JP2016099867A - Method for forming mesh for analysis of fiber and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To form mesh for analysis of fiber more suitably than before.SOLUTION: An image processing unit 20 separates fibers from each other on a CT image on which fibers are captured and extracts a fiber region for each fiber on the CT image. The image processing unit 20 extracts a center line connecting center points in a cros section in a short direction of the fiber for each fiber region. A mesh formation unit 22 forms a plurality of cross sections (cross section row) perpendicular to the center line with the points on the center line as a center. The diameter and the like of a fiber to be analyzed are instructed by a user as an area of each cross section. The mesh formation unit 22 connects apexes of adjacent two cross sections in the cross section row by a straight line and thereby a columnar analysis region is formed having two cross sections as a bottom face. Since a plurality of analysis regions are formed, mesh representing fibers is formed.SELECTED DRAWING: Figure 10

Description

  The present invention relates to a method and a program for forming a mesh for analyzing fibers.

  2. Description of the Related Art Conventionally, simulations for analyzing or predicting characteristics (for example, mechanical strength) of materials containing fibers have been performed. For example, in a composite material in which carbon fiber or glass fiber is mixed with a polymer resin, since the resin is an isotropic material and the fiber is an anisotropic material, the mechanical strength of the composite material is Depends greatly on the direction. In addition, a composite material is used by manufacturing a plate material by a method such as injection shaping and then shaping it into a desired part shape. For this reason, the mechanical strength of each part that is a product depends on how different fiber materials are contained in each part of the plate. For these reasons, the simulation of the fiber material included in the material is regarded as important.

  As a fiber material simulation method, a finite element method (FEM) is widely used. In the finite element method, a model to be analyzed is formed by dividing an analysis target into small regions called finite elements. Then, the analysis is performed in each small region of the formed model, and the combination of the analysis results in each small region is used as the analysis result of the entire analysis target. Thereby, for example, even for an analysis target having a complicated shape, the analysis process can be simplified.

  A collection of small areas for analysis, which has a property that a surface, line, or point constituting one small area is used in common with adjacent small areas is called a mesh. A surface is a figure on the same plane. Note that the analysis method using the mesh is not limited to the finite element method, and for example, the mesh is also used in the finite volume method.

  Conventionally, a mesh for analyzing fibers has been formed as follows. For example, when analyzing a fiber contained in a composite material of a fiber material and a resin material, first, the composite material is imaged with μX-ray CT having a high resolution. Next, in the 3D CT image obtained by imaging, a fiber region is extracted based on the luminance value of each pixel. Then, the surface of the extracted fiber region is covered with a triangular patch (polygon), and then the fiber region is divided and represented by a tetrahedron or a hexahedron that shares points and lines or lines and surfaces. Thereby, a mesh composed of a plurality of analysis regions is formed.

  In the above-described conventional method, the fibers that are intricately intertwined are collectively extracted as a fiber region without being divided, and thus the formed mesh does not necessarily represent each fiber individually. In such a method, for example, when a plurality of fibers are integrally represented on an image due to noise caused by CT imaging, it is difficult to form an appropriate mesh for each fiber. Specifically, it becomes difficult to form a mesh that appropriately represents the direction (direction), thickness, or length of each fiber. It can also be pointed out that the processing for mesh formation becomes complicated due to complicated polygon processing or the like, or that the number of analysis regions included in the mesh increases.

  It is an object of the present invention to form a fiber analysis mesh more suitably than before.

  In the method of forming a mesh for analyzing fibers according to the present invention, a computer separates and identifies the plurality of fibers in a CT image obtained by CT imaging of a material containing a plurality of fibers, and forms a single fiber. Extracting a corresponding fiber region, extracting a center line connecting a center point of a cross section in the short direction of the one fiber in the fiber region, and centering the point on the center line And a step of forming a plurality of columnar analysis regions each having a bottom surface with two adjacent cross-sections in the cross-sectional row. It is characterized by that.

  Preferably, the plurality of cross sections are congruent regular polygons.

  Preferably, in the step of forming the analysis region, the computer forms a polyhedral analysis region by connecting a vertex of one of the two adjacent cross sections and a vertex of the other cross section with a straight line. .

  According to the present invention, the fiber analysis mesh can be more suitably formed than in the prior art.

