CN114048663A - Method for generating two-dimensional high-volume-fraction earth-rock mixed material geometric model - Google Patents
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Abstract
The invention discloses a method for generating a two-dimensional high-volume-fraction earth-rock mixed material geometric model, which comprises the following steps of firstly, generating randomly distributed particles in any shape according to a grading curve; then carrying out Minkowski sum operation on the particles to control the minimum gap between adjacent particles; then, realizing the transition from particles to clusters by using an overlapping discrete element cluster method, and randomly placing the particles to a certain area; then, assigning a linear contact model, carrying out DEM simulation, separating overlapped clusters, and recording the initial position, displacement and rotation of the clusters; finally, the model is reconstructed based on the displacement and rotation information. The method is easy to obtain the theoretical maximum volume fraction of any particle shape, simultaneously solves the problem of boundary distribution of particles and the problem of contact between particles, and in addition, the periodic boundary condition in the DEM provides a simple implementation method for the periodic mesoscopic structure, so that the generated model is more in line with the actual situation, the reliability of the subsequent numerical method test research result can be improved, and the method has stronger application significance.
Description
Technical Field
The invention belongs to the technical field of research on mechanical parameters of inhomogeneous rock and soil materials, and particularly relates to a method for generating a two-dimensional high-volume-fraction earth-rock mixed material geometric model based on a Discrete Element Method (DEM) for generating a material numerical model test block.
Background
The method can well overcome the problems of difficult sampling, sample disturbance, large result discreteness, small test scale compared with the internal structure scale and the like in the research of real test parameters. However, the numerical method for researching the parameters of the heterogeneous material has a great problem: and (3) a model building problem, namely generating a numerical model test block meeting the numerical test requirements according to various internal structure parameters (such as aggregate gradation, aggregate shape and the like in concrete) of the accumulation body.
Currently, many scholars have made various attempts at modeling problems. The research is carried out through a cellular automaton model, and a two-dimensional random aggregate model is also used for constructing a geometric model of the concrete. Some scholars have also tried to create a three-dimensional particle model. However, the research in this aspect mainly focuses on the two-dimensional aspect, and great progress has been made, and more complex geometric models of particles can be generated. However, the existing method for generating the two-dimensional high-volume-fraction particle volume model has some disadvantages, when the high-volume-fraction aggregate model is generated, the efficiency is not high, the time consumption is long, the particles are not allowed to be placed on the boundary, and the accuracy of the modeling result is influenced.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a method for generating a geometric model of a two-dimensional high-volume-fraction earth-rock mixed material, and the generated particles can simulate the shape of aggregate particles more truly, so that a basis is provided for predicting the mechanical property of a particle-reinforced composite material by adopting a numerical simulation method.
The technical scheme is as follows: the invention provides a method for generating a two-dimensional high-volume-fraction earth-rock mixed material geometric model, which specifically comprises the following steps of:
(1) generating all particles according to the grading information;
(2) carrying out outward extension processing on the particles based on Minkowski theory, introducing processed particle coordinate data into discrete element software, replacing the particles with clusters, and setting specified domain and boundary conditions;
(3) DEM simulation is carried out in a linear contact model, and displacement rotation of the particles is obtained according to the DEM result;
(4) and positioning the final distribution of the particles based on the initial position coordinates and the rotary displacement condition of the particles, screening the particles positioned on the boundary by using a boundary positioning algorithm, copying the particles on the non-intersected boundary where the particles are positioned to generate the same particles, and generating a final earth-rock mixed material geometric model.
Further, the step (1) is realized as follows:
randomly generating particles with custom particle gradation and volume fraction in a preset coordinate area; the randomly generated custom particles are simulated by adopting Monte Carlo, the shape of the particles is a polygon, and the generation method is that (0,0) is taken as the center of a circle, a plurality of vertexes which are selected from a defined number are selected on the circumference by an appointed angle and radius, and the vertexes are connected according to the sequence; the random generation of the custom granule is to calculate all possible positions according to the specified separation distance dt before placing a particle; when a particle is placed, the point in the set will be removed and the position will be updated.
Further, the step (2) of extending the particle outwards based on minkowski and theory is implemented as follows:
the thickness shift operation after particle generation is achieved based on minkowski sum theory, the minkowski sum of the point sets a and B is determined as:
the thickness deviation operation is based on the vertex position coordinates of the particles after being put, the control is realized by setting different disc radiuses, a plurality of vertexes are added after outward deviation, a shell is added to the particles, and the minimum clearance between the aggregates is flexibly controlled by setting different disc radiuses.
