A two-dimensional discrete element numerical specimen modeling method for arbitrary-shaped aggregate particles

Abstract

The present invention relates to a two-dimensional arbitrarily shaped aggregate particle discrete element numerical sample modeling method, which belongs to the field of concrete technology and is used to provide a guarantee for the simulation of the mechanical behavior of concrete. The present invention provides a two-dimensional arbitrarily shaped aggregate particle discrete element numerical sample modeling method. First, by constructing a calculation area equal to the numerical sample size in Matlab, two-dimensional arbitrarily shaped aggregate particles of a certain gradation are randomly generated within this area; secondly, the information within the constructed calculation area is grouped, with the aggregate as one group and the remaining areas as one group, and the grouping information is exported; then, based on the specified porosity, a numerical sample area of ​​a single particle shape is generated in the discrete element software, and then the grouping information is imported to construct the aggregate area and the matrix area; finally, a multiple contact model is assigned, and relevant model parameters and physical parameters are set.

Description

Technical Field

[0001] The invention relates to the technical field of concrete, and in particular to a discrete element numerical sample modeling method for two-dimensional arbitrary-shaped aggregate particles. Background Art

[0002] Concrete is considered a three-phase composite material consisting of coarse aggregate, a mortar matrix, and an aggregate-mortar interface. Under the action of external forces, the multiphase and heterogeneous nature of concrete's microstructure controls its mesoscale damage matrix and macroscopic mechanical properties. Currently, commonly used finite element simulation software is based on continuum theory, dividing an object into a finite number of elements, with the nodes connected by mathematical equations. However, actual concrete failure is discontinuous, and discrete element methods can study the discontinuous fracture, mechanical properties, and behavior of concrete from a microstructural perspective. Consequently, their application in concrete simulation is becoming increasingly widespread.

[0003] However, it is difficult to directly generate aggregate particles of random shapes in current discrete element software, so technical means are needed to solve this defect. Summary of the Invention

[0004] The purpose of the present invention is to provide a two-dimensional discrete element numerical specimen modeling method for aggregate particles of arbitrary shape, which provides a guarantee for the subsequent simulation of the mechanical behavior of concrete.

[0005] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0006] A preparation method for a two-dimensional discrete element numerical specimen modeling method for aggregate particles of arbitrary shape, comprising the following steps:

[0007] Step S1: construct a calculation area equal to the size of the numerical sample in Matlab, and randomly generate two-dimensional arbitrary-shaped aggregate particles with a certain gradation within this area;

[0008] Step S2: Group the information in the calculation area of ​​step S1, with the aggregate as one group and the remaining areas as one group, and export the group information;

[0009] Step S3: Generate a numerical sample region (x, y) of a single particle shape in the discrete element software according to the specified porosity, where x∈[-W / 2, W / 2], y∈[-H / 2, H / 2], and then import the grouping information in step S2 to construct the aggregate region and matrix region;

[0010] Step S4, assigning multiple contact models: setting the contact model between aggregate particles to a contact bonding model, setting the contact model between matrix particles to a displacement softening model, setting the contact model between aggregate and matrix particles to a displacement softening model, setting the contact model between the wall and particles to a linear contact model, and setting relevant model parameters and physical parameters.

[0011] Furthermore, the true morphology information of the two-dimensional arbitrary-shaped aggregate particles in step S1 is obtained by X-ray CT scanning.

[0012] Furthermore, the two-dimensional arbitrary-shaped aggregate particles in step S1 are circular aggregate particles, convex polygonal aggregate particles, or irregular aggregate particles.

[0013] Furthermore, the step of generating round aggregate particles includes:

[0014] Step k1, randomly generating random circles of circular aggregate particle sizes within the sample area;

[0015] Step k2: determine whether the newly generated aggregate overlaps with the already generated aggregate. If not, generate it; otherwise, re-place it.

[0016] Step k3: When the area of ​​the random circle reaches the area of ​​the aggregate of this level, exit and generate the next level of aggregate.

[0017] Furthermore, the polygonal aggregate particle generation step includes:

[0018] Step d1, setting the volume fraction of polygonal aggregate particles, the minimum aggregate particle size, and the maximum aggregate particle size;

[0019] Step d2: Generate a random circle with a diameter close to the aggregate particle size. Based on this circle, randomly generate an n-gon inscribed in the circle. Use the Larven formula to determine the area of ​​the convex polygonal aggregate. When the area of ​​the convex polygonal aggregate is smaller than the area of ​​the corresponding circular aggregate, perform aggregate extension.

