A method and device for calculating the resistance response of a planar particle-filled composite material

Abstract

This invention discloses a method and apparatus for calculating the resistance response of planar particle-filled composite materials, comprising: constructing a strain model based on the displacement of the filler under a specified strain; dividing the filler into a mesh of a specified unit size based on the strain model; calculating the spacing matrix of all fillers based on the filler mesh; finding all boundary filler matrices as start and end points; determining the conductive channels that satisfy certain conditions based on the filler spacing matrix and the start and end points; and converting the conductive channels into equivalent circuits to solve for the equivalent resistance. The technical solution of this invention has the advantages of using fewer resources and extremely fast calculation speed.

Description

Technical Field

[0001] This invention belongs to the field of computational materials technology, and in particular relates to a method and apparatus for calculating the resistance response of a planar particle-filled composite material. Background Technology

[0002] Particle-filled composite materials possess properties such as bending resistance, good electrical conductivity, and high strength, making them a hot topic in research and application. Among these, the finite element method (FEM) has become an important tool for studying the mechanisms of particle-filled composite materials. Current FEM and other theoretical methods heavily rely on Ohm's law and the tunneling effect, and the application of the tunneling effect requires calculating the filler spacing. Due to the complexity of composite material models, mesh generation, secondary development, and filler spacing calculation are all quite difficult. Calculating the resistance response model on this basis significantly increases the computation time and resources required. Therefore, how to quickly calculate the resistance response of complex models with limited computer resources has become an urgent problem to be solved.

[0003] The finite element method (FEM) for calculating the resistivity response of graphene composites typically simplifies the graphene to two dimensions and calculates the spacing between the fillers through secondary calculations, applying the tunneling effect at specified intervals. This method involves a very cumbersome process for calculating the filler spacing, making it unsuitable for large-scale repetitive computations. Another approach is to model the graphene as a three-dimensional model considering the phase interfaces, where the interfaces are directly defined as the regions where the tunneling effect applies. This method is also very difficult in terms of modeling and mesh generation, similarly hindering large-scale repetitive computations, and requires enormous computing resources to calculate the resistivity response.

[0004] The calculation of the electrical resistance response of planar particle-filled composite materials currently has the following limitations:

[0005] 1. The calculation method for resistive response is very cumbersome. Current calculation methods involve complex steps such as mesh generation and filler spacing calculation. These steps are largely manual and difficult to automate.

[0006] 2. The finite element method (FEM) is time-consuming and resource-intensive for calculating resistance response. Due to the complexity of the calculation method, it is difficult to perform a large number of calculations. Furthermore, the degrees of freedom required for strain model calculation are six times that of electrical performance calculation, thus requiring extremely high resource consumption and a long computation time for resistance response calculation. Summary of the Invention

[0007] This invention aims to address the shortcomings of existing technologies by proposing a method and apparatus for calculating the resistance response of planar particle-filled composite materials, which features low resource consumption and extremely fast calculation speed.

[0008] To achieve the above object, the present invention provides the following solutions:

[0009] A method for calculating the resistivity response of a planar particle-filled composite material includes:

[0010] Step S1: Construct a strain model based on the displacement of the filler under specified strain.

[0011] Step S2: Divide the filler mesh into a specified unit mesh size according to the strain model;

[0012] Step S3: Calculate the spacing matrix of all packings based on the packing mesh;

[0013] Step S4: Locate all boundary filler matrices as the start and end points;

[0014] Step S5: Based on the filler spacing matrix and the start and end points, find the conductive channels that meet the conditions;

[0015] Step S6: Based on the transformation of the conductive channel into an equivalent circuit, solve for the equivalent resistance.

[0016] Preferably, in step S1, the strain model includes the coordinates of the four vertices of the geometric model of the planar packing. Two points on the diagonal are arbitrarily selected to obtain the coordinates of the centroid. According to the specified strain, the change in the position coordinates of the centroid of the packing is calculated. The change is summed with the initial coordinates of the four vertices to obtain the coordinates of the vertices of the packing after the specified displacement. Then, all packings are traversed.

