Finite element construction method of hollow sphere reinforced metal matrix composite foam
By constructing a finite element model of hollow sphere-reinforced composite foam using random variables and gravity stacking algorithms, the problems of experimental complexity and high cost were solved, and high-precision material property prediction and optimization design were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- LIAONING UNIVERSITY
- Filing Date
- 2026-04-21
- Publication Date
- 2026-05-29
AI Technical Summary
Existing technologies for preparing hollow sphere reinforced composite foam materials involve complex experimental procedures, high costs, difficulty in controlling multiple variables, and significant limitations in numerical simulation methods, making it impossible to efficiently optimize material properties.
Gaussian distributed particle size data were generated using a random variable algorithm. An interference-free geometric model was generated by combining gravity packing and intrusion discrimination algorithms. A hollow sphere reinforced composite foam material model was constructed using finite element software, and mesh generation and material property definition were performed.
It achieves efficient generation of models that truly reflect the microstructure of materials, improves the accuracy of mechanical property prediction, reduces experimental costs, and is applicable to various composite material systems and complex load conditions.
Smart Images
Figure CN122113525A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of composite material structure optimization design, specifically involving a finite element method for constructing hollow sphere reinforced metal matrix composite foam materials. Background Technology
[0002] In today's highly competitive industrial world, the demand for lightweight, impact-resistant materials is increasing across various sectors, from automotive and aerospace to armor protection. In the automotive and transportation sector, lightweight impact-resistant materials not only reduce vehicle weight and improve fuel efficiency but also enhance the cushioning and protective capabilities of body structure collision protection devices. In aerospace equipment, they serve as protective layers to shield personnel and components from hazardous stresses, improving the safety and lifespan of spacecraft. In defense equipment, lightweight impact-resistant materials enable military armored vehicles to possess better mobility and resistance to blast penetration loads, improving the lightweight nature of military vehicles and their self-protection capabilities in various environments. Therefore, advanced engineering materials, such as metal-based composite foams, are highly attractive as porous, lightweight materials.
[0003] Metal-based composite foam is a novel structural and functional porous composite material with a porous structure, composed of hollow particles and a metal matrix. It combines the high strength of the metal matrix with the excellent energy absorption capacity of foam materials. Compared to traditional metal foams, metal-based composite foams have more uniform and evenly distributed pore sizes, exhibiting better strength and stiffness, and improved energy absorption characteristics. Therefore, composite metal foam materials show uniform deformation under load and often possess superior mechanical, cushioning, and impact resistance properties. Hollow spheres, used as reinforcing particles in aluminum-based composite foams, can significantly improve the material's mechanical properties and energy absorption capacity. However, the reinforcing effect of hollow spheres is influenced by various factors, such as the volume fraction of hollow spheres, particle size, aspect ratio, and the type of metal matrix material. Experimental studies on aluminum-based composite foams with all different parameters typically require a large number of test samples and costly experimental equipment, with repetitive and cumbersome experimental operations. Furthermore, in actual experimental preparation, it is difficult to ensure that all variables are simultaneously satisfied under different experimental conditions, further increasing the difficulty and cost of the research.
[0004] Numerical simulation, as an effective research tool, can effectively solve the aforementioned problems. By establishing corresponding three-dimensional geometric models, the microstructural characteristics of porous composite foam materials can be accurately characterized, thereby analyzing the influence of different parameters on material properties. Numerical simulation not only allows for multiple parameter analyses in a short time, exploring performance changes under different hollow sphere parameters (such as volume fraction, particle size, and aspect ratio) and loading conditions, but also enables precise control of experimental variables, avoiding the complexity and uncertainty of experimental operations. Compared to experimental research, numerical simulation not only saves time and costs but also overcomes the limitations of experimental methods, providing theoretical support and practical guidance for the optimized design, production, and practical application of metal-based composite foams. Summary of the Invention
[0005] To address the challenge of modeling hollow sphere reinforced composite foam materials, this invention proposes a finite element method for constructing hollow sphere reinforced metal matrix composite foam materials. This method generates geometric models, generates meshes, assigns material properties, and performs finite element analysis. It can not only realistically reproduce the structure of composite foam materials but also improve the accuracy of mechanical property prediction, thereby providing technical support for the design and optimization of hollow sphere reinforced composite foam materials.
