CN117789885A - Finite element model building method of short fiber reinforced composite material - Google Patents
Finite element model building method of short fiber reinforced composite material Download PDFInfo
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Abstract
A finite element model building method of a short fiber reinforced composite material belongs to the field of computer aided engineering. Comprising the following steps: 1) Determining the composition of the representative volume element; 2) Selecting a suitable representative volume unit; 3) Carrying out parameterization treatment on the geometric characteristics and the spatial characteristics of the fiber; 4) Introducing a random seed function, and controlling the geometric characteristic parameters and the spatial position characteristic parameters of the fiber through the function; 5) Realizing random distribution of fibers in a representative volume unit by utilizing an improved random sequence adsorption method; 6) And automatically generating a representative voxel model of the short fiber reinforced composite material based on the generated fiber information in the database. The geometric periodicity of the RVE is achieved with a guaranteed control over the randomness of the fibers. And filtering out fibers which do not need interference judgment, so that the throwing efficiency of the fibers is improved. During the model generation, no manual operation is needed by a designer, the model generation efficiency is improved, and the simplicity and high efficiency of the design process are ensured.
Description
Technical Field
The invention belongs to the field of computer aided engineering, and particularly relates to a finite element model building method of a short fiber reinforced composite material facing a representative volume unit of the short fiber reinforced composite material.
Background
The short fiber reinforced composite material is widely applied in the industrial fields of aerospace and the like by virtue of the capability of rapidly preparing components with complex geometric shapes and the strong designability. Establishing a geometric model of the short fiber composite is a key to realizing the design of the composite product. The existing traditional design method is difficult to ensure the simplicity and rapidity of the composite design process, so that the research and development period cannot be accurately controlled. Therefore, it is necessary to propose a method of designing a short fiber reinforced composite material that can optimize the design flow.
With the great improvement of computer computing power, a computer aided engineering method based on a finite element method becomes an indispensable auxiliary link in the material design process. The general flow of the computer-aided verification method is as follows: (1) Determining the external modeling and internal structure size information of a material or a member to be researched; (2) Establishing an accurate finite element model based on the size information and inputting material attribute information; (3) And setting corresponding boundary condition submitting calculation according to specific requirements, and verifying whether the simulation result meets the design standard. Compared with the traditional material design method, the auxiliary verification method omits the preparation link of the material, and shortens the overall design period to a great extent. However, for the short fiber reinforced composite material, although clear information of the internal structure can be obtained through an electron microscope image reconstruction technology, the actual microscopic structure of the material is taken as a simulation analysis object, and the establishment cost of a corresponding finite element model and the subsequent calculation solving cost are greatly increased, and even analysis cannot be completed. Thus, researchers have proposed the concept of a Representative Volume Element (RVE) to select a reasonable fraction from macroscopic materials to represent the whole material.
The construction of the RVE model of the staple fiber composite is generally carried out by adopting a random sequence adsorption method (RSA) to realize the random distribution of the staple fibers. The method is simple in logic, and whether the fibers interfere or not is judged through the intercentroid distance. However, for the situation that interference is not possible to happen in part obviously, the traditional RSA method still needs to calculate interference judgment repeatedly, so that time is wasted. Furthermore, if the finite element analysis is performed with RVE as a target, the geometric periodicity thereof needs to be ensured. Thus, how to achieve the geometric periodicity of RVE while guaranteeing fiber randomness is a challenge.
Disclosure of Invention
The invention aims to provide a finite element model building method of a short fiber reinforced composite material based on Python language and a computer aided engineering software platform ABAQUS aiming at the defects of the existing model generation technology. On the basis of the traditional RSA method, the method improves the flow of interference judgment among fibers, solves the expression problem of fiber randomness, the interference judgment problem among fibers and the geometric periodicity problem on the corresponding boundary surface of RVE; and on the premise of ensuring that the randomness of the fibers is controllable, the geometric periodicity of the RVE model is realized. In addition, during the model generation, a designer does not need to carry out manual operation, and the simplicity and the high efficiency of the design process are ensured while the model generation efficiency is improved.