[0017] Preferably, in step S3, the spacing between two packing materials in space is calculated based on the atomic equilibrium force spacing, and all packing material combinations are traversed to obtain the packing material coordinate spacing matrix.

[0018] Preferably, in step S4, the boundary of the strained model is obtained based on strain calculation, and the coordinates of all meshed fillers are calculated with the boundary to find all fillers at the boundary.

[0019] Preferably, in step S6, the resistance on the conductive channel includes: a filler resistance and a tunneling resistance; wherein...

[0020] Calculate the filler resistance R gr for: Where, k G G represents the electrical conductivity of planar packing material. size t represents the size of the packing sheet. gr This represents the thickness of the filler.

[0021] Calculate tunneling resistance R t for: Where Planck's constant h = 6.62607015 × 10 -34 J·s, charge e=1.602176634×10 -19C and M are the number of conductive channels, and the tunneling probability τ is determined by the following formula:

[0022]

[0023]

[0024] Where d is the distance between the packings, d v For van der Waals spacing, d cut-off It is the tunnel cutoff length, in meters. e Let be the electron mass, and ΔE be the potential barrier of the composite matrix.

[0025] The present invention also provides a device for calculating the resistance response of a planar particle-filled composite material, comprising:

[0026] The building module is used to construct a strain model based on the displacement of the filler under a specified strain.

[0027] The meshing module is used to mesh the filler with a specified unit mesh size based on the strain model;

[0028] The calculation module is used to calculate the spacing matrix of all packings based on the packing mesh;

[0029] The search module is used to find all boundary filler matrices as start and end points;

[0030] The first processing module is used to determine the conductive channels that meet the conditions based on the filler spacing matrix and the start and end points.

[0031] The second processing module is used to solve for the equivalent resistance based on the transformation of the conductive channel into an equivalent circuit.

[0032] Preferably, the strain model includes the coordinates of the four vertices of the geometric model of the planar packing. Two points on the diagonal are arbitrarily selected to obtain the coordinates of the centroid. According to the specified strain, the change in the position coordinates of the centroid of the packing is calculated. The change is summed with the initial coordinates of the four vertices to obtain the coordinates of the vertices of the packing after the specified displacement. Then, all packings are traversed.

[0033] Preferably, the resistance on the conductive channel includes: filler resistance and tunneling resistance; wherein...

[0034] Calculate the filler resistance R gr for: Where, k G G represents the electrical conductivity of planar packing material. size t represents the size of the packing sheet. gr This represents the thickness of the filler.

[0035] Calculate tunneling resistance R t for: Where Planck's constant h = 6.62607015 × 10 -34 J·s, charge e=1.602176634×10 -19 C and M are the number of conductive channels, and the tunneling probability τ is determined by the following formula:

[0036]

[0037]

[0038] Where d is the distance between the packings, d v For van der Waals spacing, d cut-off It is the tunnel cutoff length, in meters. e Let be the electron mass, and ΔE be the potential barrier of the composite matrix.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] The electrical property calculation method of this invention for composite materials is fast and requires minimal memory resources. It only requires a gridded filler and can solve for the resistive response and electrical properties of the composite material through tunneling effect and Ohm's law. Furthermore, there are no restrictions on the matrix of the composite material; this invention is still applicable regardless of the agglomeration or size distribution characteristics of the filler. Attached Figure Description

[0041] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a flowchart illustrating a method for calculating the resistance response of a planar particle-filled composite material according to an embodiment of the present invention;

[0043] Figure 2 This is a flowchart of another method for calculating the resistance response of a planar particle-filled composite material according to an embodiment of the present invention;

[0044] Figure 3 This is a meshed model diagram of the planar infill composite material in an embodiment of the present invention;

[0045] Figure 4 These are the bulk resistivity diagrams of the composite materials under different filler fractions in the embodiments of the present invention;

[0046] Figure 5 This is a meshed model diagram of the planar infilled composite material after 100% strain in an embodiment of the present invention;

[0047] Figure 6 The graph shows the calculated resistance response of the composite material under different filler contents in the embodiments of the present invention. Detailed Implementation

[0048] 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, and 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.

