Method for calculating force-electricity coupling response of particle system

Abstract

The invention discloses a method for calculating force-electricity coupling response of a particle system, which comprises the following steps: establishing a particle dynamic model, and calculating to obtain tangential force and normal force between particles; establishing a particle system resistance transfer calculation model, and calculating the contact resistance between the particles and the contact resistance between the particles and the boundary in a power-on state; and establishing a particle system force-electricity response coupling model, and calculating stress and resistance between particles and between particles and boundaries under the condition of applying load and electrifying. The method not only considers the volume resistance of the particles, but also considers the influence of the particle-particle and particle-interface contact effect on the resistance distribution, and meanwhile, the method considers the interaction between electricity and mechanics, so that the numerical calculation result is more consistent with the force-electricity distribution result between real particles, and the calculation accuracy is improved. And the accuracy of a numerical calculation result is effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of simulation calculation of road material particles, and in particular relates to a method for calculating the force-electric coupling response of a particle system. Background Art

[0002] The force-electric coupling effect of granular materials plays a vital role in many industries. It can be used to detect internal damage of materials, calcination of materials and other fields. The discrete element numerical simulation method is an important means to study the force-electric coupling effect between particles. It has the advantages of high efficiency and low cost. However, the force-electric model in the discrete element numerical simulation currently has the following problems:

[0003] First, the conventional force-electric model calculates the electrical signal and mechanical information separately without considering the mutual influence between the two, resulting in low accuracy of the calculation results;

[0004] Secondly, the conventional force-electric model only considers the volume resistance of the particles, and does not analyze the impact of the contact area between different particles and between particles and boundaries on the electrical signal, which leads to inaccurate calculation results.

[0005] The invention with the publication number CN116312896A discloses a method and device for calculating the resistance response of a planar particle-filled composite material, including: constructing a strain model according to the displacement of the filler with a specified strain; dividing the filler grid with a specified unit grid size according to the strain model; calculating the spacing matrix of all fillers according to the filler grid; finding all boundary filler matrices as the starting point and end point; finding a conductive path that meets the conditions based on the filler spacing matrix and the starting point and end point; and solving the equivalent resistance based on the conversion of the conductive path into an equivalent circuit. However, the invention neither considers the mutual influence between electrical signals and mechanical information, nor analyzes the influence of the contact area between different particles and between particles and boundaries on electrical signals. Summary of the invention

[0006] In response to the above-mentioned technical problems, the present invention discloses a method for calculating the force-electric coupling response of a particle system, which not only takes into account the volume resistance of the particles themselves, but also takes into account the influence of the contact effect between particles and particles and between particles and interfaces on the resistance distribution. At the same time, the method takes into account the interaction between electricity and mechanics, so that the numerical calculation results are more consistent with the force-electric distribution results between real particles, effectively improving the accuracy of the numerical calculation results.

[0007] Technical solution:

[0008] A method for calculating a force-electric coupling response of a particle system, the method comprising the following steps:

[0009] Step 1, establish a particle dynamics model and calculate the tangential force and normal force between particles;

[0010] Step 2, establish a particle system resistance transfer calculation model to calculate the resistance between particles and between particles and boundaries in the power-on state;

[0011] Step 3: Establish a coupled force-electric response model of the particle system to calculate the force and resistance between particles and between particles and boundaries when load is applied and power is turned on.

[0012] Step 1 further comprises:

[0013] Initialize the particle system;

[0014] Apply loads and power at the boundaries, and calculate particle motion data;

[0015] Detect the contact state between internal particles and between particles and boundaries, evaluate the contact response and update the geometric state changes of particles, build a particle dynamics model, and calculate the tangential force and normal force between particles.