[0020] Step d3: determine whether the newly generated aggregate overlaps with the already generated aggregate. If not, it will be generated; otherwise, it will be re-added;

[0021] Step d4: Calculate the area of ​​the convex polygon aggregate. If the area reaches the corresponding level of aggregate, exit and generate the next level of aggregate.

[0022] Furthermore, the step of generating irregular aggregate particles includes:

[0023] Step g1: randomly generate an ellipse with a diameter close to the size of the irregular aggregate particles, and perform expansion and contraction deformation on the ellipse to obtain a single irregular aggregate;

[0024] Step g2: randomly generate a point in the simulation area and determine whether it is outside the ellipse covered by all generated particles; if it is outside, generate an ellipse centered on this point and then deform it to obtain an irregular aggregate; otherwise, regenerate a random point;

[0025] Step g3: Calculate the area of ​​irregular aggregate. If the area reaches the corresponding grade of aggregate, exit and generate the next grade of aggregate.

[0026] Furthermore, the steps of grouping the real morphology information of the aggregate are as follows:

[0027] Step t1, import the aggregate image obtained by X-ray CT scanning into Matlab;

[0028] Step t2: Binarize the imported image to obtain a 0,1 matrix, group the aggregate and matrix, and export the grouping information.

[0029] Furthermore, the steps of importing information to construct a discrete element numerical simulation specimen in step S3 are as follows:

[0030] Step p1: traverse the balls in the generated area and obtain the coordinate information of all balls;

[0031] Step p2: Move the coordinates of the ball to obtain new coordinate information;

[0032] Step p3: Get the matrix information of the balls in the generated area, determine whether the balls belong to aggregate or matrix, group them, and finally complete the grouping.

[0033] Furthermore, in step S3, the ratio of the numerical specimen size to the radius of the generated single-shaped particle sphere is greater than or equal to 80.

[0034] Furthermore, in step S4, the linear model parameters include the effective Young's modulus, the contact stiffness ratio, and the friction coefficient; the contact bonding model parameters include the effective Young's modulus of inter-particle bonding, the inter-particle bonding cohesion, the inter-particle bonding tensile strength, and the inter-particle bonding internal friction angle; the displacement softening model parameters include the inter-particle tangential stiffness, the granule normal stiffness, the inter-particle tangential strength, the inter-particle normal strength, the inter-particle bonding internal friction angle, the maximum displacement of the normal failure point, and the maximum displacement of the tangential failure point; and the physical parameters include the particle density and the acceleration of gravity.

[0035] Compared with the prior art, the present invention has the following beneficial technical effects:

[0036] (1) The present invention provides a discrete element numerical specimen modeling method for two-dimensional arbitrary-shaped aggregate particles. First, a calculation area equal to the numerical specimen size is constructed in Matlab, and two-dimensional arbitrary-shaped aggregate particles of a certain gradation are randomly generated within this area. Second, the information within the constructed calculation area is grouped, with the aggregate as one group and the remaining areas as another group, and the grouping information is exported. Then, based on the specified porosity, a numerical specimen area of ​​a single particle shape is generated in the discrete element software, and the grouping information is subsequently imported to construct the aggregate area and the matrix area. Finally, a multiple contact model is assigned, and relevant model parameters and physical parameters are set.

[0037] (2) The two-dimensional discrete element numerical specimen modeling method for arbitrary-shaped aggregate particles provided by the present invention can solve the defect that it is difficult to generate arbitrary-shaped aggregate particles in discrete element software.

[0038] (3) The present invention provides a two-dimensional discrete element numerical specimen modeling method for aggregate particles of arbitrary shape. By grouping the components of the concrete simulation specimen, aggregate particles, matrix particles, interface particles, etc. are defined, and a displacement softening model is developed to make the simulation more consistent with the actual situation.

[0039] (4) The discrete element numerical specimen modeling method for two-dimensional arbitrary-shaped aggregate particles provided by the present invention can be used to construct aggregates with actual morphological characteristics, providing a guarantee for subsequent discrete element simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of generating a concrete discrete element simulation specimen using Matlab combined with discrete element software in a two-dimensional arbitrary-shaped aggregate particle discrete element numerical specimen modeling method according to an embodiment of the present invention;

[0041] Figure 2 This is one of the constitutive relationship diagrams of the displacement softening model in the discrete element numerical specimen modeling method for two-dimensional arbitrary-shaped aggregate particles in an embodiment of the present invention;

[0042] Figure 3 This is the second constitutive relationship diagram of the displacement softening model in the discrete element numerical specimen modeling method for two-dimensional arbitrary-shaped aggregate particles in an embodiment of the present invention;