[0049] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] Example 1:

[0051] like Figure 1 As shown, this embodiment of the invention provides a method for calculating the resistance response of a planar particle-filled composite material, including:

[0052] Step S1: Construct a strain model based on the displacement of the filler under specified strain.

[0053] Step S2: Divide the filler mesh into a specified unit mesh size according to the strain model;

[0054] Step S3: Calculate the spacing matrix of all packings based on the packing mesh;

[0055] Step S4: Locate all boundary filler matrices as the start and end points;

[0056] Step S5: Based on the filler spacing matrix and the start and end points, find the conductive channels that meet the conditions;

[0057] Step S6: Based on the transformation of the conductive channel into an equivalent circuit, solve for the equivalent resistance.

[0058] As one embodiment of the present invention, in step S1, the strain model includes the coordinates of the four vertices of the geometric model of the planar packing. Two points on the diagonal are arbitrarily selected to obtain the coordinates of the centroid. According to the specified strain, the change in the position coordinates of the centroid of the packing is calculated respectively. The change is summed with the initial coordinates of the four vertices to obtain the coordinates of the vertices of the packing after the specified displacement. Then, all packings are traversed.

[0059] As one embodiment of the present invention, in step S3, the spacing between two packing materials in space is calculated based on the atomic equilibrium force spacing, and all packing material combinations are traversed to obtain the packing material coordinate spacing matrix.

[0060] As one embodiment of the present invention, in step S4, the boundary of the strained model is obtained based on strain calculation, and the coordinates of all meshed fillers are calculated with the boundary to find all fillers at the boundary.

[0061] In one embodiment of the present invention, in step S6, the resistance on the conductive channel includes: a filler resistance and a tunneling resistance; wherein...

[0062] Calculate the filler resistance R gr for: Where, k G G represents the electrical conductivity of planar packing material. size t represents the size of the packing sheet. gr This represents the thickness of the filler.

[0063] Calculate tunneling resistance R t for: Where Planck's constant h = 6.62607015 × 10 -34 J·s, charge e=1.602176634×10 -19 C and M are the number of conductive channels, and the tunneling probability τ is determined by the following formula:

[0064]

[0065]

[0066] Where d is the distance between the packings, d v For van der Waals spacing, d cut-off It is the tunnel cutoff length, in meters. e Let be the electron mass, and ΔE be the potential barrier of the composite matrix.

[0067] Example 2:

[0068] like Figure 2 As shown, this embodiment of the invention provides a method for calculating the resistance response of a planar particle-filled composite material, including the following steps:

[0069] Step 21: The filler is subjected to a displacement with a specified strain ε to establish a strain model, and the size s of the composite material geometry model is specified. R After geometric modeling, the coordinates C0 of the four vertices of the planar filler can be obtained. By arbitrarily choosing two points on the diagonal, the coordinates c of the centroid can be obtained. g Based on the specified strain ε and the formula z=Z(1+ε) (taking uniaxial tension in the z direction as an example), and The overall strain of the model can be calculated based on the formula. Linearize the strain, where sR ε represents the size of the composite material geometric model. r The strain is the linearized strain of the current packing sheet; the calculated ε r Substituting into the formula z=Z(1+ε) (taking unidirectional tension in the z direction as an example), and The displacement of the current filler can be calculated; the displacement is summed with the coordinates of the four initial vertices C0 to obtain the coordinates of the filler vertices after the specified displacement. Then, by traversing all fillers in the same way, the displacement model of the composite material can be obtained.

[0070] Step 22: Perform mesh generation for the fill material with a specified unit mesh size M. Specify the unit mesh size M; determine the projection size of the fill material coordinates onto the Cartesian coordinate system (x, y, z), and select the two directions with the largest and second largest projections as the mesh generation directions. The fill material coordinates corresponding to these mesh directions form a surface, which is discretized according to M; solve the plane equation Ax + By + Cz + D = 0 based on the fill material vertex coordinates, and substitute the discretized coordinates into the plane equation to obtain the coordinates with the smallest projection. Recombining these three results yields the meshed fill material coordinates. Traversing all fill materials yields the meshed coordinates of all fill materials; furthermore, the meshed coordinates can be easily used for truncation at model boundaries through coordinate operations.