[0016] Furthermore, the tangential force and normal force between particles are calculated using the following formula:

[0017]

[0018] In the formula, is the normal force between particles; is the tangential force between particles; m * is the equivalent mass of the particles; β is the damping coefficient between particles; δ n is the normal overlap between particles; δ t is the tangential overlap between particles; is the normal component of the relative velocity between particles; is the tangential component of the relative velocity between particles; is the equivalent Young's modulus of adjacent contact particles; r * is the effective radius of the particle; k n is the normal damping coefficient between particles; k t is the tangential damping coefficient between particles; E i is the Young's modulus of particle i; v i is the Poisson's ratio of particle i; r i is the radius of particle i; E j is the Young's modulus of particle j; v j is the Poisson's ratio of particle j; r j is the radius of particle j; E* is the equivalent Young's modulus of the particle system, and G* is the equivalent shear modulus of the particle system.

[0019] Furthermore, in step 2, the resistance between particles in the power-on state is calculated using the following formula:

[0020] R ij =R i +R c,ij +R j

[0021]

[0022] In the formula, R i is the resistance from the center of particle i to its elastic deformation position; R j is the resistance from the center of particle j to its elastic deformation position; R c,ij is the resistance of the overlapping region of particles i and j; ρ i is the resistivity of particle i; ρ j is the resistivity of particle j; r i * is the resistivity of particle i; r j is the resistivity of particle j; L ij is the distance between the centers of two contacting particles; f n is the normal component of the contact force between the particle and the boundary.

[0023] Furthermore, in step 2, the resistance between the particle and the boundary in the power-on state is calculated using the following formula:

[0024] R iw =R i,iw +R c,iw

[0025]

[0026] In the formula, R iw is the resistance between the particle and the boundary; R i,iw is the resistance of the particle in contact with the boundary; R c,iw is the resistance of the boundary in contact with the particle; ρ i is the resistivity of particle i in contact with the boundary; ρ w is the resistivity of the boundary; r i * is the resistivity of particle i in contact with the boundary; δ is the elastic deformation of the particle under the boundary load; is the equivalent Young's modulus of the particle and the boundary; f n is the normal component of the contact force between the particle and the boundary.

[0027] Furthermore, in step 3, the particle system force-electric response coupling model is:

[0028]

[0029] Where V 0is the voltage applied to the upper boundary; V 1 is the voltage of the lower boundary; V i is the voltage of different particles, i = 1, 2, 3, ..., n; R ii is the resistance between different particles, i = 1, 2, 3, ..., n; -I 0 is the current at the upper boundary; I 0 is the lower boundary current.

[0030] Beneficial effects:

[0031] First, the method for calculating the force-electric coupling response of a particle system of the present invention can be used to analyze the change in resistance inside a particle when current flows from one object to another. It not only takes into account the volume resistance of the particle itself, but also takes into account the influence of the contact effect between particles and particles and between particles and interfaces on the resistance distribution, thereby effectively improving the accuracy of the numerical calculation results.

[0032] Second, the method for calculating the force-electric coupling response of the particle system of the present invention realizes the coupled calculation of the particle mechanical model and the electrical model, avoiding the problem of low calculation efficiency and high accuracy of a single model. In addition, the present invention takes into account the interaction between electricity and mechanics, so that the numerical calculation results are more consistent with the force-electric distribution results between real particles. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of a particle system device of the present invention;

[0034] Figure 2 A flow chart of a method for calculating a force-electric coupling response of a particle system according to the present invention;

[0035] Figure 3 It is a schematic diagram of the resistance distribution of the particle system at different times of the present invention.

[0036] The reference numerals are as follows: 1, particle; 2, upper boundary; 3, lower boundary; 4, left boundary; 5, right boundary. DETAILED DESCRIPTION

[0037] The following examples will enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0038] The present invention discloses a method for calculating the force-electric coupling response of a particle system, the method comprising the following steps:

[0039] Step 1, establish a particle dynamics model and calculate the tangential force and normal force between particles;

[0040] Step 2, establish a particle system resistance transfer calculation model to calculate the resistance between particles and between particles and boundaries in the power-on state;

[0041] Step 3: Establish a coupled force-electric response model of the particle system to calculate the force and resistance between particles and between particles and boundaries when load is applied and power is turned on.

