Single-layer foamed aluminum simulation method

Abstract

The invention relates to a single-layer foamed aluminum simulation method. The method comprises the following steps: constructing a Thiessen polyhedron, generating random thickness on the surface of the Thiessen polyhedron, generating a target test piece by adopting a mapping grid method, determining material properties and the like. According to the single-layer foamed aluminum simulation method provided by the invention, the process of random pore size and random void wall thickness is realized, the closed-cell foamed aluminum modeling method based on the three-dimensional mesoscopic model is provided, the calculation efficiency is greatly improved, and the calculation time is shortened. And a theoretical basis can be provided for the design of a weight reduction device.

Description

Technical Field

[0001] The present invention relates to the technical field of materials science, and particularly relates to a method for simulating single-layer aluminum foam. Background Art

[0002] Closed-cell aluminum foam is a kind of porous metal material, which consists of thousands of random three-dimensional polyhedral pores embedded in a continuous aluminum or aluminum alloy matrix. Compared with other composite materials, closed-cell aluminum foam has dual physical properties of both function and structure, such as light weight and high strength. Due to its unique mesoscopic structural characteristics, it can have a long and almost constant plateau stress during compression, which is very beneficial for energy absorption, and has been widely used in the field of explosion shock protection.

[0003] As is well known, the local failure deformation of aluminum foam under strong dynamic load conditions is very serious, and it is difficult to obtain the local mesoscopic failure mode and failure processes (modes) such as deformation, crushing, and fracture through experimental research. Some studies have shown that the mechanical properties of aluminum foam materials exhibit obvious multi-scale characteristics. At the mesoscopic level, the mechanical behaviors such as plastic deformation, buckling, and fracture of the cell walls of aluminum foam have a great impact on the macroscopic mechanical properties. For the research on the mesoscopic modeling of porous metal materials, there are currently three main types of methods. The first type of method uses repeating unit-cell (RUC), and simulates the macroscopic mechanical properties and deformation characteristics of the aluminum foam structure by regularly repeating a pre-designed representative unit. The selection of the representative unit is relatively diverse. In order to more realistically simulate the pore structure of actual aluminum foam, the basic unit shape of this representative model has been gradually improved, and the octahedron model, Kelvin model (tetradecahedron model), and more complex cube-pyramid model and cube-sphere model have been developed successively. The main defect of this method is that it cannot reflect the randomness of the mesoscopic structure of aluminum foam. The second type of method considers the randomness of the mesoscopic structure of aluminum foam on this basis, and generates a cell structure according to certain rules to simulate the pore structure of aluminum foam. This model can more realistically reflect the mesoscopic mechanical characteristics of aluminum foam, and has great significance for the research on its energy dissipation mechanism and deformation mode, etc. However, most of the pore walls use shell elements, and their thickness is the same at any position, which is obviously not in good agreement with the experimental observation results. The third type of method is to perform three-dimensional reconstruction based on the CT scan image of the material to obtain a mesoscopic finite element model, which can truly restore the mesoscopic structural characteristics of aluminum foam. However, the number of elements in the finite element model obtained by this method is huge, and the calculation cost is far higher than the first two types of methods. Summary of the Invention

[0004] The object of the present invention is to overcome the shortcomings of the above technologies and provide a method for simulating single-layer aluminum foam that can achieve random pore sizes and random pore wall thicknesses.

[0005] To achieve the above object, the technical solution proposed by the present invention is: a method for simulating single-layer aluminum foam, comprising the following steps:

[0006] Step 1: Generate a number of discrete points in a structural member of any shape, and construct a Delaunay tetrahedron mesh in the structural member through the discrete points; then, for each face of the tetrahedron in the Delaunay tetrahedron mesh, find its perpendicular bisecting plane and construct a Voronoi polyhedron;

[0007] Step 2: Assign a random thickness to the faces of the Voronoi polyhedron through a random algorithm, and the random function of the thickness is: T d = T max -(T max - T min )×ζ random ; where T d is the thickness of the face of the Voronoi polyhedron, T min and T max are the minimum and maximum values of the thickness of the face of the Voronoi polyhedron, and ζ random is the random distribution function of the face of the polyhedron;

[0008] Step 3: Generate a target specimen and establish a cubic model surrounding the specimen. Using the mapped mesh method, map the geometric features of the structural member obtained in Step 2 into the cubic model;

[0009] Step 4: Determine the material properties of the mesh; when all or part of the nodes of the elements in the mesh are located in the Voronoi polyhedron, the material properties of the mesh are set to pores, otherwise they are defined as aluminum materials; perform specimen cutting and delete the part outside the target specimen.

