Refractory material multi-particle dispersion distribution RVE model
By using a random sequence adsorption algorithm in finite element software to generate a randomly distributed RVE model of refractory materials and applying periodic boundary conditions, the problem that the prior art is difficult to describe the nonlinear mechanical behavior of refractory materials is solved, and the accurate simulation of the thermal stress state of refractory materials and theoretical support for material design is achieved.
Patent Information
- Application Number
- CN202411630105.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-15
- Publication Date
- 2025-02-28
AI Technical Summary
The prior art is difficult to effectively describe the nonlinear mechanical behavior of refractory materials, making it difficult to accurately simulate their thermal stress state in the use environment.
Random sequence adsorption algorithm (RSA) is used to generate a random distribution RVE model of circular particles in refractory materials in finite element software, and the finite element analysis process is simplified by periodic boundary conditions.
Effective simulation of the nonlinear mechanical behavior of refractory materials is realized, the finite element analysis process is simplified, and theoretical support is provided for material design and optimization.
Smart Images
Figure CN119541729A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of numerical simulation of refractory materials, in particular to a RVE model of multi-particle dispersion distribution of refractory materials. Background Art
[0002] Energy conservation and emission reduction is an important foundation for sustainable development in contemporary society, a common social responsibility of the government, enterprises and the public, and an important driving force for scientific and technological innovation. It plays an important role in society. High temperature industry is a key energy conservation area in the country. The energy consumption in this area accounts for about 50% of the total energy consumption, and it is the top priority of energy conservation and emission reduction. High temperature industry involves industries such as steel, non-ferrous metals, and refractory materials, which consume a lot of energy and have great energy-saving potential.
[0003] As for the refractory industry, refractory is a high-temperature resistant composite material, which is an indispensable basic material for manufacturing furnace linings and high-temperature container parts. With the advent of the low-carbon economy, refractory materials as furnace linings play a very important role in energy conservation and emission reduction of industrial furnaces. The harsh use environment and complex working conditions of refractory materials seriously restrict the service life of refractory materials. Therefore, it is particularly important to improve the service life of refractory materials and reduce the loss of refractory materials in industrial production. The macroscopic failure of refractory materials is usually caused by the accumulation and evolution of damage to their mesostructure. It is of great significance to study the influence of their mesoscopic damage forms on macroscopic mechanical behavior.
[0004] At present, researchers at home and abroad have developed thermoelastic models, thermoelastic-plastic models, virtual crack models, viscoplastic models considering damage and phase transformation, and neural network models to characterize the constitutive relationship of refractory materials using methods such as elastoplastic mechanics, damage mechanics, fracture mechanics, and neural network technology. However, these models are either too simple to fully describe all factors affecting the nonlinear behavior of refractory materials, or too complex. The material parameters involved in the model must be obtained through a large number of experiments, and these parameters are not universal. Materials with different compositions and different manufacturing processes must be obtained through repeated experiments, making the model very difficult to implement. Therefore, there is still a lack of a relatively simple and universally applicable constitutive relationship model to describe the nonlinear mechanical behavior of complex refractory materials, which makes it very difficult to accurately simulate the thermal stress state of refractory materials in the use environment.
[0005] In view of this, it is necessary to develop a multi-particle dispersed distribution RVE model of refractory materials to study the nonlinear mechanical behavior of refractory materials in order to solve the above problems. Summary of the invention
[0006] (I) Technical solution
[0007] The present invention provides the following technical solution: a refractory multi-particle dispersion distribution RVE model, comprising the following steps:
[0008] S1. Use the random sequence adsorption algorithm RSA to generate the position coordinates of particles of predetermined size in a given numerical region, and determine whether the new particles overlap or interfere with existing particles.
[0009] S2. Through the secondary development of finite element software, based on the RSA algorithm, a mesoscopic RVE model of refractory round particles randomly distributed in the matrix phase was constructed using Python programming.
[0010] S3. According to the periodic boundary conditions, using the displacement continuity conditions and stress continuity conditions, combined with the principle of virtual work, the expression of the external load that should be applied to the RVE model is derived, and it is deduced that the position of the constrained node can be determined by the position of the constraining node, and the external load on the model can be equivalent to a concentrated load applied on the vertex.