[0006] A finite element modeling method for hollow sphere reinforced metal matrix composite foam materials includes the following steps: Step 1: Based on the actual dimensions of the mechanical specimen of hollow sphere reinforced composite foam material, set the basic dimensions of the finite element material model and calculate the target volume fraction of hollow spheres in the composite foam material; Step 2: Generate particle size data that conforms to a Gaussian distribution using a random variable algorithm; Step 3: Generate the coordinates of the center of the spheres in a random distribution within a specified space using a random gravity stacking algorithm. Combine this with an intrusion detection algorithm to eliminate interference between the hollow spheres, thereby generating an interference-free geometric model and finally obtaining the hollow sphere distribution data. Step 4: Based on the hollow sphere distribution data in Step 3, generate a hollow sphere-reinforced composite foam model using the Python script interface of the finite element software; Step 5: Based on the composite foam model generated in Step 4, define the corresponding material properties of the hollow spheres and metal matrix according to user requirements, select the mesh element type and complete the mesh generation, and define the model nodes, element sets and surface sets so that the model can accurately reflect the mechanical behavior characteristics of the composite foam material.
[0007] The basic dimensions of the finite element material model include the length, width, and height of the composite foam sample, as well as the outer diameter and wall thickness of the hollow sphere.
[0008] The random variable algorithm described above generates independent Gaussian random variables using the Box-Muller transformation.
[0009] The aforementioned random gravity stacking algorithm utilizes pseudo-random variables generated by the Monte Carlo random simulation method as corresponding random sphere center coordinates. It stacks spheres layer by layer from the bottom up, setting boundary constraints to ensure that each hollow sphere does not exceed the model boundary. The sphere center coordinates (x, y, z) satisfy x∈(0+Ri, L-Ri), y∈(0+Ri, W-Ri), z∈(0+Ri, H-Ri), where L, W, H, and Ri represent the length, width, height, and outer diameter of the hollow spheres of the composite foam model, respectively. Combined with the target volume fraction of the hollow spheres, the number of stacking layers is iteratively adjusted to ensure that the composite foam model meets both randomness and volume fraction requirements.
[0010] In the aforementioned random gravity stacking algorithm, the volume fraction of hollow spheres in the stacking process ranges from 30% to 60%.
[0011] The intrusion detection algorithm detects the distance between two hollow spheres and determines whether the geometric models of the two hollow spheres overlap. If there is an overlap, the coordinates of the sphere center are discarded and a new sphere center position is generated.
[0012] The hollow sphere distribution data includes hollow sphere diameter data and hollow sphere center coordinate data.
[0013] The hollow sphere reinforced composite foam model consists of a hollow sphere model and a corresponding matching matrix model, which are combined through assembly and Boolean operations to generate a hollow sphere reinforced metal matrix composite foam model.
[0014] The significant advantages and beneficial effects of this invention are as follows: 1. This invention provides a finite element modeling method for hollow sphere-reinforced metal-based composite foam materials. This method, specifically designed for metal-based composite foam materials, can efficiently generate geometric models that closely approximate the microstructure of the actual material. This modeling method not only fully considers the random distribution and particle size variation of the hollow spheres but also allows for flexible adjustment of the volume fraction, spatial arrangement, and wall thickness parameters of the hollow spheres, providing a highly reliable model foundation for the mechanical property analysis of composite foam materials.
[0015] 2. This invention uses a random variable algorithm to generate particle size data that conforms to a Gaussian distribution. This method scientifically simulates the sieving statistical characteristics of hollow spheres in actual experiments, significantly improving the realism and rationality of the geometric model. By precisely controlling the particle size distribution range and concentration trend, it effectively improves the accuracy of mechanical behavior prediction in subsequent finite element simulations.
[0016] 3. This invention innovatively employs a gravity-based stacking algorithm and an intrusion detection algorithm to highly replicate the natural stacking and filling process of hollow spheres in composite foam preparation during the modeling process. This method not only effectively avoids the overlapping and interference problems between hollow spheres during model generation but also ensures the randomness, uniformity, and stability of the final model's spatial distribution. The established model strictly follows actual physical laws, thus more realistically reflecting the structural characteristics of composite foam materials and further improving the reliability of the model's mechanical response prediction under various load conditions.
