0091] In this embodiment, the above S4 is implemented by the following preferred scheme: In S4, the non-spherical particle contact network is characterized with the average number of contacts and the average cluster size as a bridge, such asFigure 2 As shown, mapping the continuous percolation model in three-dimensional space to the lattice percolation model, the average cluster size C of the resolvable Bethe lattice percolation BL and the average coordination number Z BL are related as follows:

[0092] C BL = 1 + Z BL T BL (9)

[0093] Construct the relationship between the cluster size and the average coordination number under the mean-field model, which is expressed as:

[0094] C MF = 1 + Z MF T MF (10)

[0095] In this embodiment, the above S5 is preferably implemented as follows: In S5, the shape factor M of non-spherical particles with smooth surfaces and sharp surfaces is given f , which is expressed as:

[0096]

[0097]

[0098] where V is the particle volume, V normalized is the volume of a normalized sphere with a radius equal to the average curvature radius of the particle, m BL is the number of sites in the outermost layer after magnifying the Bethe lattice sites, m MF is the corresponding number of outermost sites in the mean-field model, κ is the aspect ratio, V superball is the volume of a hyperspherical particle. For Platonic regular polyhedra, E is the total number of edges of the polyhedron, f and n represent the number of faces connected to each vertex and the number of edges of each face, respectively, and b is a parameter related to the type of polyhedron and can be obtained from Table 1.

[0099] Table 1 Sphericity ss, number of faces f connected to each vertex, number of edges n of each face, number of edges E, and five Platonic particle parameters b

[0100]

[0101] Introduce the shape information M of non-spherical particles f , and the mean-field cluster C MF is expressed as:

[0102]

[0103] In this embodiment, the above S6 is implemented by the following preferred solution: In S6, based on the scale theory and critical exponents, the mean-field cluster transition is transformed back to the original three-dimensional space. As Figure 2 shown, the mean coordination number Z of the mean-field model is derived MF and expressed as:

[0104]

[0105] Furthermore, the limit of t→0 is taken to solve for Z MF . The volume fraction of the intermediate phase is expanded in the form given above:

[0106]

[0107] For hard-particle contact, substituting the limit of the intermediate-phase thickness t = 0 for Taylor expansion. Through L'Hopital's rule, the final packing ratio can be obtained, covering the analytical relationship between Z MF and .

[0108]

[0109] In this embodiment, the above S7 is implemented by the following preferred solution: In S7, the mean coordination number is regulated, and the random packing fraction of non-spherical particles with a jamming transition can be measured. For the random packing structure of hard spheres, the packing ratio relationship is expressed as:

[0110]

[0111] In three-dimensional space, the critical exponent is reasonably approximated as γ = 1.7 - 1.8, and at this time, the sphere packing is isostatic. Substituting the mean coordination number Z = 6, the packing fraction φ≈0.638 can be measured, as Figure 3 shown. For the random packing structure of non-spherical particles, the packing structure is hyperstatic for solids, and the number of constraints of non-spherical particles is greater than one times the system degrees of freedom and less than two times the system degrees of freedom. Ellipsoid packing and sphere-column packing satisfy 6 < Z < 10, hyper-sphere and polyhedron random packing satisfy 6 < Z < 10, and hyper-ellipsoid random packing satisfies 6 < Z < 12. The packing ratio relationship of non-spherical particles is expressed as:

[0112]

[0113] Figure 3 The measured relationship of the hard-sphere packing ratio shown is compared with the existing numerical results. Figure 3 The subfigure shows the radial distribution function obtained by the mean-field theory, and the divergence at the particle surface is caused by the close contact of hard particles. Compared with the existing numerical results, the order degree of hard-sphere packing is quite stable.

[0114] Select the corresponding shape factor to measure the random jammed packing of hyperspheres and regular polyhedron particles. These particles do not have an elongation effect and are completely caused by particle deformation. When the deformation parameter deviates from 1, it will lead to two branches of the hypersphere tending to the octahedron shape [0.5, 1) and the hexahedron shape (1, ∞). The maximum random jammed packing of the hypersphere is solid, and as the shape deviates from the sphere, the packing fraction φ will increase significantly. Figure 4 It is a measurement diagram of the packing fraction and the deformation parameter of the random jammed packing of hypersphere particles. Figure 5 It is a measurement diagram of the packing fraction and the average number of contacts of the random jammed packing of polyhedrons.

