Foam structure model design method based on gradient Voronoi

Abstract

The invention belongs to the technical field of finite element model generation and numerical simulation, and particularly relates to a foam structure model design method based on gradient Voronoi. The method specifically comprises the steps that firstly, N control points are continuously and randomly generated in a three-dimensional space area V0, the generated control points meet the condition that the Euclidean distance dist (Qi, Qj) between every two adjacent control points is larger than the minimum distance Dmin, and the minimum distance Dmin is determined based on a gradient function gamma (X); 2, sequentially calculating vertical bisecting surfaces of a connecting line between two adjacent control points, respectively offsetting the generated vertical bisecting surfaces by a set distance along the positive and negative directions of the connecting line of the two control points, and forming a Voronoi polyhedron with actual wall thickness by two new vertical bisecting surfaces generated by offsetting; and step 3, generating a gradient foam structure numerical model based on the Voronoi polyhedron with the actual wall thickness.

Description

Technical Field

[0001] The invention belongs to the technical field of finite element model generation and numerical simulation, and in particular relates to a gradient Voronoi foam structure model design method. Background Art

[0002] Foam structures have low relative density, high energy absorption, and excellent thermal insulation and sound absorption properties. They are increasingly used as impact and shock absorption devices in the aerospace, automotive industry, and defense fields. They have been widely used in aerospace, military protection, automotive industry, and other fields. However, material optimization requires a deep understanding of the effects of impact velocity and strain rate on their dynamic compression response. Foam structures exhibit complex behavior patterns under dynamic loading, including buckling, plastic collapse, and cell wall fracture. In particular, structural behavior dominated by plastic instability can lead to significant stress softening, thereby weakening the energy absorption capacity of the material. Therefore, computational models that can accurately capture the deformation and failure behavior of foams have become the key to optimizing the performance of foam structures.

[0003] The Voronoi model can effectively simulate the randomness of the foam structure and accurately reflect the deformation and failure behavior of the foam structure during loading. Existing studies have shown that density gradient, relative density and cell regularity have a significant impact on the compression response and energy absorption performance of the foam structure. In particular, density gradient has been established as a promising design concept to improve the mechanical properties of foam structures. By introducing density gradients in foam materials, the local mechanical properties of the material can be optimized, so that it exhibits different strengths and energy absorption capabilities in different parts, thereby better meeting the performance requirements of specific applications. At present, the research on Voronoi foam materials focuses on uniformly distributed structures. In order to further study the failure mode and energy absorption effect of foam materials, it is necessary to construct a three-dimensional solid gradient Voronoi foam model with actual wall thickness. Summary of the invention

[0004] In view of this, the present invention provides a design method based on a gradient Voronoi foam structure model, which can realize the accurate construction of a three-dimensional solid gradient Voronoi foam model with actual wall thickness.

[0005] The technical solution for implementing the present invention is as follows:

[0006] A design method of gradient Voronoi foam structure model, the specific process is:

[0007] Step 1: Continuously randomly generate N control points in the three-dimensional space region V0, and the generated control points satisfy the Euclidean distance dist(Q i ,Q j ) is greater than the minimum distance Dmin , the minimum distance D min Determined based on the gradient function Γ(X);

[0008] Step 2: Calculate the perpendicular bisectors of the line between two adjacent control points in sequence, and offset the generated perpendicular bisectors by a set distance in the positive and negative directions of the line between the two control points. The two new perpendicular bisectors generated by the offset form a Voronoi polyhedron with actual wall thickness.

[0009] Step three, generating a gradient foam structure numerical model based on the Voronoi polyhedron with actual wall thickness.

[0010] Furthermore, the minimum distance D of the present invention min for

[0011]

[0012] Among them, R represents the cell regularity, Γ(X) represents the gradient function, represents the critical minimum distance function.

[0013] Furthermore, the cell regularity R of the present invention has a value of 0.8.

[0014] Furthermore, the critical minimum distance function of the present invention is for:

[0015]

[0016] Among them, (L x , L y , L z ) represents the size of the three-dimensional space region V0, and N represents the number of control points.

[0017] Furthermore, the gradient function Γ(X) of the present invention satisfies the following form:

[0018] Γ(X)=kX+g min

[0019] Where k is the cell size coefficient of the gradient foam structure, g min is the minimum cell size gradient, X is the Lagrangian position along the foam structure, 0 <X<1。

[0020] Furthermore, the cell size coefficient k of the gradient foam structure of the present invention is 1.5; the minimum cell size gradient g min Take 0.5.