It is a hardware schematic diagram for carrying out the method concerning this embodiment. It is a flowchart which shows the procedure of the process of this embodiment. It is a figure which shows CT image. It is a figure which shows an identification image. It is a conceptual diagram which shows the separation process of each fiber. It is a figure which shows the example of a centerline. It is a figure which shows a centerline extraction image. It is a figure which shows the cross section defined on a centerline. It is a side view of a section row and a center line. It is a figure which shows the formed mesh. It is an image which shows the formed mesh group. It is a figure which shows the enlarged image of the formed mesh group.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. Note that the present invention is not limited to the embodiments described herein.

  FIG. 1 is a schematic configuration diagram of hardware for executing the method according to the present embodiment. The method according to the present embodiment is implemented by executing a program on the computer 10. The computer 10 may be a computer that can execute the program, such as a general-purpose PC (Personal Computer).

  The computer 10 includes a processing unit 12 including a CPU, a storage unit 14 including a hard disk or a memory, a keyboard, a mouse, a touch panel, and the like, and is used for inputting user instructions to the processing unit 12. An input unit 16 and a display unit 18 including a liquid crystal panel are connected to each other via a bus. In addition, the computer 10 may be provided with a communication unit for connecting to a network.

  The program may be stored in advance in the storage unit 14, may be provided in the form of a DVD, or may be provided via a network. The processing unit 12 also functions as an image processing unit 20 that processes a CT image or the like, or a mesh forming unit 22 that forms a mesh according to a program command. These functions are described in detail below.

  FIG. 2 is a flowchart showing a processing procedure of the present embodiment. The processing procedure of this embodiment will be described below along the flowchart of FIG. 2 with reference to FIG. 1 and also with reference to FIGS. In the present embodiment, in order to analyze a composite material in which fibers and a resin are mixed, a mesh of each fiber included in the composite material is formed.

  In step S10, a three-dimensional CT image of the composite material to be analyzed is acquired. A CT image can be acquired using a known X-ray machine or the like. The CT image is stored in the storage unit 14 of the computer 10. It is preferable that the acquired CT image has a relatively high resolution so that the subsequent image processing can be suitably performed.

  FIG. 3 shows an example of the acquired CT image. Since the fiber and the resin have different X-ray absorption coefficients, in the CT image 30, the fiber is expressed with a relatively high luminance (for example, white), and the resin is expressed with a relatively low luminance (for example, black).

  Returning to FIG. 2, in step S <b> 12, the image processing unit 20 performs image analysis on the CT image, and identifies the fiber region and the resin region in the CT image. In the CT image, since the brightness is different between the fiber and the resin, both can be identified based on the brightness. Therefore, the image processing unit 20 identifies a region having a luminance higher than a predetermined threshold as a fiber region. Other than fiber is identified as resin. It is also possible to separate and identify the resin portion into a plurality of resins and voids having different densities.

  FIG. 4 shows an identification image 32 obtained by performing the above-described identification processing on the CT image 30 shown in FIG. In FIG. 4, the fiber region is shown in white or gray, and the other part (that is, the resin region) is shown in black. In the identification image 32, the fiber region and the resin region are identified, but each fiber is not yet separated in the fiber region.

  Returning to FIG. 2, in step S <b> 14, the image processing unit 20 performs image analysis on the identification image and performs a process of separating each fiber in the identified fiber region. Details of the processing will be described with reference to FIG. The fibers are usually not linear but curved. However, if viewed locally, it is possible to define a straight section. The curved fiber can be regarded as a series of linear sections. Therefore, the image processing unit 20 first analyzes the fiber region (for example, edge detection processing, edge length value comparison processing, etc.) and divides the fiber region into a plurality of linear sections. In dividing the linear section, a known fiber size (such as a diameter) may be considered.

  It is assumed that the fiber region is divided into linear sections 40a to 40l by the division processing by the image processing unit 20, for example, as shown in FIG. The image processing unit 20 performs a process of combining these linear sections, and recognizes the combined plurality of linear sections as one fiber. For example, when focusing on the straight upper section 40c in FIG. 5, first, the image processing unit 20 searches for another straight section existing near the lower end of the straight section 40c. In this case, for example, it is assumed that the linear sections 40b, 40d, and 40g are searched. Among them, a linear section that continues to the linear section 40c is selected. Specifically, a linear section extending along an extension line of the linear section 40c is selected. At this time, when the angle formed by the extension line of the linear section 40c and the extending direction of the other linear section is within an allowable range (for example, within 30 degrees), the other linear section is defined as the linear section 40c. Judge that it is on the extension line. In the example of FIG. 5, since the straight section 40d corresponds to this condition, the straight section 40d is selected. Then, the straight sections 40c and 40d are connected to form a straight section group.