[0115] Since the packing fraction is related to the geometric shape and the average number of contacts, we further measure the structural characteristics of the random packing of other non-spherical particles. We use the average number of contacts Z obtained by counting in the literature. Figure 7 It shows the theoretical prediction results and numerical data of these non-spherical particles, and there is a good match for all the observed shapes. Figure 6 It is a measurement diagram of the packing fraction and the aspect ratio of the random packing of non-spherical particles. Figure 7 It is a measurement diagram of the average number of contacts and the aspect ratio of the random packing of non-spherical particles.

[0116] The above embodiments are only used to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for measuring the random close packing fraction of non-spherical particles, characterized in that It includes the following steps: S1. Construct non-spherical particles as the hard core, construct an intermediate phase with equal thickness around the particles as the soft shell, and introduce a non-spherical hard-core / soft-shell parallel structure to quantify the intermediate phase region; Based on geometric probability, the average curvature is used to derive the excluded volume of non-spherical particles and the excluded influence region of the surrounding intermediate phase; S2. Based on the excluded influence region of the intermediate phase, the radial distribution function, and the volume fraction of the intermediate phase, characterize the percolation network of the non-spherical hard-core / soft-shell structure under repulsive characteristics; S3. Based on the percolation phase transition that preferentially occurs before the jamming phase transition, rapidly apply pressure to the soft shell of the hard-core / soft-shell percolation network to densify and form a non-spherical particle percolation network; based on the local conditional probability of percolation, characterize the baseline model of the average number of contacts in the non-spherical particle percolation network; S4. Use the average number of contacts and the average cluster size as a bridge to characterize the non-spherical particle contact network, map the continuous percolation model in three-dimensional space to the lattice percolation model, design a mean-field model based on the analytic Bethe lattice percolation, and construct the relationship between the cluster size and the average number of contacts under the mean-field model; S5. Introduce the non-spherical particle shape information into the mean-field cluster size to characterize the scale law of the mean-field clusters of the non-spherical particle random packing structure; S6. Based on the scale theory and critical exponents, transform the mean-field cluster back to the original three-dimensional space, and use the volume fraction of the intermediate phase, the excluded volume of non-spherical particles, the geometric shape factor, and the fluid state equilibrium equation to derive the limiting form of the non-spherical particle random packing fraction function; S7. The packing fraction covers the particle shape information, the repulsive short-range correlation, and the long-range correlation of the percolation phase transition, construct an implicit relationship between the non-spherical particle packing fraction and the average number of contacts, regulate the average number of contacts, and measure the non-spherical particle random packing fraction with a jamming phase transition.

2. The method for measuring the random close packing fraction of non-spherical particles according to claim 1, characterized in that, In S1, the mesophase repulsive influence region V of the non-spherical hard-core soft-shell parallel structure ex ITZ is expressed as: Among them, is the average curvature diameter of the particles, t is the mesophase thickness, D eq is the equivalent diameter, defined as the diameter of an equivalent sphere having the same volume as the non-spherical particle, and ss is the sphericity.

3. The method for determining the random close packing fraction of non-spherical particles according to claim 1, characterized in that, In S2, the percolation network characterizing the non-spherical hard-core / soft-shell structure under the influence of the mesophase repulsion, and the number of connections n of the non-spherical hard-core / soft-shell parallel structure c is expressed as: wherein, is the particle volume fraction, g CS is the radial distribution function for congruent hard spheres, and is expressed using the classical CS model as: Intermediate phase volume fraction Expressed as: where λ = t / D eq , <·> represents averaging processing based on the number of particles, and f(t) is expressed as: Percolation Threshold of Non-Spherical Hard-Core Soft-Shell Percolation Networks is an implicit function, expressed as: Among them, is the critical volume fraction of the particles as the percolation threshold of the particle packing structure, is the critical volume fraction of the non-spherical hard core-soft shell parallel structure as the percolation threshold of the percolation network of the non-spherical hard core-soft shell parallel structure.