[0021] Furthermore, the present invention is based on the control point Q i To control point Q j The unit vector of the direction is denoted by Control Point Q i With control point Q j The midpoint of the line is denoted as M ij , according to (1) vector is the unit normal vector of the perpendicular bisector, (2) the midpoint M ij On the perpendicular bisector plane, determine two adjacent control points Q i and Q j The perpendicular bisector of

[0022] Furthermore, the vertical bisecting plane of the present invention The following relationship is further satisfied:

[0023]

[0024] in, is the coordinate vector of any point on the plane.

[0025] Furthermore, the specific process of step three of the present invention is: outputting the obtained Voronoi polyhedrons to ABAQUS software, assembling all Voronoi polyhedrons according to their spatial positions, and performing subtraction Boolean operations with the model generation space to obtain a gradient foam structure numerical model.

[0026] Furthermore, in step 2 of the present invention, the generated vertical plane is offset by a distance of T / 2 in the positive and negative directions of the line connecting the two control points, where T is the actual wall thickness of the Voronoi foam structure.

[0027] Beneficial effects:

[0028] First, the present invention has a gradient density Voronoi foam structure design method, which determines the minimum distance D based on the gradient function Γ(X). min , the Euclidean distance between two adjacent control points generated is made greater than the minimum distance to give the randomness of the control points generated in the model, so as to ensure the randomness of the foam structure.

[0029] Second, for a given cell regularity R, the present invention changes with the change of the Lagrangian position X of the cell nucleus, thereby forming a gradient relative density that changes with the cell size. Since the cell size is positively correlated with X, a positive density gradient can be obtained (the density increases along the X direction), and a Voronoi foam structure with a density gradient is obtained, which can make the structure exhibit different strengths and energy absorption capabilities in different regions, and better meet the performance requirements in specific applications.

[0030] Thirdly, by setting constraints to obtain the vertex coordinates of the Voronoi polyhedron, and performing parameter processing through the geometric editing function of the finite element software ABAQUS, a model was established that can accurately reflect the randomness of the solid gradient Voronoi foam structure, supporting the precise prediction of the mechanical behavior of the gradient Voronoi foam structure through finite element calculation and analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0032] Figure 1 This is a flow chart of the design method of the gradient Voronoi foam structure model of the present invention;

[0033] Figure 2 A flow chart of the generation of pore wall polyhedrons based on a gradient Voronoi foam structure according to the present invention;

[0034] Figure 3 It is a three-dimensional geometric model based on the gradient Voronoi foam structure of the present invention. DETAILED DESCRIPTION

[0035] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0036] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

[0037] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0038] The embodiment provides a method for designing a gradient Voronoi foam structure model, such as Figure 1 As shown, the specific implementation includes the following steps:

[0039] Step 1: Continuously randomly generate N control points in the three-dimensional space region V0, and the generated control points satisfy the Euclidean distance dist(Q i ,Q j ) is greater than the minimum distance D min , the minimum distance D min Determined based on the gradient function Γ(X);

[0040] In the specific implementation of this step: define a dimension L in the three-dimensional Cartesian coordinate system C x *L y *L z In this embodiment, L x =L y =L z = 60mm spatial domain V0, N = 600 control points Q are randomly generated in V0 i (i=1,2,…,N), each control point Q i =(x i ,y i ,z i ) must satisfy the distance constraint between control points. Specifically, any pair of adjacent control points Q i and Q j (i≠j) the Euclidean distance dist(Q i ,Q j ) must satisfy the following constraints:

[0041]

[0042] Among them, D min Represents the minimum distance, which can be obtained from the cell regularity R, gradient Γ(X) and critical minimum distance function The product of is:

[0043]

[0044] Among them, 0<R≤1 is a parameter that quantitatively describes the regularity of random Voronoi foam. In this model, the regularity parameter R is set to 0.8. When R→0 + When R = 1, it corresponds to a completely random Voronoi foam structure; when R = 1, it corresponds to a spacing of all control points of Perfect regular Kelvin foam structure.

[0045] When the Euclidean distances between any two adjacent control points are equal, there is a limiting case where a critical value of the minimum distance is obtained:

[0046]

[0047] The gradient is introduced along the Lagrangian position X of the foam structure, and the gradient function Γ(X) satisfies the following form

[0048] Γ(X)=kX+g min ,(0 <X<1)

[0049] Wherein, k is 1.5, which is the cell size coefficient of the gradient foam structure; g min Take 0.5 as the minimum cell size gradient. For a given cell regularity R, the gradient function Γ(X) allows a minimum distance D min It changes with the Lagrangian position X of the nucleus, thus forming a gradient relative density that changes with the cell pore size. Since the cell pore size is positively correlated with X, a positive density gradient can be obtained (density increases along the X direction).

[0050] When this step is implemented, each time a control point is generated, the above constraint conditions are judged, and when the constraint conditions are not met, the control point is regenerated.