  Thereafter, the straight sections are connected in the same manner, and the straight section connected to the straight section group no longer exists (that is, there is no straight section extending along the extension line of the straight section group). To) stop processing.

  The straight section group thus formed represents one fiber. In FIG. 5, by the above-described processing, the fibers 42 including the straight sections 40c, 40d, 40e, and 40f, the fibers 44 including the straight sections 40g, 40j, 40k, and 40l, and the straight sections 40a, 40b, Fibers 46 including 40h and 40i are recognized. By the processing from step S10 to step S14, a plurality of fiber regions corresponding to each fiber are identified from the CT image.

  Returning to FIG. 2, in step S <b> 16, the image processing unit 20 extracts the center line of each identified fiber region. The center line is a line connecting the center points of the cross-sections in the short direction of the fiber. As shown in FIG. 6, for example, as the center line of the fiber region 48, it passes through the center of each short direction cross section of the fiber region 48 along the extending direction of the fiber region from the center of the end cross section of the fiber region 48. A line 48a extending to is extracted. Here, the term “center” includes not only the center of the cross section in a mathematical sense but also a region having a certain range based on it.

  The image processing unit 20 can extract the center line of each fiber region based on the coordinate information of each fiber region that the CT image has. Alternatively, the cross-section recognition process may be performed on the identified fiber region, and the center line may be extracted by connecting the center points of the plurality of extracted cross-sections.

  When the center line is extracted for each fiber region, a center line extraction image 50 as shown in FIG. 7 is formed. In the centerline extraction image 50, the centerline extracted is indicated by a black line.

  Returning to FIG. 2, in step S <b> 18, for each center line, the mesh forming unit 22 forms a cross-sectional row including a plurality of cross-sections constituting a part of the mesh (as described later, the formed cross-sectional row is a mesh). It becomes the bottom of each analysis area). Hereinafter, the description will be given focusing on one fiber region corresponding to one fiber.

  FIG. 8 shows one center line 60 extracted in step S16. The mesh forming portion 22 is provided along the center line 60 and forms a plurality of cross sections having a predetermined area. In the example of FIG. 8, four cross sections 62, 64, 66, and 68 are formed with respect to the center line 60. Hereinafter, the formed cross section will be described in detail.

  The shape of the cross section may be a circle or a polygon. Since the cross section is the bottom surface of the analysis region to be formed later, the shape of the analysis region is determined by the shape of the cross section. Therefore, it is desirable that the shape of the cross section is a regular polygon so that the shape of the analysis region to be formed becomes a shape suitable for later analysis. For the same reason, it is desirable that a plurality of cross sections formed on one center line have the same shape.

  As the number of vertices of the cross section increases, the formed analysis region (mesh) more accurately represents the shape of the fiber, but there is a demerit that the amount of calculation required for analysis increases. On the other hand, when the number of vertices in the cross section decreases (that is, the angle of one vertex decreases), stress concentrates on the vertex in the analysis and affects the simulation result. Therefore, the cross-sectional shape is determined in consideration of the balance between the simulation accuracy and the calculation amount. In this embodiment, as shown in FIG. 8, the cross-sectional shape is a regular hexagon.

  The area of the cross section is given by the user. The user inputs cross-sectional area information (for example, information such as the cross-sectional shape width) to the computer 10 based on the diameter of the fiber included in the composite material to be analyzed. The mesh forming unit 22 determines the area (size) of the cross section based on the area information given by the user. In the present embodiment, the width W (see FIG. 8) of the regular hexagon that is a cross section is 7 μm.

  Each cross section included in the cross section row has a center (center of gravity) at a point on the center line. In the example of FIG. 8, the center of the cross section 62 is a point 60a on the center line. Similarly, the center of the cross section 64 is the point 60b on the center line, the center of the cross section 66 is the point 60c on the center line, and the center of the cross section 68 is the point 60d on the center line. Here, the term “center” includes not only the center (center of gravity) of the cross section in the mathematical sense but also a region having a certain range based on it.

  The position where the cross section is formed may be arbitrary, but the cross section is formed at least at both ends of the center line. In the example of FIG. 8, a cross section 62 centering on the upper end 60a of the center line 60 and a cross section 68 centering on the lower end 60d of the center line 60 are formed. Note that the greater the number of cross-sections formed for one center line, the greater the number of analysis regions that the mesh representing the fiber has.