[0010] A further improvement of the above solution is that in Step 1, by adjusting the number of discrete points, the diameter range of the circumscribed sphere of the Voronoi polyhedron is between 1 mm and 3 mm, and the average value is 2 mm.

[0011] A further improvement of the above solution is that in Step 2, T min and T max are 0.03 mm and 0.4 mm respectively, and the value range of ζ random is from 0 to 1.

[0012] A further improvement of the above solution is that in Step 3, the element characteristic size of the mapped mesh method is 0.2 mm, and the cubic model is uniformly meshed using a spatial eight-node hexahedron element.

[0013] A further improvement of the above solution is that in Step 4, after deleting the part outside the target specimen, the particle model part therein is removed.

[0014] A further improvement of the above solution is as follows: after the step 4, a modeling of the aluminum foam sandwich core structure is carried out; specifically, an air grid model is established, explosives are filled into the air grid, and the explosives and the air grid share nodes; geometric models of the sleeve, the cover plate, and the bottom plate are established; then the geometric models are meshed, the K files of all fluid and solid grids are output, and are assembled with the K file of the aluminum foam z model to finally obtain the model and the K file of the aluminum foam sandwich core structure.

[0015] The single-layer aluminum foam simulation method provided by the present invention realizes the process of random pore size and random wall thickness of the voids, proposes a modeling method for closed-cell aluminum foam based on a three-dimensional mesoscopic model, greatly improves the calculation efficiency, and shortens the calculation time. It can provide a theoretical basis for the design of weight reduction devices. Description of the Drawings

[0016] Figure 1 It is a schematic diagram of a structural member after generating the Voronoi polyhedron in an embodiment of the present invention.

[0017] Figure 2 It is a schematic diagram of a structural member obtained from the random wall thickness of the Voronoi polyhedron in an embodiment of the present invention.

[0018] Figure 3 It is a schematic diagram of the generation process of the mesoscopic model of closed-cell aluminum foam in an embodiment of the present invention.

[0019] Figure 4 It is a schematic diagram of the model of the aluminum foam sandwich core structure in an embodiment of the present invention.

[0020] Figure 5 It is a comparison diagram of the numerical simulation results and the test results of the peak strain at each measuring point on the bottom plate of three groups of aluminum foams with different porosities under the explosive shock wave of the charge in an embodiment of the present invention. Detailed Embodiments

[0021] Embodiment: In this embodiment, a single-layer aluminum foam simulation method is proposed, including the following steps:

[0022] Step 1: Generate a number of discrete points in a structural member of any shape. In this embodiment, a structural member in the shape of a cube is used. According to the Voronoi algorithm, the discrete data points are reasonably connected to construct a Delaunay tetrahedral mesh in the structural member; then for each face of each tetrahedron in the Delaunay tetrahedral mesh, its perpendicular bisecting plane is found to construct a Voronoi polyhedron, and the result is as Figure 1 shown. By adjusting the number of discrete points, the diameter range of the circumscribed sphere of the Voronoi polyhedron (that is, the pore size after final generation) is between 1 mm and 3 mm, and the average value is 2 mm.

[0023] Step 2: Using Python and Fortron, we wrote a random algorithm for wall thickness. We used the random algorithm to assign random thickness to the faces of the Thiessen polyhedron. The random function of thickness is: T d =T max -(T max -T min )×ζ random ; where T d is the thickness of the face of the Thiessen polyhedron, T min and T max is the minimum and maximum thickness of the face of the Thiessen polyhedron, ζ random is the random distribution function of the faces of the polyhedron; T min and T max They are 0.03mm and 0.4mm respectively, random The value range is 0 to 1, and the result is as follows Figure 2 As shown, the diameter range of the circumscribed sphere of the Thiessen polyhedron can be fine-tuned again by the wall thickness.