The invention comprises the following steps:
1) According to the structural characteristics of the short fiber reinforced composite material, determining the RVE model composition form of the short fiber reinforced composite material is as follows: the fiber is an ideal cylinder, and the fiber and the matrix are well combined without defects such as pores;
2) From the viewpoint of simplifying the calculation flow, the selection principle for determining RVE is as follows: the area range of RVE is cuboid, and the shortest length is more than twice the height of the fiber;
3) According to the definition of the short fibers, any short fiber existing in the space is parameterized;
4) Introducing a random seed function, and controlling the geometric characteristic parameters and the spatial position characteristic parameters of the fiber through the function;
5) The improved random sequence adsorption method is utilized to realize random distribution of fibers in RVE, so that the geometric periodicity of RVE is realized while interference among the fibers is not ensured;
6) Based on the generated fiber information in the database, generating a random distribution geometric model of the fibers through a computer aided engineering software platform ABAQUS, generating a geometric model of a matrix by using Boolean operation in software, and cutting out fiber parts beyond RVE boundaries; in the subsequent research, the RVE model can be subjected to modulus analysis, strength analysis and other treatments according to different research requirements, so that the design process of the short fiber reinforced composite material is quickened.
In step 3), any one short fiber existing in the space is parameterized, and the method comprises the following steps:
3.1 Parameterizing the geometric characteristics of the staple fibers: the geometry of the cylindrical short fiber is completely determined by two parameters, namely the radius of the fiber end face circle and the fiber height;
3.2 Parameterizing the spatial location characteristics of the staple fibers: the position information of the cylindrical short fiber in the space is completely determined by the centroid coordinates of the fiber and the orientation angle of the fiber axis; the orientation angle includes an in-plane orientation angle and an out-of-plane orientation angle.
In step 4), the random seed function is introduced, and the geometric characteristic parameter and the spatial position characteristic parameter of the fiber are controlled by the random seed function and are generated based on the uniform distribution probability density function.
In step 5), the specific steps for realizing the random distribution of the fibers in the RVE are as follows:
5.1 Generating a first fiber, copying the fiber to the determined 26 directions in order to meet the requirement of geometric periodicity, and recording the spatial position information of the first fiber and 26 copied fibers thereof;
5.2 A fiber is generated again and is duplicated in the same 26 directions; sequentially calculating the distance between newly generated fibers and the generated fiber cores in the database:
a) If the distance is smaller than the sum of the radii of the two fiber circumscribed circles, judging whether interference occurs or not through an interference judging algorithm;
b) If the distance is equal to the sum of the radii of the two fiber circumscribed circles, interference judgment is not needed, and next centroid distance calculation is directly carried out;
5.3 Recording the result of each interference judgment:
a) If interference occurs, the fiber delivery fails, and the step (5.2) is returned to regenerate;
b) If no interference occurs, the secondary fiber is put successfully, and the spatial position information of the fiber and 26 replicated fibers thereof is recorded;
5.4 Calculating the volume fraction of the fiber in the RVE according to the number of times of successful fiber throwing, and judging whether the volume fraction reaches a set value or not:
a) If the set value is not reached, returning to the step (5.2) and putting new fibers;
b) And stopping generating and throwing the fiber if the set value is reached.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention provides a finite element model modeling method for a short fiber reinforced composite material. The method solves the expression problem of the randomness of the fibers, the interference judgment problem among the fibers and the geometric periodicity problem on the boundary surface corresponding to the RVE, and can realize the geometric periodicity of the RVE under the condition of ensuring the control of the randomness of the fibers.
2. The method provided by the invention improves the traditional RSA method flow, and filters out the fibers which do not need interference judgment by judging the distance between fiber cores, thereby accelerating the fiber throwing efficiency.