[0051] Step 2: Calculate the perpendicular bisectors of the line between two adjacent control points in sequence, and offset the generated perpendicular bisectors by a set distance in the positive and negative directions of the line between the two control points. The two new perpendicular bisectors generated by the offset constitute a Voronoi polyhedron with actual wall thickness.

[0052] In the specific implementation of this step: establish the control point Q i and Q j The perpendicular bisector of the line between The unit normal vector of the perpendicular bisector is the vector from the control point Q i To Q j The specific algorithm is as follows: control point Q i and Q j The midpoint of the line connecting ij , the expression is

[0053]

[0054] From the control point Q i To control point Q j The direction vector is normalized to be expressed as is the unit normal vector of the perpendicular bisector, and point M ij On this perpendicular bisector On, the following relationship is satisfied

[0055]

[0056] in, is the coordinate vector of any point on the plane.

[0057] During the model generation process, all perpendicular bisectors of all Voronoi polyhedra are calculated in turn, and 600 Voronoi polyhedra controlled by 600 control points are obtained.

[0058] like Figure 2 As shown, the generated vertical plane is offset by a distance of T / 2 in the positive and negative directions of the line connecting the two control points, where T is the actual wall thickness of the Voronoi foam structure. The original vertical bisector is deleted, and the two new vertical bisectors generated by the offset form a Voronoi polyhedron with actual wall thickness.

[0059] Step 3: Output the model size, model control parameters, wall thickness, etc. of the Voronoi polyhedron obtained by the loop algorithm to the ABAQUS software, assemble all the Voronoi polyhedrons according to their spatial locations, and perform Boolean subtraction operations with the model generation space to obtain the gradient foam structure numerical model. The final effect is as follows Figure 3 shown.

[0060] In summary, the Voronoi foam structure design method and modeling process with gradient density described in the present invention establish a three-dimensional model that can accurately reflect the randomness of the gradient Voronoi foam structure.

[0061] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for designing a gradient Voronoi foam structure model, characterized in that: The specific process is: Step 1: Continuously randomly generate N control points in the three-dimensional space region V0, and the generated control points satisfy the Euclidean distance dist(Q i , Q j ) is greater than the minimum distance D min , the minimum distance D min Determined based on the gradient function Γ(X); Step 2: Calculate the perpendicular bisectors of the line between two adjacent control points in sequence, and offset the generated perpendicular bisectors by a set distance in the positive and negative directions of the line between the two control points. The two new perpendicular bisectors generated by the offset form a Voronoi polyhedron with actual wall thickness. Step three, generating a gradient foam structure numerical model based on the Voronoi polyhedron with actual wall thickness.

2. The gradient Voronoi foam structure model design method according to claim 1, characterized in that: The minimum distance D min for: Among them, R represents the cell regularity, Γ(X) represents the gradient function, represents the critical minimum distance function.

3. The gradient Voronoi foam structure model design method according to claim 2, characterized in that: The gradient function Γ(X) satisfies the following form: Γ(X)=kX+g min Where k is the cell size coefficient of the gradient foam structure, g min is the minimum cell size gradient, X is the Lagrangian position along the foam structure, 0<X<1.

4. The gradient Voronoi foam structure model design method according to claim 2, characterized in that: The cell regularity R has a value of 0.

8.

5. The gradient Voronoi foam structure model design method according to claim 2, characterized in that: The critical minimum distance function for: Among them, (L x , L y , L z ) represents the size of the three-dimensional space region V0, and N represents the number of control points.

6. The gradient Voronoi foam structure model design method according to claim 3, characterized in that: The cell size coefficient k of the gradient foam structure is 1.5; the minimum cell size gradient g min Take 0.

5.

7. The gradient Voronoi foam structure model design method according to claim 1, characterized in that: From the control point Q i To control point Q j The unit vector of the direction is denoted by Control Point Q i With control point Q j The midpoint of the line is denoted as M ij , according to (1) vector is the unit normal vector of the perpendicular bisector, (2) the midpoint M ij On the perpendicular bisector plane, determine two adjacent control points Q i and Q j The perpendicular bisector of 8. The gradient Voronoi foam structure model design method according to claim 7, characterized in that: The perpendicular bisector The following relationship is further satisfied: in, is the coordinate vector of any point on the plane.

9. The gradient Voronoi foam structure model design method according to claim 1, characterized in that: The specific process of step three is: outputting the obtained Voronoi polyhedrons to ABAQUS software, assembling all Voronoi polyhedrons according to their spatial positions, and performing subtraction Boolean operations with the model generation space to obtain a gradient foam structure numerical model.

10. The gradient Voronoi foam structure model design method according to claim 1, characterized in that: In the step 2, the generated vertical plane is offset by a distance of T / 2 in the positive and negative directions of the line connecting the two control points, where T is the actual wall thickness of the Voronoi foam structure.

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