[0043] Figure 4 Schematic diagram of generating random circular aggregates in the discrete element numerical specimen modeling method for two-dimensional arbitrary-shaped aggregate particles in an embodiment of the present invention;

[0044] Figure 5 Schematic diagram of constructing a concrete model by generating random circular aggregate discrete elements in a two-dimensional arbitrary-shape aggregate particle discrete element numerical specimen modeling method according to an embodiment of the present invention;

[0045] Figure 6Schematic diagram of generating random polygonal convex aggregates in the discrete element numerical specimen modeling method for two-dimensional arbitrary-shaped aggregate particles in an embodiment of the present invention;

[0046] Figure 7 Schematic diagram of constructing a concrete model by generating random polygonal convex aggregate discrete elements in a two-dimensional arbitrary-shape aggregate particle discrete element numerical specimen modeling method according to an embodiment of the present invention;

[0047] Figure 8 Schematic diagram of generating irregular aggregate in the discrete element numerical specimen modeling method of two-dimensional arbitrary-shaped aggregate particles in an embodiment of the present invention;

[0048] Figure 9 Schematic diagram of constructing a concrete model by generating irregular aggregate discrete elements in a two-dimensional arbitrary-shape aggregate particle discrete element numerical specimen modeling method according to an embodiment of the present invention;

[0049] Figure 10 Schematic diagram of constructing the true morphology of aggregate based on X-ray CT scanning in the discrete element numerical specimen modeling method for two-dimensional arbitrary-shaped aggregate particles in an embodiment of the present invention;

[0050] Figure 11 Schematic diagram of the method for numerically modeling a two-dimensional discrete element sample of aggregate particles of arbitrary shape in an embodiment of the present invention, in which Matlab and discrete elements are combined to generate the real morphology of the aggregate. DETAILED DESCRIPTION

[0051] The following is a further detailed description of the two-dimensional arbitrary-shaped aggregate particle discrete element numerical specimen modeling method proposed by the present invention in conjunction with the accompanying drawings and specific embodiments. According to the following description, the advantages and features of the present invention will become clearer. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention. For the convenience of description, the "upper" and "lower" mentioned below are consistent with the upper and lower directions of the accompanying drawings, but this cannot be a limitation of the technical solution of the present invention.

[0052] The following combination Figures 1 to 11 , a detailed description is given of the two-dimensional arbitrary shape aggregate particle discrete element numerical specimen modeling method of the present invention.

[0053] Example 1: Construction of circular aggregate concrete discrete element numerical specimen.

[0054] Step S1: Generate a 50mm×50mm numerical sample in Matlab. The particle size range of the circular aggregate is 5mm-12.5mm, of which 10mm-12.5mm aggregate accounts for 0.5% of the numerical sample area, 8mm-10mm aggregate accounts for 8% of the numerical sample area, 6.3mm-8mm aggregate accounts for 16% of the numerical sample area, 5mm-6.3mm aggregate accounts for 6% of the numerical sample area, and 4mm-5mm aggregate accounts for 3.5% of the numerical sample area. The generated sample is as follows: Figure 4 shown.

[0055] Step S2: Group the interior of the circular aggregate particles and the rest of the numerical sample, and export the grouping information to provide a basis for the subsequent construction of circular aggregate particles in discrete elements.

[0056] Step S3, set the calculation area boundary: construct a rectangular calculation area equal to the size of the numerical sample: (x, y), where x∈[-W / 2, W / 2], y∈[-H / 2, H / 2]. In this embodiment, a 50mm×50mm rectangular sample is selected to generate, and small particles with a particle size of 0.05mm are generated in the rectangular sample. The total number of small particles is 251001.

[0057] Step S4: setting the contact model between small particles to a linear contact model, and setting relevant contact model parameters and particle physical property parameters to gradually eliminate the overlap between small spherical particles.

[0058] Step S5: Import the grouping information in step S2 into the numerical sample generated in step S3 to obtain a concrete numerical sample that can be used for discrete element simulation, such as Figure 5 shown.

[0059] Step S6: Set the contact model between aggregate particles to a contact bonding model, the contact model between matrix particles to a displacement softening model, the contact model between aggregate and matrix particles to a displacement softening model, and the contact model between the wall and particles to a linear contact model, and set relevant model parameters and physical parameters.

[0060] Example 2: Construction of discrete element numerical specimen of convex polygonal aggregate concrete.