Further, the boundary conditions in step (2) include a periodic boundary and a rigid boundary; periodic modeling applies periodic boundary conditions, and when the cluster centroid falls outside the model domain, the cluster is converted back to the other side of the model.
Further, the step (3) is realized as follows:
recording the centroid of the beam before DEM packing; after the DEM simulation is completed, obtaining the displacement and rotation of each beam; calculating the geometrical structure of the aggregate according to translation and rotation transformation; for beam contact, a linear model with normal stiffness and tangential stiffness is used; the contact forces in the normal and shear directions are:
in the formula (I), the compound is shown in the specification,
for normal contact force, KnFor normal secant contact stiffness, UnTotal normal displacement, niIs a vector of the normal vector of the unit,
for increase in shear stress, ksIn order to be able to achieve a shear stiffness,
is the shear displacement increment;
the friction parameter, which affects the rotation of the cluster, is set to 0 in the simulation; the rotation of the cluster is fixed if the clusters are distributed in a certain direction.
Further, the final distribution of the particles in step (4) includes the X, Y coordinates and vertex order of each vertex of the polygon relative to (0, 0).
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the invention greatly improves the upper limit of the volume fraction of the generative model and the generation efficiency, simultaneously solves the boundary distribution problem of particles and the contact problem between the particles, ensures that the generated model is more in line with the actual situation, can improve the reliability of the subsequent numerical method test research result, and has stronger application significance.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic representation of Minkowski and theoretical applications;
FIG. 3 is an exemplary graph of a periodic boundary condition;
FIG. 4 is a schematic diagram of particle position transformation;
FIG. 5 is a schematic diagram of a process for generating a model according to the method of the present invention, wherein (a) is an initial particle distribution diagram; (b) converting the particles into a cluster profile; (c) distributing a DEM simulation result map; (d) the final particle profile.
Detailed Description
The invention will be further explained with reference to the drawings.
The invention provides a method for generating a two-dimensional high-volume-fraction earth-rock mixed material geometric model, which specifically comprises the following steps as shown in figure 1:
step 1: all particles are generated according to the grading information.
Randomly generating particles with custom particle gradation and volume fraction in a preset coordinate area. Particles of specified composition and volume fraction were randomly generated using a monte carlo simulation in a pre-defined 50 x 100 cartesian coordinate system region using Matlab. The random generation of the user-defined particles adopts Monte Carlo simulation, the shape of the particles is a polygon, and the generation method is that (0,0) is used as the center of a circle, a plurality of vertexes which are selected from a defined number are selected on the circumference by an appointed angle and radius, and the vertexes are connected according to the sequence. The random generation of custom granules is done by calculating all possible locations based on the specified separation distance dt before placing a particle. When a particle is placed, the points in the set will be removed and the possible locations will be updated. Therefore, the collision area between the new aggregate and the existing aggregate is reduced, and the subsequent DEM simulation performance is improved.
The area is generally a 50 x 100 coordinate area, a point is randomly selected from the area, the coordinate is added with the polygon coordinate of claim 4 to complete particle throwing, after the throwing is completed, the information of the point in the particle is deleted, the random point selection in the area is not participated, and the efficiency is improved.
Step 2: the particles are outwardly extended based on minkowski's sum theory, as shown in figure 2, the processed particle coordinate data is imported into discrete-element software, the particles are replaced by clusters and specified domain and boundary conditions are set.
The thickness shift operation after the particle generation is realized based on Minkowski theory, and a shell with a certain thickness is added on the outer surface of the particle; the minkowski sum of the point sets a and B is determined as:
the minimum clearance between the aggregates can be flexibly controlled by setting different disc radiuses. Thickness skew operation is based on the summit position coordinate of the granule after throwing in, through setting up different disc radius controls, increases a plurality of summits after outwards squinting, makes the granule increase a shell, prevents that follow-up calculation result from appearing the granule condition of contacting.
Introducing the processed aggregate particle shape distribution coordinate data into Flac 2D; and replacing the particles with discrete element clusters, and calculating a redistribution result of the particles in a preset periodic boundary structure by using a collision detection algorithm after a certain time.
The boundary conditions include periodic boundaries and rigid boundaries; periodically modeled region boundary conditions, when the cluster centroid falls outside the model domain, the cluster is converted back to the other side of the model, as shown in FIG. 3.