[0042] See also Figure 2 The particle system force-electric coupling response calculation method of the present invention specifically includes the following steps:

[0043] S1. Calculate the normal force and tangential force of the particle. Figure 1 The figure is a schematic diagram of the particle system device of the present invention. A load is applied to the top of the upper boundary 2 and electricity is turned on. Contact will occur between particles inside the boundary and between particles and the lower boundary 3, the left boundary 4 and the boundary 5. The displacement and rotation of the internal particle 1 are calculated, and the contact force components of the particle in the normal and tangential directions are obtained using the following model:

[0044]

[0045]

[0046] In the formula, is the normal force between particles; is the tangential force between particles; m * is the equivalent mass of the particles; β is the damping coefficient between particles; δ n is the normal overlap between particles; δ t is the tangential overlap between particles; is the normal component of the relative velocity between particles; is the tangential component of the relative velocity between particles; E 1 * is the equivalent Young's modulus of adjacent contact particles; r * is the effective radius of the particle; k n is the normal damping coefficient between particles; k t is the tangential damping coefficient between particles; E i is the Young's modulus of particle i; v i is the Poisson's ratio of particle i; r i is the radius of particle i; E j is the Young's modulus of particle j; v j is the Poisson's ratio of particle j; r j is the radius of particle j; E* is the equivalent Young's modulus of the particle system, and G* is the equivalent shear modulus of the particle system.

[0047] S2. Calculate the resistance distribution between particles. When two solids are compressed together under external force, a conduction path is formed in their contact area, allowing electrons to flow freely through the contact area. Table 1 shows the material parameters of the particles in the calculation process of this embodiment. The following formula is used to calculate the resistance between particles on the conduction path:

[0048] R ij =R i +R c,ij +R j

[0049]

[0050] In the formula, R i is the resistance from the center of particle i to its elastic deformation position; R j is the resistance from the center of particle j to its elastic deformation position; R c,ij is the resistance of the overlapping region of particles i and j; ρ i is the resistivity of particle i; ρ j is the resistivity of particle j; r i * is the resistivity of particle i; r j is the resistivity of particle j; L ij is the distance between the centers of two contacting particles.

[0051] Table 1 Granular material parameters during calculation

[0052]

[0053]

[0054] S3. Calculate the resistance distribution between the particles and the boundary. When a mechanical load is applied to the particle system, some particles will contact the boundary wall and generate channels in the overlapping area that allow electrons to pass freely, thereby causing electrical transfer between the particles and the wall. Table 2 shows the material parameters of the boundary during the calculation process of this embodiment.

[0055] Table 2 Boundary material parameters during calculation

[0056] project unit Numeric Poisson's ratio — 0.343 density <![CDATA[kg / m 3 ]]> 8960 Young's modulus GPa 129.8 Resistivity Ωm <![CDATA[1.8×10 -8 ]]>

[0057] The resistance between the particle and the boundary on the conductive path is calculated using the following formula:

[0058] R iw =R i,iw +R c,iw

[0059]

[0060] In the formula, Riw is the resistance between the particle and the boundary; R i,iw is the resistance of the particle in contact with the boundary; R c,iw is the resistance of the boundary in contact with the particle; ρ i is the resistivity of particle i in contact with the boundary; ρ w is the resistivity of the boundary; r i * is the resistivity of particle i in contact with the boundary; δ is the elastic deformation of the particle under the boundary load; is the equivalent Young's modulus of the particle and the boundary; f n is the normal component of the contact force between the particle and the boundary.

[0061] S4. Calculate the mechanical-electrical coupling response of the particle system. Couple the particle-particle and particle-boundary mechanical models with the electrical model, and use the following model to calculate the mechanical-electrical coupling response of the particle system:

[0062]

[0063] Where V 0 is the voltage applied to the upper boundary; V 1 is the voltage of the lower boundary; V i is the voltage of different particles, i = 1, 2, 3, ..., n; R ii is the resistance between different particles, i = 1, 2, 3, ..., n; -I 0 is the current at the upper boundary; I 0 is the lower boundary current.