[0011] Preferably, in step S1, the basic principle of RSA is to generate the position coordinates of particles of predetermined size one by one within a given numerical range. When a new particle is added, it is determined whether its position and size meet the preset conditions, that is, whether it overlaps or interferes with the existing particles. If there is overlap or interference, the position and orientation of the current particle are regenerated until the newly generated particle does not overlap or interfere with the previously existing particles. The position and orientation of the particle are accepted as the existing particle. This method is used to establish a three-dimensional multi-reinforcement RVE model containing a specific number of randomly distributed positions and orientations.
[0012] Preferably, in step S2, the method for constructing the RVE model comprises the following steps:
[0013] S21. According to the RVE schematic diagram of the composite material and the characteristic that the particle reinforcement phase of the refractory material is randomly and irregularly distributed, the RVE numerical model of multi-particle random distribution morphology is selected as the research object.
[0014] S22. Through the secondary development of the nonlinear finite element software ABAQUS, based on the random sequence adsorption algorithm, the contact behavior between particles and the matrix was cyclically added using the Python language, and a microscopic RVE model of refractory materials with multi-particle random distribution was established.
[0015] Preferably, in step S22, the side length of the RVE model is l=30 mm, the radius of the circular particle is r=2.0 mm, the number of particles n=20, and the volume fraction occupied by the particles is ≈28%.
[0016] Preferably, in step S3, the method for implementing the periodic boundary condition comprises the following steps:
[0017] S31. According to the content of the periodic boundary conditions, the displacements and stresses of the corresponding nodes on the relative boundaries of the RVE model must always remain consistent.
[0018] S32. Taking the two-dimensional RVE model as an example, according to the displacement continuity condition, the constraint equation on the relative boundary can be obtained:
[0019] The nodes corresponding to the upper and lower boundaries satisfy:
[0020]
[0021] The nodes corresponding to the right and left boundaries satisfy:
[0022]
[0023] Where: Vertex A i The displacement vector of , (i=0, 1, 2). is the RVE boundary i The displacement vector of , (i=0, 1, 2, 3).
[0024] S33. According to the principle of virtual work, the expression of the external load to be applied to the RVE model is:
[0025]
[0026] Where: The external force on the boundary l i The distributed load on l is the Cauchy stress tensor on the boundary l, n l is the unit vector of the external normal on the boundary l.
[0027] S34. According to the continuous stress condition, the stress vectors on the opposite edges of the RVE model are equal in magnitude and opposite in direction, that is, the stresses of the corresponding nodes on the opposite edges must satisfy the following relationship:
[0028]
[0029] S35. Combining the expressions in steps S33 and S34, we can get
[0030] Preferably, in step S32, according to the constraint equation, the displacement of the constrained node can be determined by the displacement of the constraining node.
[0031] Preferably, in step S33, according to the expression, the external load on the RVE model can be equivalent to a concentrated load applied on the vertex.
[0032] Preferably, in step S3, the realization of the periodic boundary conditions mainly includes two aspects: displacement continuity conditions and stress continuity conditions, which are realized by adding linear constraint equations and natural boundary conditions.
[0033] (II) Beneficial effects
[0034] Compared with the prior art, the present invention provides a refractory multi-particle dispersed distribution RVE model, which has the following beneficial effects:
[0035] 1. The multi-particle dispersed distribution RVE model of refractory materials implements the random sequence adsorption RSA algorithm in the finite element software, and uses Python to establish the random distribution RVE model of round particles in refractory materials. This model can effectively simulate the microstructure of composite materials such as refractory materials, and associate it with macroscopic properties, providing theoretical support for material design and optimization.
[0036] 2. The RVE model of multi-particle dispersed distribution of refractory materials imposes periodic boundary conditions, including displacement continuity conditions and stress continuity conditions, on the RVE model of multi-particle dispersed distribution of refractory materials. The external load acting on the RVE model can be determined and equivalent to the concentrated load applied on the vertex, thereby simplifying the finite element analysis process.