[0024] Compared with other algorithms, this algorithm can ensure the randomness of wall thickness and pore size while effectively shortening modeling time and improving calculation efficiency.

[0025] Step 3: Use TUREGRID software to read the structural parts obtained in the above two steps and extract the geometric features. Generate the target specimen and build a cube model surrounding the specimen. Use the mapping grid method to map the geometric features of the structural parts obtained in step 2 to the cube model.

[0026] The grid model of Tyson polyhedral particles and random wall thickness is established by using the mapping grid method. According to the characteristics of the pore delivery area of ​​the closed-cell aluminum foam micro-model, structured grid division is performed, and the characteristic size of the unit is determined according to the pore size and wall thickness. In order to take into account both computational efficiency and simulation accuracy, the unit characteristic size is set to 0.2 mm in this embodiment. The regular unit distribution characteristics ensure the computational efficiency of subsequent material determination and are conducive to programming implementation. The spatial eight-node hexahedral unit is used to perform uniform grid division on the overall delivery area to obtain a regular initialization grid structure. The fine and uniform grid improves the computational efficiency while ensuring accuracy.

[0027] The specific method is: first build a cube model surrounding the cylinder, such as Figure 3 As shown in a in the figure; then the extracted geometric features are Figure 3 Mapping in a, we get Figure 3b in; According to the position of the grid in the specimen, the material properties of the grid are determined. When all or part of the nodes of an element are located in the Thiessen polyhedron, the material property is set to porosity, otherwise it is defined as aluminum material. Then, cylindrical cutting is performed to delete the aluminum foam model outside the cylinder, and the remaining part is Figure 3 as shown in c; Then, the particle model part is removed to obtain the grid model of aluminum foam Figure 3 as shown in d, and the K file is output. The three-dimensional view of aluminum foam is as Figure 3 as shown in e. To facilitate the observation of the internal structure of aluminum foam, a quarter model is intercepted, as Figure 3 shown in f.

[0028] Modeling of aluminum foam sandwich structure; Specifically, the TUREGRID software is used to establish an air grid model, and the air grid is filled with explosives. The explosives and the air grid share nodes; The SCDM software is used to establish the geometric models of the sleeve, cover plate, and bottom plate; Then, the ICEM software is used to mesh the geometric models, and the K files of all fluid and solid grids are output. The K files are assembled in the LS-PrePost software together with the K file of aluminum foam to finally obtain the model and K file of the aluminum foam sandwich structure. The quarter model and dimensions are as Figure 4 shown. The size of the air domain is 0.82m×0.42m×0.4m, the radius of the explosive is 0.043m, the thickness of the cover plate is 0.01m, and the thickness of the bottom plate is 0.02m.

[0029] The non-reflective boundary condition is added to the outer surface of the air layer, the bottom of the bottom plate is set as the fixed boundary, the cover plate and the bottom plate are connected by tying, *CONTACT_TIED_SURFACE_TO_SURFACE, and the cover plate and aluminum foam, aluminum foam and the bottom plate adopt automatic surface-to-surface contact *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE.

[0030] To accurately analyze the nonlinear behavior of the aluminum foam sandwich panel under strong dynamic loads, the system bottom plate, sleeve, bracket, and end cover are made of Q235 steel. The above materials and aluminum foam are numerically simulated using the PLASTIC KINEMATIC material model in LS-DYNA for metal materials. The air adopts the *MAT_NULL material model, and the equation of state is described by *EOS_LINEAR_POLYNOMIAL. The high-energy combustion explosive adopts the *MAT_HIGH_EXPLOSIVE_BURN material model, and the equation of state uses *EOS_JWL to represent the pressure of the explosion products.

[0031] The ALE algorithm (*CONTROL_ALE) is adopted for solution, the explosive and air form an Eulerian multi-material group (*ALE_MULTI-MATERIAL_GROUP), and the fluid domain and solid domain are set for fluid-structure interaction (*CONSTRAINED_LAGRANGE_IN_SOLID). Finally, it is submitted to ANSYS / LS-DYNA for solution.