[0064] S5. Synthesis of force-electric coupling response model. Generate a text document with the model obtained in the above four steps, and import the document into discrete element commercial analysis software to obtain the resistance distribution result of the particle system, such as Figure 3 shown.

[0065] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for calculating the mechanical-electrical coupling response of a particle system, characterized in that: The method comprises the following steps: Step 1, establish a particle dynamics model and calculate the tangential force and normal force between particles; Step 2, establish a particle system resistance transfer calculation model to calculate the resistance between particles and between particles and boundaries in the power-on state; Step 3: Establish a coupled force-electric response model of the particle system to calculate the force and resistance between particles and between particles and boundaries when load is applied and power is turned on.

2. The method for calculating the force-electric coupling response of a particle system according to claim 1, characterized in that: Step 1 further comprises: Initialize the particle system; Apply loads and power at the boundaries, and calculate particle motion data; Detect the contact state between internal particles and between particles and boundaries, evaluate the contact response and update the geometric state changes of particles, build a particle dynamics model, and calculate the tangential force and normal force between particles.

3. The method for calculating the force-electric coupling response of a particle system according to claim 1, characterized in that: The tangential force and normal force between particles are calculated using the following formula: In the formula, is the normal force between particles; is the tangential force between particles; m * is the equivalent mass of the particles; β is the damping coefficient between particles; δ n is the normal overlap between particles; δ t is the tangential overlap between particles; is the normal component of the relative velocity between particles; is the tangential component of the relative velocity between particles; is the equivalent Young's modulus of adjacent contact particles; r * is the effective radius of the particle; k n is the normal damping coefficient between particles; k t is the tangential damping coefficient between particles; E i is the Young's modulus of particle i; v i is the Poisson's ratio of particle i; r i is the radius of particle i; E j is the Young's modulus of particle j; v j is the Poisson's ratio of particle j; r j is the radius of particle j; E* is the equivalent Young's modulus of the particle system, and G* is the equivalent shear modulus of the particle system.

4. The method for calculating the force-electric coupling response of a particle system according to claim 1, characterized in that: In step 2, the resistance between particles in the energized state is calculated using the following formula: R ij =R i +R c,ij +R j In the formula, R i is the resistance from the center of particle i to its elastic deformation position; R j is the resistance from the center of particle j to its elastic deformation position; R c,ij is the resistance of the overlapping region of particles i and j; ρ i is the resistivity of particle i; ρ j is the resistivity of particle j; r i * is the resistivity of particle i; r j is the resistivity of particle j; L ij is the distance between the centers of two contacting particles; f n is the normal component of the contact force between the particle and the boundary.

5. The method for calculating the force-electric coupling response of a particle system according to claim 1, characterized in that: In step 2, the resistance between the particle and the boundary in the powered state is calculated using the following formula: R iw =R i,iw +R c,iw In the formula, R iw is the resistance between the particle and the boundary; R i,iw is the resistance of the particle in contact with the boundary; R c,iw is the resistance of the boundary in contact with the particle; ρ i is the resistivity of particle i in contact with the boundary; ρ w is the resistivity of the boundary; r i * is the resistivity of particle i in contact with the boundary; δ is the elastic deformation of the particle under the boundary load; is the equivalent Young's modulus of the particle and the boundary; f n is the normal component of the contact force between the particle and the boundary.

6. The method for calculating the force-electric coupling response of a particle system according to claim 1, characterized in that: In step 3, the particle system force-electric response coupling model is: Where V0 is the voltage applied at the upper boundary; V1 is the voltage applied at the lower boundary; V i is the voltage of different particles, i = 1, 2, 3, ..., n; R ii is the resistance between different particles, i=1, 2, 3,…, n; -I0 is the current at the upper boundary; I0 is the current at the lower boundary.

Images