[0017] 4. The finite element model constructed by this invention has good versatility and wide adaptability. The parameterization characteristics of this model are applicable to a variety of composite material systems, including ceramic hollow sphere / metal matrix composite foam, metal hollow sphere / metal matrix composite foam, ceramic hollow sphere / epoxy resin matrix composite foam, etc. At the same time, this model can be directly applied to the simulation of various complex working conditions such as static load, impact load and bending load. Attached Figure Description
[0018] Figure 1 This is a flowchart illustrating the modeling process of the present invention; Figure 2 The particle size distribution and cumulative distribution probability in the hollow sphere particle size data generated by the random variable algorithm of this invention; Figure 3 The hollow sphere model generated from the hollow sphere distribution data of this invention; Figure 4 The hollow sphere reinforced composite foam model constructed for this invention is shown in the figure, where (a) is the matrix model, (b) is the hollow sphere model, and (c) is the hollow sphere reinforced composite foam model. Figure 5 This is a schematic diagram of the mesh generation for the hollow sphere-reinforced composite foam model of the present invention; Figure 6 This is a schematic diagram of the boundary conditions and load application of the hollow sphere reinforced composite foam model of the present invention. Detailed Implementation
[0019] A finite element modeling method for hollow sphere-reinforced composite foam materials based on a stochastic gravity stacking algorithm includes the following steps: Step 1: Based on the actual dimensions of the hollow sphere reinforced composite foam material mechanical specimen, set the basic dimensions of the finite element material model. The basic dimensions of the finite element material model include the length, width, and height of the composite foam specimen, as well as the outer diameter and wall thickness of the hollow spheres. Calculate the target volume fraction of the hollow spheres in the composite foam material.
[0020] Step Two: Generate hollow sphere particle size data conforming to a Gaussian distribution using a random variable algorithm based on Box-Muller transform. Specifically, taking a hollow sphere with a nominal diameter of 3.55 mm as an example, 500 hollow sphere particle size data were generated. Statistical analysis shows that the particle size distribution conforms to a Gaussian distribution, such as... Figure 2 As shown, the sizes of the hollow spheres all range from 3.40 mm to 3.70 mm, with hollow spheres between 3.50 mm and 3.60 mm accounting for 60% of the total. This particle size distribution characteristic indicates that the generated hollow spheres have good particle size concentration and conform to the dimensional deviations commonly seen in actual manufacturing processes.
[0021] Step 3: A randomized distribution of sphere center coordinates within a specified space is generated using a random gravity stacking algorithm. This, combined with an intrusion detection algorithm, eliminates interference between hollow spheres, thereby generating an interference-free geometric model and ultimately obtaining the hollow sphere distribution data. Specifically: The stochastic gravity stacking algorithm utilizes pseudo-random variables generated by Monte Carlo stochastic simulation as the corresponding random sphere center coordinates. Boundary constraints are set to ensure that each hollow sphere does not exceed the model boundary. The sphere center coordinates (x, y, z) satisfy x∈(0+Ri, L-Ri), y∈(0+Ri, W-Ri), z∈(0+Ri, H-Ri), where L, W, H, and Ri represent the length, width, height, and outer diameter of the hollow spheres in the composite foam model, respectively. An intrusion detection algorithm is also used to detect the distance between two hollow spheres, determining whether their geometric models overlap. If overlap exists, the sphere center coordinates are discarded, and a new sphere center position is generated. Stacking begins from the bottom layer and proceeds upwards, iteratively adjusting the number of stacking layers based on the target volume fraction of the hollow spheres. This ensures the composite foam model meets both randomness and volume fraction requirements, ultimately yielding the hollow sphere distribution data. In the random gravity stacking algorithm, the volume fraction of hollow spheres in the stacking is between 30% and 60%, and the hollow sphere distribution data includes hollow sphere diameter data and hollow sphere center coordinate data. Figure 3 The hollow sphere model is generated by the random gravity stacking algorithm, where the volume fraction of the hollow spheres is 58%.
[0022] Step 4: Based on the hollow sphere distribution data, and using the Python script interface of the finite element software, create and generate the matrix model and hollow sphere model. Then, use the Boolean summation and merging function in the assembly module of the finite element software to generate the hollow sphere-reinforced composite foam material. The assembly and merging process is as follows: Figure 4 As shown.