[0037] 3. The RVE model of multi-particle dispersed distribution of refractory materials can be used to study the nonlinear mechanical behavior of refractory materials, provide an effective theoretical basis for the microstructure analysis and macroscopic performance prediction of refractory materials and other composite materials, and provide an important reference for material design and optimization. It has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS
[0038] Figure 1 A schematic diagram of a typical composite material RVE of the present invention;
[0039] Figure 2 It is the flow chart of RSA algorithm of the present invention;
[0040] Figure 3 It is a schematic diagram of the mesoscopic RVE model of the multi-particle dispersed distribution of the refractory material of the present invention;
[0041] Figure 4 It is a geometrical schematic diagram of the two-dimensional RVE model of the multi-particle dispersed distribution of the refractory material of the present invention. DETAILED DESCRIPTION
[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0043] See also Figure 1-4 The present invention provides a technical solution: a refractory multi-particle dispersion distribution RVE model, comprising the following steps:
[0044] S1. Use the random sequence adsorption algorithm RSA to generate the position coordinates of particles of predetermined size in a given numerical region, and determine whether the new particles overlap or interfere with existing particles.
[0045] For composite materials with dispersed particles such as refractory materials, it can be approximated that their interior is composed of a periodic microstructure, which does not affect their macroscopic mechanical properties. Therefore, representative volume units are used to analyze such composite materials with random distribution of reinforcement phases, and their macroscopic properties are studied based on the microstructure. A typical RVE schematic diagram of a composite material is shown in Figure 2. Figure 1 As shown, Figure 1 (a) is a macroscopic schematic diagram of the composite material. Figure 1 (b) is a schematic diagram of single particle inclusion RVE. Figure 1 (c) is a schematic diagram of multi-particle inclusion RVE. In the refractory, the particle reinforcement phase is randomly and irregularly distributed. Therefore, the single-particle inclusion RVE model is not suitable as a mesoscopic model of refractory to study its overall macroscopic mechanical behavior. Figure 1 The RVE numerical model with multi-particle random distribution morphology shown in (c) is used to simulate and analyze the nonlinear mechanical behavior of particle-reinforced refractory materials.
[0046] The basic principle of the random sequence adsorption algorithm (RSA) is to generate the position coordinates of particles of predetermined sizes one by one in a given numerical region. When a new particle is added, its position and size are judged to see whether they meet the preset conditions, that is, whether they overlap or interfere with existing particles. If there is overlap or interference, the position and orientation of the current particle are regenerated until the newly generated particle does not overlap or interfere with the previously existing particles, and the position and orientation of the particle are accepted as the existing particle. When the reinforcement reaches a certain volume content, the existing randomly distributed reinforcements occupy too much space, and the remaining gaps cannot accommodate new complete reinforcement particles, and the reinforcement in the RVE reaches saturation. The algorithm flow chart is as follows: Figure 2 This method can be used to establish a three-dimensional RVE model with a specific number of randomly distributed reinforcements in different positions and orientations.
[0047] S2. Through the secondary development of finite element software, based on the RSA algorithm, a mesoscopic RVE model of refractory round particles randomly distributed in the matrix phase was constructed using Python programming.
[0048] In step S2, the method for constructing the RVE model includes the following steps:
[0049] S21. According to the RVE schematic diagram of the composite material and the characteristic that the particle reinforcement phase of the refractory material is randomly and irregularly distributed, the RVE numerical model of multi-particle random distribution morphology is selected as the research object.
[0050] S22. Through the secondary development of the nonlinear finite element software ABAQUS, based on the random sequence adsorption algorithm, the contact behavior between particles and the matrix was cyclically added using the Python language, and a microscopic RVE model of refractory materials with multi-particle random distribution was established.
[0051] The side length of the RVE model is l = 30 mm, the radius of the circular particle is r = 2.0 mm, the number of particles is n = 20, and the volume fraction occupied by the particles is ≈28%.
[0052] By establishing the microscopic RVE model of refractory materials, the finite element analysis process can be simplified, the microstructure of refractory materials can be correlated with their macroscopic properties, and an effective theoretical basis can be provided for the microstructure analysis and macroscopic property prediction of composite materials such as refractory materials.