[0061] Step a. Generate a 50 mm × 50 mm numerical specimen in Matlab. The particle size range of the convex polygonal aggregate used is 5 mm–12.5 mm, with 10 mm–12.5 mm aggregate accounting for 0.5% of the numerical specimen area, 8 mm–10 mm aggregate accounting for 8%, 6.3 mm–8 mm aggregate accounting for 16%, 5 mm–6.3 mm aggregate accounting for 6%, and 4 mm–5 mm aggregate accounting for 3.5%.

[0062] The generated samples are as follows Figure 6 As shown;

[0063] Step b. Grouping the interior of the aggregate particles and the rest of the numerical specimen, and exporting the grouping information to provide a basis for the subsequent construction of convex polygonal aggregate particles in discrete element methods;

[0064] Step c. Set the calculation area boundary: Construct a rectangular calculation area equal to the size of the numerical sample, generate a 50 mm × 50 mm rectangular sample, generate small particles with a particle size of 0.05 mm in the rectangular sample, and the total number of small particles is 251001.

[0065] Step d. Setting the contact model between small particles to a linear contact model, and setting relevant contact model parameters and particle physical property parameters, gradually eliminating the overlap between small spherical particles.

[0066] Step e. Import the grouping information in step b into the numerical sample generated in step c to obtain a concrete numerical sample that can be used for discrete element simulation, such as Figure 7 shown.

[0067] Step f. Set the contact model between aggregate particles to a contact bonding model, the contact model between matrix particles to a displacement softening model, the contact model between aggregate and matrix particles to a displacement softening model, the contact model between the wall and particles to a linear contact model, and set relevant model parameters and physical parameters.

[0068] Example 3: Construction of discrete element numerical specimens of irregular aggregate concrete:

[0069] Step 1: Generate a 50mm×50mm numerical sample in Matlab. The aggregate size range is 5mm-12.5mm, of which 10mm-12.5mm aggregate accounts for 0.5% of the numerical sample area, 8mm-10mm aggregate accounts for 8% of the numerical sample area, 6.3mm-8mm aggregate accounts for 16% of the numerical sample area, 5mm-6.3mm aggregate accounts for 6% of the numerical sample area, and 4mm-5mm aggregate accounts for 3.5% of the numerical sample area. The generated sample is as follows: Figure 8 shown.

[0070] Step 2: Group the interior of the aggregate particles and the rest of the numerical sample, and export the grouping information to provide a basis for the construction of aggregate particles in the subsequent discrete element.

[0071] Step 3: Set the calculation area boundary: Construct a rectangular calculation area equal to the size of the numerical sample, generate a 50mm×50mm rectangular sample, generate small particles with a particle size of 0.05mm in the rectangular sample, and the total number of small particles is 251001.

[0072] Step 4: Set the contact model between small particles to a linear contact model, and set the relevant contact model parameters and particle physical property parameters to gradually eliminate the overlap between small spherical particles.

[0073] Step 5: Import the grouping information in step 2 into the numerical sample generated in step 3 to obtain a concrete numerical sample that can be used for discrete element simulation, such as Figure 9 As shown;

[0074] Step 6: Set the contact model between aggregate particles to the contact bonding model, the contact model between matrix particles to the displacement softening model, the contact model between aggregate and matrix particles to the displacement softening model, and the contact model between the wall and particles to the linear contact model, and set the relevant model parameters and physical parameters.

[0075] Example 4: Construction of concrete discrete element numerical specimens based on the actual aggregate morphology using X-ray CT scanning.

[0076] Step (1) Import the sample generated by X-ray CT into Matlab as Figure 10 As shown;

[0077] Step (2) groups the interior of the aggregate particles and the rest of the numerical sample, and exports the grouping information to provide a basis for the construction of aggregate particles in the subsequent discrete element method;

[0078] Step (3) Set the calculation area boundary: Construct a rectangular calculation area larger than the numerical sample size, generate a circular sample with a diameter of 170 mm, generate small particles with a particle size of 0.05 mm in the rectangular sample, and the total number of small particles is 2910411.

[0079] Step (4) setting the contact model between small particles to a linear contact model, and setting relevant contact model parameters and particle physical property parameters to gradually eliminate the overlap between small spherical particles;

[0080] Step (5) imports the grouping information in step (2) into the numerical sample generated in step (3), and then deletes the redundant balls to obtain a circular concrete numerical sample that can be used for discrete element simulation. Figure 11 As shown;

[0081] Step (6) sets the contact model between aggregate particles to a contact bonding model, the contact model between matrix particles to a displacement softening model, the contact model between aggregate and matrix particles to a displacement softening model, the contact model between the wall and particles to a linear contact model, and sets relevant model parameters and physical parameters.

[0082] The above description is only a description of the preferred embodiments of the present invention and does not limit the scope of the present invention. Any changes and modifications made by ordinary technicians in the field of the present invention based on the above disclosure shall fall within the scope of protection of the claims.