[0071] Step 23: Calculate the spacing matrix D of all packing materials. gr Specify the minimum spacing d between packing materials v The spacing between the two packing materials is... The calculation yielded, where A2 B 2 This is the sum of the squares of all coordinates after the mesh is formed from a single packing material, and then summed row by row. However, A and B cannot point to the same packing material. In the formula, A... 2 The constructed matrix (A) 2 A 2 ,…,A 2 ), A in the matrix 2 The number is determined by B 2 The number of rows is determined by B. 2 The constructed matrix (B) 2 B 2 ,…,B 2 ) T In the matrix B 2 The number is determined by A 2 The number of rows determines their arrangement, so they form a square matrix, and finally, a matrix 2AB is subtracted. T Finally, iterate through all packing combinations. If the calculated spacing d... min Less than this value d vAccording to molecular forces, the spacing between the fillers should be d. v ;

[0072] Step 24: Locate all boundary filler matrices D x+ D x- D y+ D y- D z+ D z- The boundary of the model can be calculated based on the strain ε and formulas such as z=Z(1+ε). The coordinates of all the meshed filler material are then calculated with the boundary. Coordinates outside the model boundary are discarded, while those inside the model are retained.

[0073] Step 25: Based on the packing spacing matrix D gr Given the found start and end points, find the conductive paths that satisfy the conditions. Once the packing boundaries and packing spacing are known, traverse all start and end points, and use the packing spacing matrix D... gr Find paths that meet the conditions; any shortest path algorithm can be used (using Dijkstra's algorithm as an example). The goal is to find paths that satisfy the conditions among all possible paths. The tunneling effect is generally effective within 3 nm; therefore, in the found paths, the spacing between all fillers should be less than 3 nm. Save all paths that meet the conditions. If no path meets the conditions, only save the shortest path. If there is no starting or ending point, treat it as a non-conductive case.

[0074] Step 26: Based on the transformation of the conductive channel into an equivalent circuit, solve for the equivalent resistance and save it, specifying the calculation parameter filler conductivity k. G Matrix conductivity k r Filler thickness t GR Once the conductive path is known, it can be transformed into an equivalent circuit.

[0075] First, calculate the filler resistance using the formula. Where, k G G represents the electrical conductivity of planar packing material. size t represents the size of the packing sheet. gr This represents the thickness of the filler.

[0076] Then calculate the tunneling resistance using the formula. Where Planck's constant h = 6.62607015 × 10 -34 J·s, charge e=1.602176634×10 -19 C and M are the number of conductive channels, and the tunneling probability is determined by the following formula:

[0077]

[0078]

[0079] Where d is the distance between the packings, d v For van der Waals spacing, d cut-off It is the tunnel cutoff length, in meters. e Let be the electron mass, and ΔE be the potential barrier of the composite matrix. The resistance of all conductive channels is calculated from this. When multiple conductive channels exist, the total resistance is solved using the parallel resistance formula. The conductive channels of the composite material can be considered equivalent to the electrical properties of the composite material. The results obtained from the MATLAB solution are basically consistent with the results in the commercial software ABAQUS, and also basically consistent with the experimental results. See [link to MATLAB solution]. Figure 4 .

[0080] Example 3:

[0081] This invention provides a method for calculating the resistivity response of a composite material filled with planar particles, comprising the following steps:

[0082] Step 31: The filler is subjected to a displacement with a specified strain ε = 0 to establish a strain model, and the size s of the composite material geometry model is specified. R =100.

[0083] Step 32: Perform mesh generation for the filler material with a specified unit mesh size M=1. This yields the meshed model of the planar infill composite material, as shown below. Figure 3 .