  An interval L between the cross sections (see FIG. 8) is designated by the user. The length of the analysis region is determined by the interval between the cross sections. Therefore, if the cross-sectional interval is shortened, the analysis region is provided more finely in the formed mesh. This allows the mesh to more accurately represent the shape of the fiber, but increases the amount of computation in the analysis. Therefore, the cross-sectional interval is also determined in consideration of the balance between the simulation accuracy and the calculation amount. In consideration of these balances, the cross-sectional interval (length of the analysis region) is generally preferably 5 to 10 times the cross-sectional diameter. In this embodiment, the cross-sectional interval is set to 35 to 70 μm. Of course, the setting of the cross-sectional interval may be appropriately changed according to the analysis object, the analysis purpose, and the like.

  The interval between the cross sections included in the cross section row may not be the same. For example, the cross-sectional interval may be made shorter than the other portions at the location where the center line 60 is bent frequently. In this case, it is preferable that the processing section 12 calculates and determines the interval between the cross sections based on, for example, the bending rate of the center line 60. Thereby, a mesh can be suitably formed also in the location where the fiber is bent finely.

  The direction of each cross section (the rotation angle when the center line 60 is the rotation axis) is the same in each cross section. For example, the cross section 62 formed at the end of the center line 60 is used as a reference, and the cross section 64 is a cross section in a direction in which the cross section 62 is translated along the center line 60 to the point 60b.

  Each section included in the section row does not necessarily have to be parallel. Hereinafter, the angle with respect to the center line of each cross section will be described. As shown in FIG. 8, the extending direction of the perpendicular 62v of the cross section 62 located at the end of the cross section row and the center line 60 coincide. Similarly, the extending direction of the vertical line 68v of the cross section 68 located at the end of the cross section row and the center line 60 are the same. However, in the present embodiment, the center line 60 is bent (curved) at the point 60 b, and the perpendicular 64 v of the cross section 64 centering on the point 60 b that is the bending point coincides with the extending direction of the center line 60. Absent. That is, the cross section 62 and the cross section 64 are not parallel. As described above, the cross section centered on the bending point of the center line is provided to be inclined at a predetermined angle from a plane parallel to the cross section 62.

  The inclination angle of the cross section 64 will be described with reference to FIG. FIG. 9 is a partial side view of the cross-sectional row and the center line shown in FIG. The center line 60 extends from the point 60a to the point 60b to form a line segment 60 '(a part of the center line 60). Further, the center line is inclined by an angle θ with respect to the extending direction of the line segment 60 ′ and extends toward the point 60c (not shown in FIG. 9, refer to FIG. 8). Part). That is, as shown in FIG. 9, the angle formed by the line segment 60 ′ and the line segment 60 ″ is θ. In FIG. 9, a broken line indicates an extension line of the line segment 60 ″. At this time, the cross section 64 centered on the point 60b has an angle at which the angle between the perpendicular 64v and the line segment 60 ′ (and the line segment 60 ″) is θ / 2 (that is, half the bending angle of the center line). It is generated in a tilted state.

  As described above, each cross section included in the cross section row (strictly, a cross section other than the cross section positioned at the end portion) is generated in a state of being inclined at an angle corresponding to the bending angle of the center line.

  Returning to FIG. 2, in step S <b> 20, the mesh forming unit 22 performs a process of connecting the vertices of two adjacent cross sections in a cross section row with a straight line. Thereby, the side surface of the columnar analysis region is formed. The process will be described with reference to FIG.

  When attention is paid to the cross section 62 and the cross section 64, the vertex of the cross section 62 and the corresponding vertex of the cross section 64 are connected by a straight line. For example, the vertex 62a of the cross section 62 and the vertex 64a of the cross section 64 are connected by a straight line 70a. Further, the vertex 62b of the cross section 62 and the vertex 64b of the cross section 64 are connected by a straight line 70b. As a result, a surface 70 having one side of the cross section 62 (between the vertex 62a and the vertex 62b), one side of the cross section 64 (between the vertex 64a and the vertex 64b), the straight line 70a, and the straight line 70b is formed. When this processing is performed for all the vertices of the cross section 62 and the cross section 64, a regular hexagonal analysis region 80a having the cross section 62 and the cross section 64 as bottom surfaces and six surfaces defined by straight lines between the two cross sections as side surfaces is obtained. It is formed.

  By performing the same processing as described above between the cross section 64 and the cross section 66 and also between the cross section 66 and the cross section 68, regular hexagonal columnar analysis regions 80b and 80c are formed. Analysis regions 80a and 80b share a cross section 64, and analysis regions 80b and 80c share a cross section 66. Accordingly, the plurality of analysis regions 80a, 80b, and 80c constitute a mesh 80 in the fiber region.