And step 3: DEM simulation is carried out in a linear contact model, and displacement rotation of the particles is obtained according to the DEM result; as shown in fig. 4.
Recording the centroid of the beam before DEM packing; after the DEM simulation is completed, obtaining the displacement and rotation of each beam; calculating the geometrical structure of the aggregate according to translation and rotation transformation; for cluster contacts, a linear model with normal and tangential stiffness was used. The contact forces in the normal and shear directions are:
in the formula (I), the compound is shown in the specification,
for normal contact force, KnFor normal secant contact stiffness, UnTotal normal displacement, niIs a vector of the normal vector of the unit,
for increase in shear stress, ksIn order to be able to achieve a shear stiffness,
in shear displacement increments.
The friction parameter affects the rotation of the cluster and can be set to 0 in the simulation. Furthermore, the rotation of the clusters is fixed if the clusters are distributed in a certain direction. When these parameters are set correctly, the simulation can be easily performed.
For the case that the aggregate cannot be located at the boundary, a rigid boundary is realized by using a wall in the PFC; the domain size should be slightly larger than the sample to ensure that aggregates cannot reach the domain boundary; otherwise, the rigid wall should be slightly smaller in size than the sample so that the focused beam will be confined to a designated area.
And 4, step 4: and positioning the final distribution of the particles based on the initial position coordinates and the rotary displacement conditions of the particles, screening the particles positioned at the boundary by using a boundary positioning algorithm, copying the particles on the non-intersected boundary where the particles are positioned to generate the same particles, and generating a final earth-rock mixed material model, as shown in fig. 5.
Recording the distribution coordinates and rotation conditions of the redistributed particles, and introducing data into Matlab; the position and direction of the particle distribution are adjusted within the coordinate region by importing data. And screening out the particles positioned on the boundary by using a boundary positioning algorithm, and copying the particles on the boundary where the particles are positioned and do not intersect to generate the same particles so as to generate a final earth-rock mixed material model.
Outputting the generated model as a geometric format file of corresponding aggregate particles, wherein the geometric format file is a DXF file, can be suitable as a template library file applied to various numerical tests, and can be a file with other geometric formats; for other numerical tests on the corresponding aggregate particles. The numerical model generated by the method has portability, and the corresponding numerical model can be obtained only by importing the file with the corresponding geometric format during the experiment.
The final distribution position information of the particles includes X, Y coordinates and vertex order of each vertex of the polygon with respect to (0, 0). The data from which the model output is generated should include the coordinates of the center of gravity of the multiple spheres, and the angles of rotation of the vertices relative to the center of gravity. And the final particle coordinate calculation method is characterized in that the coordinates relative to the origin point generated randomly by the particles are added with the corresponding gravity center coordinates derived after calculation, and then the coordinates after rotation are calculated by each vertex through the rotation angle. And judging whether the particles are positioned on the boundary or not through a particle position boundary detection algorithm, and if so, translating and cloning the particles to the opposite boundary of the boundary where the particles are positioned, so as to realize the arrangement of the boundary particles. The output data of the model has various formats, preferably the output is a DXF format file, and the generation mode is to generate self-coding codes of DXF.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (6)
1. A generation method of a two-dimensional high-volume-fraction earth-rock mixed material geometric model is characterized by comprising the following steps of:
(1) generating all particles according to the grading information;
(2) carrying out outward extension processing on the particles based on Minkowski theory, introducing processed particle coordinate data into discrete element software, replacing the particles with clusters, and setting specified domain and boundary conditions;
(3) DEM simulation is carried out in a linear contact model, and displacement rotation of the particles is obtained according to the DEM result;
(4) and positioning the final distribution of the particles based on the initial position coordinates and the rotary displacement condition of the particles, screening the particles positioned on the boundary by using a boundary positioning algorithm, copying the particles on the non-intersected boundary where the particles are positioned to generate the same particles, and generating a final earth-rock mixed material geometric model.
2. The generation method of the two-dimensional high volume fraction earth-rock mixture material geometric model according to claim 1, characterized in that the step (1) is realized by the following steps:
randomly generating particles with custom particle gradation and volume fraction in a preset coordinate area; the randomly generated custom particles are simulated by adopting Monte Carlo, the shape of the particles is a polygon, and the generation method is that (0,0) is taken as the center of a circle, a plurality of vertexes which are selected from a defined number are selected on the circumference by an appointed angle and radius, and the vertexes are connected according to the sequence; the random generation of the custom granule is to calculate all possible positions according to the specified separation distance dt before placing a particle; when a particle is placed, the point in the set will be removed and the position will be updated.