[0023] Step 5: Based on the hollow sphere reinforced composite foam model, define material properties according to user requirements, including constitutive equation parameters and interface properties of the matrix material and hollow sphere material; select the finite element mesh type (such as C3D4 or C3D10M element) and complete the mesh generation. A schematic diagram of the model mesh generation is shown below. Figure 5 As shown, model nodes, element sets, and surface sets are defined, and boundary conditions and loads are set to ensure that the model accurately reflects the mechanical behavior of the composite foam material. A schematic diagram of the model's boundary conditions and load application is shown below. Figure 6 As shown.
[0024] This invention is not limited to the specific embodiments described above. The invention extends to any new features or combinations disclosed in this specification, as well as any new methods or processes or combinations disclosed herein.
[0025] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.
Claims
1. A finite element method for constructing hollow sphere-reinforced metal-based composite foam materials, characterized in that, Includes the following steps: Step 1: Based on the actual dimensions of the mechanical specimen of hollow sphere reinforced composite foam material, set the basic dimensions of the finite element material model and calculate the target volume fraction of hollow spheres in the composite foam material; Step 2: Generate particle size data that conforms to a Gaussian distribution using a random variable algorithm; Step 3: Generate randomly distributed sphere center coordinates in a specified space using a random gravity stacking algorithm, and combine this with an intrusion detection algorithm to eliminate interference between hollow spheres, generating an interference-free geometric model, and finally obtaining hollow sphere distribution data; Step 4: Based on the hollow sphere distribution data in Step 3, generate a hollow sphere-reinforced composite foam model using the Python script interface of the finite element software; Step 5: Based on the composite foam model generated in Step 4, define the material properties of the hollow spheres and metal matrix according to user requirements, select the mesh element type and complete the mesh generation, define the model nodes, element sets and surface sets, and set the boundary conditions and loads so that the model can reflect the mechanical behavior characteristics of the composite foam material.
2. The finite element method for constructing hollow sphere-reinforced metal-based composite foam material according to claim 1, characterized in that, In step one, the basic dimensions of the finite element material model include the length, width, and height of the composite foam sample, as well as the outer diameter and wall thickness of the hollow sphere.
3. The finite element method for constructing hollow sphere-reinforced metal-based composite foam material according to claim 1, characterized in that, In step two, the random variable algorithm uses independent Gaussian random variables generated by the Box-Muller transformation.
4. The finite element method for constructing hollow sphere-reinforced metal-based composite foam material according to claim 1, characterized in that, In step three, the random gravity stacking algorithm uses pseudo-random variables generated by the Monte Carlo random simulation method as the corresponding random sphere center coordinates. It stacks the spheres layer by layer from the bottom up, and sets boundary constraints to ensure that each hollow sphere does not exceed the model boundary. The sphere center coordinates (x, y, z) satisfy x∈(0+Ri, L-Ri), y∈(0+Ri, W-Ri), z∈(0+Ri, H-Ri), where L, W, H, and Ri represent the length, width, height, and outer diameter of the hollow spheres of the composite foam model, respectively. Combined with the target volume fraction of the hollow spheres, the number of stacking layers is iteratively adjusted to make the composite foam model meet the dual requirements of randomness and volume fraction.
5. The finite element method for constructing hollow sphere-reinforced metal-based composite foam material according to claim 4, characterized in that, In the aforementioned random gravity stacking algorithm, the volume fraction of hollow spheres in the stacking process ranges from 30% to 60%.
6. The finite element method for constructing hollow sphere-reinforced metal-based composite foam material according to claim 1, characterized in that, In step three, the intrusion detection algorithm detects the distance between two hollow spheres and determines whether the geometric models of the two hollow spheres overlap. If there is an overlap, the coordinates of the sphere center are discarded and a new sphere center position is generated.
7. The finite element method for constructing hollow sphere-reinforced metal-based composite foam material according to claim 1, characterized in that, In step three, the hollow sphere distribution data includes hollow sphere diameter data and hollow sphere center coordinate data.
8. The finite element method for constructing hollow sphere-reinforced metal-based composite foam material according to claim 1, characterized in that, In step four, the hollow sphere reinforced composite foam model consists of a hollow sphere model and a corresponding matching matrix model, which are combined through assembly and Boolean operations to generate a hollow sphere reinforced metal matrix composite foam model.