[0084] Step 33: Calculate the spacing matrix D of all packing materials. gr Specify the minimum spacing d between packing materials v =0.34.

[0085] Step 34: Locate all boundary filler matrices D x+ D x- D y+ D y- D z+ D z- , as the starting point or the end point.

[0086] Step 35: Based on the packing spacing matrix D gr Given the starting and ending points, find the conductive path that satisfies the given conditions.

[0087] Step 36: Based on the transformation of the conductive channel into an equivalent circuit, solve for the equivalent resistance and save it, specifying the calculation parameter filler conductivity k. G =1000S / cm, matrix conductivity k r =10 -13 S / cm, filler thickness t gr=0.34. The electrical properties of planar filled composite materials are shown in [reference needed]. Figure 4 .

[0088] Example 4:

[0089] This invention provides a method for calculating the resistivity response of a composite material filled with planar particles, comprising the following steps:

[0090] Step 41: The filler is subjected to a displacement of 100% of the specified strain ε to establish a strain model, and the size s of the composite material geometry model is specified. R =100.

[0091] Step 42: Perform mesh generation for the filler material with a specified unit mesh size M=1. This yields the meshed model of the planar infill composite material, as shown below. Figure 5 .

[0092] Step 43: Calculate the spacing matrix D of all packing materials. gr Specify the minimum spacing d between packing materials v =0.34.

[0093] Step 44: Locate all boundary filler matrices D x+ D x- D y+ D y- D z+ D z- , as the starting point or the end point.

[0094] Step 45: Based on the packing spacing matrix D gr Given the starting and ending points, find the conductive path that satisfies the given conditions.

[0095] Step 46: Based on the transformation of the conductive channel into an equivalent circuit, solve for the equivalent resistance and save it, specifying the calculation parameter filler conductivity k. G =1000S / cm, matrix conductivity k r =10 -13 S / cm, filler thickness t gr =0.34. The resistivity response properties of planar filled composite materials are shown in [reference needed]. Figure 6 .

[0096] Example 5:

[0097] This invention also provides a device for calculating the resistance response of a planar particle-filled composite material, comprising:

[0098] The building module is used to construct a strain model based on the displacement of the filler under a specified strain.

[0099] The meshing module is used to mesh the filler with a specified unit mesh size based on the strain model;

[0100] The calculation module is used to calculate the spacing matrix of all packings based on the packing mesh;

[0101] The search module is used to find all boundary filler matrices as start and end points;

[0102] The first processing module is used to determine the conductive channels that meet the conditions based on the filler spacing matrix and the start and end points.

[0103] The second processing module is used to solve for the equivalent resistance based on the transformation of the conductive channel into an equivalent circuit.

[0104] As one embodiment of the present invention, the strain model includes the coordinates of the four vertices of the geometric model of the planar packing. Two points on the diagonal are arbitrarily selected to obtain the coordinates of the centroid. According to the specified strain, the change in the position coordinates of the centroid of the packing is calculated. The change is summed with the initial coordinates of the four vertices to obtain the coordinates of the vertices of the packing after the specified displacement. Then, all packings are traversed.

[0105] In one embodiment of the present invention, the resistance on the conductive channel includes: a filler resistance and a tunneling resistance; wherein...

[0106] Calculate the filler resistance R gr for: Where, k G G represents the electrical conductivity of planar packing material. size t represents the size of the packing sheet. gr This represents the thickness of the filler.

[0107] Calculate tunneling resistance R t for: Where Planck's constant h = 6.62607015 × 10 -34 J·s, charge e=1.602176634×10 -19 C and M are the number of conductive channels, and the tunneling probability τ is determined by the following formula:

[0108]

[0109] Where d is the distance between the packings, d v For van der Waals spacing, d cut-off It is the tunnel cutoff length, in meters. e Let be the electron mass, and ΔE be the potential barrier of the composite matrix.