4. The method for determining the random close packing fraction of non-spherical particles according to claim 3, characterized in that, In S3, rapidly apply pressure to the intermediate phase of the hard-core / soft-shell percolation network to densify and form a non-spherical particle percolation network; using the limit of t→0, obtain the average number of contacts Z of hard particles, expressed as: where ρ is the number density of the particles, and g2 is the radial distribution function for the non-spherical hard-core / soft-shell parallel structure; The baseline model of the average number of contacts is expressed as:

5. The method for determining the random close packing fraction of non-spherical particles according to claim 1, characterized in that, In S4, the contact network of non-spherical particles is characterized by the average number of contacts and the average cluster size as a bridge, and the continuous percolation model in three-dimensional space is mapped to the lattice percolation model. The average cluster size C of the resolvable Bethe lattice percolation BL and the average number of contacts Z BL The relationship can be expressed as: C BL = 1 + Z BL T BL (9) Among them, T BL is the average cluster size contributed by a branch connected to the central site in the Bethe lattice percolation; Construct the relationship between the cluster size and the average number of contacts under the mean-field model, expressed as: C MF = 1 + Z MF T MF (10) where the subscript "MF" represents the corresponding mean-field quantity, C MF characterizes the mean-field cluster size, Z MF is the non-spherical particle contact number of the mean-field model, T MF is the mean cluster size contributed by one branch connecting the central particle.

6. The method for measuring the random close packing fraction of non-spherical particles according to claim 1, wherein In S5, the influence of anisotropy and spatial arrangement order on the random packing structure is considered, and the shape factor M of non-spherical particles with smooth surfaces and sharp surfaces is given f , expressed as: Among them, V is the particle volume, V normalized is the volume of a normalized sphere with a radius equal to the average curvature radius of the particle, m BL is the number of sites in the outermost layer after magnification of the Bethe lattice sites, m MF is the corresponding number of outermost sites in the mean-field model, κ is the aspect ratio, V superball is the volume of the hyperspherical particle. For Platonic solids, E is the total number of edges of the polyhedron, f and n represent the number of faces connected to each vertex and the number of edges of each face respectively, and b is a parameter related to the type of polyhedron; Introduce the shape information M of non-spherical particles f , Using the percolation probability \(p\) and the percolation threshold \(p_c\) c to describe the MF scaling law of \(C\); \(C\) BL provides the critical exponent \(\gamma\) of \(C\) as an intermediate quantity, and the mean-field cluster \(C\) MF is expressed as: MF as follows:

7. The method for measuring the random close packing fraction of non-spherical particles according to claim 1, wherein In S6, based on the scaling theory and critical exponents, the mean-field cluster transition is reverted back to the original three-dimensional space, and the mean contact number Z of the mean-field model MF is expressed as: where C3 is the average cluster size in three-dimensional space; Solve for Z by taking the limit as t → 0 MF , the volume fraction of the intermediate phase Expand in the form given in the previous text: For hard particle contacts, substitute the intermediate phase thickness limit t = 0 into the Taylor expansion; the final packing fraction can be obtained through L'Hopital's rule, covering the analytical relationship between Z MF and for determining the random packing fraction of non-spherical particles at the jamming transition; Among them, R Vn (t), R φn (t) is the high-order remainder of Taylor expansion.

8. The method for determining the random close packing fraction of non-spherical particles according to claim 1, characterized in that, In S7, regulate the average number of contacts and measure the non-spherical particle random packing fraction with a jamming phase transition. For the random packing structure of hard spheres, the packing fraction relationship is expressed as: In three-dimensional space, the critical exponent is reasonably approximated as γ = 1.7 - 1.

8. At this time, the sphere packing is isostatic. Substituting the average number of contacts Z = 6, the packing fraction φ≈0.638 can be measured; for the non-spherical particle random packing structure, the packing structure is hyperstatic of the solid type, and the number of constraints of non-spherical particles is greater than one times the system degrees of freedom and less than two times the system degrees of freedom; ellipsoid packing and sphere-column packing satisfy 6 < Z < 10, super-sphere and polyhedron random packing satisfy 6 < Z < 10, and super-ellipsoid random packing satisfies 6 < Z < 12; the packing fraction relationship of non-spherical particles is expressed as: The physical quantities and parameters therein can be obtained through S1 - S7.

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