  As described above, since the area of the cross section 62 is determined based on the width of the analysis target fiber, the thickness of the analysis regions 80a, 80b, and 80c is equal to the thickness of the analysis target fiber. Further, since the length of the center line 60 represents the length of the fibers separated one by one in step S14, the length of the mesh 80 is also equal to the length of the fibers. Each analysis region is formed along the center line 60. That is, the mesh 80 is a mesh that suitably represents one fiber.

  The method for forming the analysis region may be a method other than the method of connecting the vertices of the two cross sections with a line. For example, the side surface formed by moving the cross section 62 along the center line 60 (maintaining the relationship that the center of the cross section 62 is on the center line 60) to the position of the cross section 64 and the movement locus of each side of the cross section 62. A columnar region having the cross section 62 and the cross section 64 as the bottom surface may be used as the analysis region.

  Returning to FIG. 2, in step S <b> 22, the processing unit 12 determines whether or not the processing of step S <b> 18 and step S <b> 20 has been completed for all fiber regions (that is, all center lines). If there is a center line that has not been processed yet, the processes of steps S18 and S20 are performed on the center line. If the processing has been completed for all the center lines, the program for mesh formation is terminated.

  An example of the mesh group formed by the above processing is shown in the mesh group image 90 of FIG. FIG. 12 shows an enlarged view 92 of the mesh group image 90. The mesh group image 90 corresponds to the CT image shown in FIG. 3, the identification image shown in FIG. 4, and the centerline extraction image shown in FIG. As shown in FIG. 11, according to this embodiment, a mesh is individually formed for each fiber included in the composite material. Using these mesh groups, it becomes possible to analyze the composite material to be analyzed by the finite element method. The enlarged view 92 is an example in which the cross-sectional shape is a regular dodecagon.

  According to the mesh forming method according to the present embodiment, since the mesh is formed after separating the fibers one by one on the CT image, it is possible to form a mesh that more appropriately represents each fiber. Specifically, a mesh that appropriately expresses the direction (direction), thickness, and length of each fiber can be formed. In the present embodiment, a mesh can be formed by a relatively simple process of extracting a center line, forming a section row along the center line, and connecting the sections with lines. Furthermore, in the present embodiment, since the number of analysis regions included in the mesh is appropriately changed according to the use of the mesh and the state of the fiber to be analyzed, a more flexible mesh can be formed.

  10 computers, 12 processing units, 14 storage units, 16 input units, 18 display units, 20 image processing units, 22 mesh forming units, 30 CT images, 32 identification images, 40a-l linear sections, 42, 44, 46, 48 fiber region, 48a line, 50 center line extraction image, 60 center line, 60 ', 60' 'line segment, 62, 64, 66, 68 cross section, 62v, 64v, 68v perpendicular line, 62a, 64a, 62b, 64b point , 70a, 70b straight line, 70 plane, 80 mesh, 80a, 80b, 80c analysis region, 90 mesh group image, 92 enlarged view.

Claims (4)

Computer
In a CT image obtained by CT imaging of a material containing a plurality of fibers, separating and identifying the plurality of fibers, extracting a fiber region corresponding to one fiber;
In the fiber region, extracting a center line that connects the center points of the cross-sections in the short direction of the one fiber; and
Forming a cross-sectional row consisting of a plurality of cross-sections centered on a point on the center line and perpendicular to the center line and having a predetermined area;
Forming a plurality of columnar analysis regions having two cross sections adjacent to each other in the cross section row, and
The method for forming a mesh for analyzing fibers is characterized in that: The plurality of cross-sections are congruent regular polygons,
The method for forming a mesh for analyzing fibers according to claim 1, wherein: In the step of forming the analysis region, the computer forms a polyhedral analysis region by connecting a vertex of one of the two adjacent cross sections and a vertex of the other cross section with a straight line.
The method for forming a mesh for analyzing fibers according to claim 2, wherein: On the computer,
In a CT image obtained by CT imaging of a material containing a plurality of fibers, separating and identifying the plurality of fibers, extracting a fiber region corresponding to one fiber;
In the fiber region, extracting a center line that connects the center points of the cross-sections in the short direction of the one fiber; and
Forming a cross-sectional row consisting of a plurality of cross-sections centered on a point on the center line and perpendicular to the center line and having a predetermined area;
Forming a plurality of columnar analysis regions having two cross sections adjacent to each other in the cross section row, and
A program for running