[0053] S3. According to the periodic boundary conditions, using the displacement continuity conditions and stress continuity conditions, combined with the principle of virtual work, the expression of the external load that should be applied to the RVE model is derived, and it is deduced that the position of the constrained node can be determined by the position of the constraining node, and the external load on the model can be equivalent to a concentrated load applied on the vertex.
[0054] Periodic boundary conditions mainly include stress continuity conditions and displacement continuity conditions. In the finite element analysis process, the stress boundary conditions of the model can be automatically satisfied based on the principle of minimum potential energy. Such boundary conditions are also called natural boundary conditions. The periodic displacement boundary conditions of the interface are achieved by adding linear constraint equations to the corresponding nodes on the parallel opposite faces or edges of the RVE model.
[0055] In order to study the specific implementation method of the periodic boundary conditions of the RVE model in the finite element software, a geometric diagram of the two-dimensional RVE model is made, as shown in the figure. Figure 4As shown. Let the lengths of the quadrilateral be l, l1, l2, l3, l4, corresponding to the four boundaries of RVE at x=0, x=L, y=0, y=L, respectively. A0, A1, A2, A3 correspond to the four vertices of RVE, and their coordinates are A0(0,0), A1(l,0), A2(0,l) and A3(l,l) respectively.
[0056] According to the displacement continuity condition, the shape of the opposite boundary of the RVE model should always be consistent. At all nodes corresponding to the upper and lower boundaries of the model, the following conditions should be satisfied:
[0057]
[0058] At all nodes corresponding to the right and left boundaries of the model, the following should be satisfied:
[0059]
[0060] in, Vertex A i The displacement vector of , (i=0, 1, 2).
[0061] use Represents the RVE boundary l i The displacement vector of , the above constraint equation can be simplified to:
[0062]
[0063] Therefore, the nodes on the boundaries l1 and l3 can be called constraining nodes, the nodes on the boundaries l2 and l4 (excluding vertices) can be called constrained nodes, and the displacement vectors of the constrained nodes are determined by the displacement vectors of the constraining nodes.
[0064] According to the principle of virtual work, the expression of the external load that should be applied to the RVE model is:
[0065]
[0066] Where: The external force on the boundary l i The distributed load on l is the Cauchy stress tensor on the boundary l, n l is the unit vector of the external normal on the boundary l.
[0067] According to the continuous stress condition, the stress vectors on the opposite boundaries of the RVE model are equal in magnitude and opposite in direction, that is, the stresses of the corresponding nodes on the opposite boundaries must satisfy the following relationship:
[0068]
[0069] Simplifying and combining the above expressions, we can get
[0070] From the above derivation, it can be seen that after adding periodic boundary conditions to the RVE model, the position of the constrained node can be determined by the position of the constrained node, and the external load on the model can be equivalent to the concentrated load applied to the vertex. The main function of the realization of periodic boundary conditions is to link the microscopic behavior of refractory materials with macroscopic effective performance, ensure that the displacement and stress on the boundaries of adjacent RVE models remain consistent, simplify the finite element analysis process, and improve the calculation efficiency.
[0071] The RVE model of multi-particle dispersed distribution of refractory materials is developed through secondary development of finite element software, using Python language programming, and based on the RSA algorithm, a microscopic RVE model of refractory circular particles randomly distributed in the matrix phase is established. In order to ensure that the displacement and stress fields between adjacent RVE models remain continuous and coordinated, the present invention proposes a method for implementing periodic boundary conditions. By adding linear constraint equations to the corresponding nodes on the parallel opposite faces or edges of the RVE model, the displacement continuity condition is achieved. At the same time, based on the stress continuity condition and the principle of virtual work, an equivalent expression of the RVE model under external load is derived. The RVE model can be used to study the nonlinear mechanical behavior of refractory materials, provide theoretical support for optimizing the microstructure design of refractory materials, and has high application value.
[0072] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.