3. The method provided by the invention is based on Python language programming, and can directly generate a corresponding RVE model in the ABAQUS software without redundant manual operation; the model generation efficiency is improved, and meanwhile, simplicity and high efficiency of the design process are ensured.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
figure 2 is a schematic view of the RVE model selection range of the present invention;
FIG. 3 is a schematic view of the spatial position orientation of fibers of the present invention;
FIG. 4 is a schematic diagram of the positional relationship of any two fibers in the space according to the present invention;
FIG. 5 is a graph showing the position of the fibers after the fibers are completely thrown in when the fiber volume ratio is 5.48% in the present invention;
figure 6 is an RVE model of a short fiber reinforced composite material constructed in the present invention.
Detailed Description
The following examples are set forth to provide those of ordinary skill in the art with a more complete understanding of the present invention, and are not intended to limit the invention in any way.
The flow of the steps of the method in the embodiment of the invention is shown in the figure 1, and the method comprises the following steps:
(1) Determining the RVE model composition form of the short fiber reinforced composite material according to the structural characteristics of the short fiber reinforced composite material. The short fiber reinforced composite material can be regarded as a solid material consisting of short fibers and a matrix, and for the convenience of mathematical modeling and analysis, the fiber is assumed to be an ideal cylinder, and the fiber and the matrix are well combined without defects such as pores.
(2) From the standpoint of simplifying the calculation flow, the area range of RVE in this embodiment is determined to be a regular hexahedron, as shown in fig. 2, whose geometric dimensions are 100 μm×100 μm, and ensuring that the height of the fiber does not exceed 50 μm when the fiber is subsequently produced.
(3) According to the definition of the short fibers, any short fiber existing in the space is parameterized, and the specific implementation steps are as follows:
3.1 Parameterizing the geometric characteristics of the staple fibers: an ideal cylinder can be considered as a geometric body surrounded by a rectangular plane rotating around its edges. The geometry of the cylindrical staple fibers can thus be determined entirely by two parameters, the radius of the fiber end face circle and the fiber height. In addition, for convenience of description, in this embodiment, r is used for the radius of the fiber end face circle and the fiber height f 、L f Reference is made to this.
3.2 Parametrically characterizing the spatial position of the staple fibersAnd (5) digitizing: as shown in FIG. 3, a fiber can be considered to be a fiber that is perpendicular to the xOy plane and whose centroid coincides with the origin of coordinates, rotated by θ about the y-axis and then about the z-axisObtaining; wherein, theta,The out-of-plane deflection angle and in-plane deflection angle of the fiber axis are shown, respectively, and the rotation follows the right-hand spiral rule. Generalizing to fibers arbitrarily distributed in space, if the centroid coordinates (x, y, z) of the fibers are known, they can be obtained from the initial fiber by similar rotation steps and translations (translation from origin of coordinates to (x, y, z)). Therefore, the position information of the cylindrical staple fiber in space can be determined by the centroid coordinates (x, y, z) of the fiber and the orientation angle of the fiber axis +.>To be fully determined.
(4) A random seed function is introduced, and the geometric characteristic parameters and the spatial position characteristic parameters of the fiber are controlled through the function. For ease of illustration, the fibers in this example are all defined as cylinders of uniform shape and size, where r f 、L f 5 μm and 50 μm respectively. The spatial position characteristics of the fibers are imparted by a random function, wherein x, y, z are randomly generated within the region of the regular hexahedron of RVE, θ,Randomly generated in the range of 0 to 2 pi. Notably, the random generation algorithms described above are each generated based on a uniformly distributed probability density function.