[0110] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the resistivity response of a planar particle-filled composite material, characterized in that, include: Step S1: Construct a strain model based on the displacement of the filler under specified strain. Step S2: Divide the filler mesh into a specified unit mesh size according to the strain model; Step S3: Calculate the spacing matrix of all packings based on the packing mesh; Step S4: Locate all boundary filler matrices as the start and end points; Step S5: Based on the filler spacing matrix and the start and end points, find the conductive channels that meet the conditions; Step S6: Based on the transformation of the conductive channel into an equivalent circuit, solve for the equivalent resistance.

2. The method for calculating the resistivity response of planar particle-filled composite materials according to claim 1, characterized in that, In step S1, the strain model includes the coordinates of the four vertices of the geometric model of the planar packing. Two points on the diagonal are arbitrarily selected to obtain the coordinates of the centroid. According to the specified strain, the change in the position coordinates of the centroid of the packing is calculated. The change is summed with the initial coordinates of the four vertices to obtain the coordinates of the vertices of the packing after the specified displacement. Then, all packings are traversed.

3. The method for calculating the resistivity response of planar particle-filled composite materials according to claim 2, characterized in that, In step S3, the spacing between two packing materials in space is calculated based on the atomic equilibrium force spacing, and all packing material combinations are traversed to obtain the packing material coordinate spacing matrix.

4. The method for calculating the resistivity response of planar particle-filled composite materials according to claim 3, characterized in that, In step S4, the boundary of the strained model is obtained based on strain calculation. The coordinates of all meshed fillers are calculated with the boundary to find all fillers at the boundary.

5. The method for calculating the resistivity response of planar particle-filled composite materials according to claim 4, characterized in that, In step S6, the resistance on the conductive channel includes: filler resistance and tunneling resistance; wherein, Calculate the filler resistance R gr for: Where, k G G represents the electrical conductivity of planar packing material. size t represents the size of the packing sheet. gr This represents the thickness of the filler. Calculate tunneling resistance R t for: Where Planck's constant h = 6.62607015 × 10 -34 J·s, charge e=1.602176634×10 -19 C and M are the number of conductive channels, and the tunneling probability τ is determined by the following formula: Where d is the distance between the packings, d v For van der Waals spacing, d cut-off It is the tunnel cutoff length, in meters. e Let be the electron mass, and ΔE be the potential barrier of the composite matrix.

6. A device for calculating the resistance response of a planar particle-filled composite material, characterized in that, include: The building module is used to construct a strain model based on the displacement of the filler under a specified strain. The meshing module is used to mesh the filler with a specified unit mesh size based on the strain model; The calculation module is used to calculate the spacing matrix of all packings based on the packing mesh; The search module is used to find all boundary filler matrices as start and end points; The first processing module is used to determine the conductive channels that meet the conditions based on the filler spacing matrix and the start and end points. The second processing module is used to solve for the equivalent resistance based on the transformation of the conductive channel into an equivalent circuit.

7. The resistivity response calculation device for planar particle-filled composite materials according to claim 6, characterized in that, The strain model includes the coordinates of the four vertices of the geometric model of the planar packing. By arbitrarily selecting two points on the diagonal, the coordinates of the centroid are obtained. Based on the specified strain, the change in the coordinates of the centroid of the packing is calculated. This change is summed with the initial coordinates of the four vertices to obtain the coordinates of the packing vertices after the specified displacement. Then, all packings are traversed.

8. The resistivity response calculation device for planar particle-filled composite materials according to claim 7, characterized in that, The resistance on a conductive channel includes: filler resistance and tunneling resistance; among which, Calculate the filler resistance R gr for: Where, k G G represents the electrical conductivity of planar packing material. size t represents the size of the packing sheet. gr This represents the thickness of the filler. Calculate tunneling resistance R t for: Where Planck's constant h = 6.62607015 × 10 -34 J·s, charge e=1.602176634×10 -19 C and M are the number of conductive channels, and the tunneling probability τ is determined by the following formula: Where d is the distance between the packings, d v For van der Waals spacing, d cut-off It is the tunnel cutoff length, in meters. e Let be the electron mass, and ΔE be the potential barrier of the composite matrix.

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