Claims
1. A refractory multi-particle dispersion distribution RVE model, characterized in that: The following steps are involved: S1. Using a random sequence adsorption algorithm (RSA) to generate position coordinates of particles of predetermined size in a given numerical region, and determining whether the new particles overlap or interfere with existing particles; S2. Through the secondary development of finite element software, based on the RSA algorithm, the mesoscopic RVE model of refractory round particles randomly distributed in the matrix phase was constructed using Python programming; S3. According to the periodic boundary conditions, using the displacement continuity conditions and stress continuity conditions, combined with the principle of virtual work, the expression of the external load that should be applied to the RVE model is derived, and it is deduced that the position of the constrained node can be determined by the position of the constraining node, and the external load on the model can be equivalent to a concentrated load applied on the vertex.
2. A refractory multi-particle dispersion distribution RVE model according to claim 1, characterized in that: In step S1, the basic principle of RSA is to generate the position coordinates of particles of predetermined sizes one by one in a given numerical range. When a new particle is added, its position and size are judged to see whether they meet the preset conditions, that is, whether they overlap or interfere with the existing particles. If there is overlap or interference, the position and orientation of the current particle are regenerated until the newly generated particle does not overlap or interfere with the previously existing particles. The position and orientation of the particle are then accepted as the existing particles. This method is used to establish a three-dimensional multi-reinforcement RVE model containing a specific number of randomly distributed positions and orientations.
3. A refractory multi-particle dispersion distribution RVE model according to claim 1, characterized in that: In step S2, the method for constructing the RVE model includes the following steps: S21. According to the RVE schematic diagram of composite materials and the characteristics of random and irregular distribution of refractory particle reinforcement phase, the RVE numerical model of multi-particle random distribution morphology is selected as the research object; S22. Through the secondary development of the nonlinear finite element software ABAQUS, based on the random sequence adsorption algorithm, the contact behavior between particles and the matrix was cyclically added using the Python language, and a microscopic RVE model of refractory materials with multi-particle random distribution was established.
4. A refractory multi-particle dispersion distribution RVE model according to claim 3, characterized in that: In step S22, the side length of the RVE model is l=30 mm, the radius of the circular particle is r=2.0 mm, the number of particles is n=20, and the volume fraction of the particles is ≈28%.
5. A refractory multi-particle dispersion distribution RVE model according to claim 1, characterized in that: In step S3, the method for implementing the periodic boundary condition comprises the following steps: S31. According to the content of the periodic boundary conditions, the displacements and stresses of the corresponding nodes on the relative boundaries of the RVE model must always remain consistent; S32. Taking the two-dimensional RVE model as an example, according to the displacement continuity condition, the constraint equation on the relative boundary can be obtained: The nodes corresponding to the upper and lower boundaries satisfy: The nodes corresponding to the right and left boundaries satisfy: Where: Vertex A i The displacement vector of , (i = 0, 1, 2); is the RVE boundary i The displacement vector of , (i = 0, 1, 2, 3); S33. According to the principle of virtual work, the expression of the external load to be applied to the RVE model is: Where: The external force on the boundary l i The distributed load on l is the Cauchy stress tensor on the boundary l, n l is the external normal unit vector on the boundary l; S34. According to the continuous stress condition, the stress vectors on the opposite edges of the RVE model are equal in magnitude and opposite in direction, that is, the stresses of the corresponding nodes on the opposite edges must satisfy the following relationship: S35. Combining the expressions in steps S33 and S34, we can get p l1 =p l3 =0.
6. A refractory multi-particle dispersion distribution RVE model according to claim 5, characterized in that: In the step S32, according to the constraint equation, the displacement of the constrained node can be determined by the displacement of the constraining node.
7. A refractory multi-particle dispersion distribution RVE model according to claim 5, characterized in that: In step S33, according to the expression, the external load on the RVE model can be equivalent to a concentrated load applied on the vertex.
8. A refractory multi-particle dispersion distribution RVE model according to claim 5, characterized in that: In step S3, the realization of the periodic boundary conditions mainly includes two aspects: displacement continuity conditions and stress continuity conditions, which are realized by adding linear constraint equations and natural boundary conditions.