Claims

1. A two-dimensional discrete element numerical specimen modeling method for arbitrary-shaped aggregate particles, characterized in that: The steps include: Step S1: constructing a calculation region equal to the size of the numerical sample in Matlab, and randomly generating two-dimensional arbitrary-shaped aggregate particles of a certain grade within this region, wherein the true morphology information of the two-dimensional arbitrary-shaped aggregate particles is obtained by X-ray CT scanning, and the two-dimensional arbitrary-shaped aggregate particles are circular aggregate particles, convex polygonal aggregate particles, or irregular aggregate particles; Step S2: Group the information in the calculation area of ​​step S1 into groups of aggregates and other areas into one group, and export the group information. The steps for grouping the real morphology information of the aggregates are as follows: Step t1, import the aggregate image obtained by X-ray CT scanning into Matlab; Step t2: Binarize the imported image to obtain a 0,1 matrix, group the aggregate and matrix, and export the grouping information; Step S3: Based on the specified porosity, a numerical specimen region (x, y) of a single particle shape is generated in the discrete element software, where x∈[-W / 2, W / 2] and y∈[-H / 2, H / 2]. Subsequently, the grouping information in step S2 is imported to construct the aggregate region and the matrix region, i.e., to construct the discrete element numerical simulation specimen. The specific steps are as follows: Step p1: traverse the balls in the generated area and obtain the coordinate information of all balls; Step p2: Move the coordinates of the ball to obtain new coordinate information; Step p3: Obtain matrix information of the balls in the generated area, determine whether the balls belong to aggregate or matrix, group them, and finally complete the grouping; The ratio of the numerical sample size to the radius of the generated single-shaped particle sphere is greater than or equal to 80; Step S4, assigning a multiple contact model: setting the contact model between aggregate particles to a contact bonding model, setting the contact model between matrix particles to a displacement softening model, setting the contact model between aggregate and matrix particles to a displacement softening model, setting the contact model between the wall and particles to a linear contact model, and setting relevant model parameters and physical parameters; the linear model parameters include the effective Young's modulus, contact stiffness ratio, and friction coefficient; the contact bonding model parameters include the effective Young's modulus of inter-particle bonding, inter-particle bonding cohesion, inter-particle bonding tensile strength, and inter-particle bonding internal friction angle; the displacement softening model parameters include the inter-particle tangential stiffness, the granule normal stiffness, the inter-particle tangential strength, the inter-particle normal strength, the inter-particle bonding internal friction angle, the maximum displacement of the normal failure point, and the maximum displacement of the tangential failure point; and the physical parameters include the particle density and gravitational acceleration.

2. The modeling method according to claim 1, characterized in that The step of generating round aggregate particles comprises: Step k1, randomly generating random circles of circular aggregate particle sizes within the sample area; Step k2: determine whether the newly generated aggregate overlaps with the already generated aggregate. If not, generate it; otherwise, re-place it. Step k3: When the area of ​​the random circle reaches the area of ​​the aggregate of this level, exit and generate the next level of aggregate.

3. The modeling method according to claim 1, characterized in that The step of generating convex polygonal aggregate particles comprises: Step d1, setting the volume fraction of polygonal aggregate particles, the minimum aggregate particle size, and the maximum aggregate particle size; Step d2: Generate a random circle with a diameter close to the aggregate particle size. Based on this circle, randomly generate an n-gon inscribed in the circle. Use the Larven formula to determine the area of ​​the convex polygonal aggregate. When the area of ​​the convex polygonal aggregate is smaller than the area of ​​the corresponding circular aggregate, perform aggregate extension. Step d3: determine whether the newly generated aggregate overlaps with the already generated aggregate. If not, it will be generated; otherwise, it will be re-added; Step d4: Calculate the area of ​​the convex polygon aggregate. If the area reaches the corresponding level of aggregate, exit and generate the next level of aggregate.

4. The modeling method according to claim 1, characterized in that The irregular aggregate particle generation step comprises: Step g1: randomly generate an ellipse with a diameter close to the size of the irregular aggregate particles, and perform expansion and contraction deformation on the ellipse to obtain a single irregular aggregate; Step g2: randomly generate a point in the simulation area and determine whether it is outside the ellipse covered by all generated particles; if it is outside, generate an ellipse centered on this point and then deform it to obtain an irregular aggregate; otherwise, regenerate a random point; Step g3: Calculate the area of ​​irregular aggregate. If the area reaches the corresponding grade of aggregate, exit and generate the next grade of aggregate.

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