[0032] In the geometric nonlinear analysis of explosion shock, materials often undergo large deformations. In order to better fit the change form of the pore walls of aluminum foam in the real situation, the material erosion method is often used to process the distorted elements. When the stress or strain in the element reaches the erosion failure condition, we consider this element to fail and remove it from the model. The failure criterion of aluminum foam adopts the maximum strain failure criterion. According to the research results, the maximum failure strain value of the aluminum foam material in this paper is 0.37.

[0033] Through the comparison of the numerical simulation results and experimental results of the peak strain values at each measuring point on the bottom plate of three groups of aluminum foams with different porosities under the explosion shock wave of the charge, as Figure 5 shown, with the numerical simulation results of strain as the X-axis and the experimental results as the Y-axis, the straight line with a slope of 1 in the figure indicates that the numerical simulation results are completely consistent with the experimental results. From Figure 5 it can be intuitively seen that the experimental points basically fall between the solid line with a slope of 1 and the dashed lines with slopes of 0.90 and 1.1, and the error is within 10%. The maximum error is only 8.6%. The numerical simulation results of the strain values at different measuring points under different porosities are in good agreement with the experimental results, indicating that the simulation effect is good and verifying the correctness of the three-dimensional mesoscopic model of aluminum foam.

[0034] The present invention is not limited to the specific technical solutions described in the above embodiments. In addition to the above embodiments, the present invention can also have other implementation manners. For those skilled in the art, any technical solutions formed by making any modifications, equivalent replacements, improvements, etc. within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A single-layer aluminum foam simulation method, characterized in that: The steps include: Step 1: Generate a number of discrete points in a structural part of any shape, and construct a Delaunay tetrahedron network in the structural part through the discrete points; then find the perpendicular bisector of each tetrahedron face in the Delaunay tetrahedron network to construct a Thiessen polyhedron; Step 2: Use a random algorithm to assign random thickness to the faces of the Thiessen polyhedron. The random function of the thickness is: T d =T max -(T max -T min )×ζ random ; where T d is the thickness of the face of the Thiessen polyhedron, T min and T max is the minimum and maximum thickness of the face of the Thiessen polyhedron, ζ random is the random distribution function of the faces of the polyhedron; Step 3: Generate the target specimen and establish a cubic model surrounding the specimen. Use the mapping grid method to map the geometric features of the structural parts obtained in step 2 to the cubic model. Step 4: Determine the material properties of the mesh; when all nodes of the elements in the mesh are fully or partially located in the Thiessen polyhedron, the material properties of the mesh are set to pores, otherwise they are defined as aluminum materials; perform specimen cutting and delete the parts outside the target specimen.

2. The single-layer aluminum foam simulation method according to claim 1, characterized in that: In step 1, by adjusting the number of discrete points, the diameter of the circumscribed sphere of the Thiessen polyhedron ranges from 1 mm to 3 mm, and the average value is 2 mm.

3. The single-layer aluminum foam simulation method according to claim 1, characterized in that: In step 2, T min and T max They are 0.03mm and 0.4mm respectively, random The value range is 0 to 1.

4. The single-layer aluminum foam simulation method according to claim 1, characterized in that: In the step 3, the unit characteristic size of the mapping grid method is 0.2 mm, and the cubic model is uniformly gridded using spatial eight-node hexahedral units.

5. The single-layer aluminum foam simulation method according to claim 1, characterized in that: In step 4, after deleting the portion outside the target specimen, the particle model portion is eliminated.

6. The single-layer aluminum foam simulation method according to claim 1, characterized in that: After step 4, the foam aluminum sandwich core structure is modeled; specifically, an air grid model is established, and the air grid is filled with explosives, and the explosives and the air grid share nodes; a geometric model of the sleeve, the cover plate, and the bottom plate is established; then the geometric model is meshed, and the K files of all fluid and solid grids are output, and the meshes are assembled with the K file of the foam aluminum z model, and finally the model and K file of the foam aluminum sandwich core structure are obtained.

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