(5) Based on the random algorithm, the random distribution of the fibers in the RVE is realized by utilizing an improved random sequence adsorption method, the geometric periodicity of the RVE is realized while the interference among the fibers is ensured not to occur, and the specific implementation steps are as follows:
5.1 A first fiber is generated, as the intersection of the fiber with the RVE boundary is unknown, in order to meet the requirements of geometric periodicity, the fiber is replicated in the determined 26 directions, and the spatial location information of the first fiber and its 26 replicated fibers is recorded. The number of directions for 26 directions can be expressed as follows:
(i, j, k) i= ±100, 0j= ±100, 0k= ±100,0i, j, k are not 0 at the same time
5.2 A fiber is regenerated and the fiber is replicated in the same 26 directions. And sequentially calculating the distance between the newly generated fiber and the generated fiber shape center in the database. As shown in fig. 4, the distance between two identical fiber-shaped centers in space can be expressed as:
the radius of the circumscribed circle of fibers A and B can be expressed as:
wherein the subscripts a, B respectively represent the centroids of fiber A, fiber B, d AB Represents the distance between the fibrous cores, R A 、R B The radius of the circumscribed circle of the fiber A and the fiber B are shown. Judging the distance between the centroids of the fiber A and the fiber B:
a) If the distance between the fiber cores is smaller than the sum of the radii of the two fiber circumscribing circles, whether interference occurs is judged by an interference judging algorithm. From the discretization point of view, the axis segments of the fiber A and the fiber B are equally divided into n parts, and the coordinates of the segment points on each fiber can be respectively expressed as:
thus, the shortest distance between fiber a and fiber B axis can be represented by the shortest distance between the segmentation points:
i,j＝0,1,2,…,n
if the shortest distance between fibers is less than the sum of the two fiber radii, then this indicates that interference between fibers occurs.
b) If the distance between the fiber cores is equal to the sum of the radii of the two fiber circumscribed circles, the next calculation of the distance between the fiber cores is directly performed without interference judgment.
(5.3) recording the result of each interference judgment:
a) If interference occurs, the fiber delivery fails, and the step (5.2) is returned to regenerate;
b) If no interference occurs, the secondary fiber is put successfully, and the spatial position information of the fiber and 26 replicated fibers thereof is recorded;
(5.4) calculating the volume fraction of the fiber in the RVE according to the number of times of successful fiber feeding, and judging whether the volume fraction reaches a set value or not:
a) If the set value is not reached, the process returns to the step (5.2) to carry out the throwing of new fibers.
b) And stopping generating and throwing the fiber if the set value is reached. In this example, assuming a fiber volume fraction of 5.48%, the finished fiber is shown in fig. 5.
(6) Based on the generated fiber information in the database, generating a random distribution geometric model of the fibers through a computer aided engineering software platform ABAQUS, generating a geometric model of a matrix by using Boolean operation in software, and cutting out fiber parts beyond RVE boundaries; all the steps are written into Python script, and the ABAQUS is submitted to be automatically executed, and the generated RVE model of the short fiber reinforced composite material is shown in figure 6. In the subsequent research, the RVE model can be subjected to modulus analysis, strength analysis and other treatments according to different research requirements, so that the design process of the short fiber reinforced composite material is quickened.
The invention solves the expression problem of the randomness of the fibers, the interference judgment problem among the fibers and the geometric periodicity problem on the boundary surface corresponding to the RVE, and can realize the geometric periodicity of the RVE under the condition of ensuring the control of the randomness of the fibers. Meanwhile, the judgment step of the distance between fiber shaped centers is added on the basis of the traditional RSA method, so that fibers which do not need interference judgment are filtered, and the fiber throwing efficiency is improved. In addition, during the model generation, a designer does not need to carry out manual operation, and the simplicity and the high efficiency of the design process are ensured while the model generation efficiency is improved.
The above is a specific implementation procedure of the present invention, and does not limit the protection scope of the present invention; any person skilled in the art, within the scope of the disclosure of the present invention, adopts equivalent transformation or equivalent substitution to form technical solutions, and falls within the scope of the protection of the claims of the present invention.
Claims (5)
1. A finite element model building method of a short fiber reinforced composite material is characterized by comprising the following steps:
1) Determining the RVE model composition form of the short fiber reinforced composite material according to the structural characteristics of the short fiber reinforced composite material;
2) From the viewpoint of simplifying the calculation flow, the selection principle for determining RVE is as follows: the area range of RVE is cuboid, and the shortest length is more than twice the height of the fiber;
3) According to the definition of the short fibers, any short fiber existing in the space is parameterized;
4) Introducing a random seed function, and controlling the geometric characteristic parameters and the spatial position characteristic parameters of the fiber through the function;
5) The improved random sequence adsorption method is utilized to realize random distribution of fibers in RVE, so that the geometric periodicity of RVE is realized while interference among the fibers is not ensured;
6) Based on the generated fiber information in the database, generating a random distribution geometric model of the fibers through a computer aided engineering software platform ABAQUS, generating a geometric model of a matrix through Boolean operation in software, and shearing out fiber parts beyond RVE boundaries to obtain an RVE model of the short fiber reinforced composite material.