3. A method for generating a geometric model of two-dimensional high-volume-fraction earth-stone mixture material as claimed in claim 1, wherein the step (2) of extending the particles outwards based on minkowski's sum theory is implemented as follows:
the thickness shift operation after particle generation is achieved based on minkowski sum theory, the minkowski sum of the point sets a and B is determined as:
the thickness deviation operation is based on the vertex position coordinates of the particles after being put, the control is realized by setting different disc radiuses, a plurality of vertexes are added after outward deviation, a shell is added to the particles, and the minimum clearance between the aggregates is flexibly controlled by setting different disc radiuses.
4. The generation method of the geometric model of the two-dimensional high volume fraction earth-rock mixture material as claimed in claim 1, wherein the boundary conditions of the step (2) include periodic boundary and rigid boundary; periodic modeling applies periodic boundary conditions, and when the cluster centroid falls outside the model domain, the cluster is converted back to the other side of the model.
5. The generation method of the two-dimensional high volume fraction earth-rock mixture material geometric model according to claim 1, characterized in that the step (3) is realized by the following steps:
recording the centroid of the beam before DEM packing; after the DEM simulation is completed, obtaining the displacement and rotation of each beam; calculating the geometrical structure of the aggregate according to translation and rotation transformation; for beam contact, a linear model with normal stiffness and tangential stiffness is used; the contact forces in the normal and shear directions are:
in the formula, Fi nFor normal contact force, KnFor normal secant contact stiffness, UnTotal normal displacement, niIs a unit normal vector,. DELTA.Fi sFor increase in shear stress, ksIn order to be able to achieve a shear stiffness,
is the shear displacement increment;
the friction parameter, which affects the rotation of the cluster, is set to 0 in the simulation; the rotation of the cluster is fixed if the clusters are distributed in a certain direction.
6. The method for generating a geometric model of a two-dimensional high volume fraction earth-rock mixture material as claimed in claim 1, wherein the final distribution of the particles in step (4) includes the X, Y coordinates and vertex order of each vertex of the polygon relative to (0, 0).
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Cited By (4)
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| CN115270477A (en) * | 2022-08-01 | 2022-11-01 | 河海大学 | Method for simulating generation of pores in two-dimensional concrete by adopting discrete elements |
| CN115618702A (en) * | 2022-10-21 | 2023-01-17 | 河海大学 | Method for generating two-dimensional ultrahigh volume fraction hybrid rock numerical simulation model by adopting overlapped contact cutting algorithm |
| CN116071447A (en) * | 2022-12-19 | 2023-05-05 | 中山大学 | Method for generating two-dimensional particle filling model |
| CN116975969A (en) * | 2023-07-19 | 2023-10-31 | 武汉大学 | Method and system for real-time positioning and damage quantification of concrete dam crack expansion under explosive load |
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- 2021-09-30 CN CN202111160413.2A patent/CN114048663A/en active Pending
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115270477A (en) * | 2022-08-01 | 2022-11-01 | 河海大学 | Method for simulating generation of pores in two-dimensional concrete by adopting discrete elements |
| CN115618702A (en) * | 2022-10-21 | 2023-01-17 | 河海大学 | Method for generating two-dimensional ultrahigh volume fraction hybrid rock numerical simulation model by adopting overlapped contact cutting algorithm |
| CN115618702B (en) * | 2022-10-21 | 2023-05-09 | 河海大学 | Method for generating two-dimensional ultrahigh volume fraction mixed rock numerical simulation model by adopting overlapping contact cutting algorithm |
| CN116071447A (en) * | 2022-12-19 | 2023-05-05 | 中山大学 | Method for generating two-dimensional particle filling model |
| CN116071447B (en) * | 2022-12-19 | 2024-05-31 | 中山大学 | Method for generating two-dimensional particle filling model |
| CN116975969A (en) * | 2023-07-19 | 2023-10-31 | 武汉大学 | Method and system for real-time positioning and damage quantification of concrete dam crack expansion under explosive load |
| CN116975969B (en) * | 2023-07-19 | 2024-02-09 | 武汉大学 | Method and system for real-time positioning and damage quantification of concrete dam crack expansion under explosive load |
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