2. A method of finite element modeling a short fiber reinforced composite material according to claim 1, wherein in step 1) the RVE model is comprised of fibers and a matrix, the fibers being ideal cylinders, the fibers and matrix being well bonded without voids.
3. A method for building a finite element model of a short fiber reinforced composite material according to claim 1, characterized in that in step 3) any one of the short fibers present in the space is parameterized, comprising the steps of:
(1) Parameterizing the geometric characteristics of the staple fibers: the geometry of the cylindrical short fiber is completely determined by two parameters, namely the radius of the fiber end face circle and the fiber height;
(2) Parameterizing the spatial position characteristics of the short fibers: the position information of the cylindrical short fiber in the space is completely determined by the centroid coordinates of the fiber and the orientation angle of the fiber axis; the orientation angle includes an in-plane orientation angle and an out-of-plane orientation angle.
4. A method of finite element modeling a short fiber reinforced composite material as defined in claim 1, wherein in step 4), the introducing of a random seed function by which both the geometric feature parameters and the spatial location feature parameters of the fiber are controlled is based on a uniformly distributed probability density function.
5. A method for building a finite element model of a short fiber reinforced composite material according to claim 1, wherein in step 5), the specific steps for realizing random distribution of fibers in RVE are as follows:
(1) Generating a first fiber, wherein the intersection condition of the fiber and the RVE boundary is unknown, considering all possible intersection conditions to meet the requirement of geometric periodicity, copying the fiber to the determined 26 directions, and recording the spatial position information of the first fiber and 26 copied fibers thereof; the number of directions for 26 directions is expressed as follows:
(i, j, k) i= ±100, 0j= ±100, 0k= ±100,0i, j, k are not 0 at the same time
(2) Regenerating a fiber, and copying the fiber to the same 26 directions; sequentially calculating the distance between the newly generated fibers and the generated fiber cores in the database; the centroid distance of any two identical fibers A, B in space is expressed as:
the radius of the circumscribed circle of fibers A and B is expressed as:
wherein the subscripts a, B respectively represent the centroids of fiber A, fiber B, d AB Represents the distance between the fibrous cores, R A 、R B The radius of the circumscribed circle of the fiber A and the fiber B are respectively represented;
(3) If the distance between the fiber cores is smaller than the sum of the radii of the two fiber circumscribing circles, judging whether interference occurs or not through an interference judging algorithm; from the perspective of discretization, the axial sections of the fiber A and the fiber B are equally divided into n parts, and the coordinates of the segmentation points on each fiber are respectively expressed as follows:
thus, the shortest distance between the axes of fiber a and fiber B is represented by the shortest distance between the segmentation points:
if the shortest distance between the fibers is less than the sum of the two fiber radii, indicating that the fibers interfere with each other;
(4) If the distance between the fiber cores is equal to the sum of the radii of the two fiber circumscribed circles, interference judgment is not needed, and next calculation of the distance between the fiber cores is directly carried out;
(5) Recording the result of each interference judgment:
5.1 If interference occurs, the fiber is put in failure, and the step (2) is returned to regenerate;
5.2 If no interference occurs, the secondary fiber is put successfully, and the spatial position information of the fiber and 26 replicated fibers thereof is recorded;
(6) Calculating the volume fraction of the fiber in the RVE according to the number of times of successful fiber throwing, and judging whether the volume fraction reaches a set value or not:
6.1 If the set value is not reached, returning to the step (2) to throw in new fibers;
6.1 If the set value is reached, stopping the generation and the delivery of the fiber.
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