CN115985421A - Fabric composite finite element modeling method based on microcosmic geometric model - Google Patents
Fabric composite finite element modeling method based on microcosmic geometric model Download PDFInfo
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Abstract
The invention relates to the field of woven composite material modeling, in particular to a fabric composite material finite element modeling method based on a micro-geometric model, which comprises the steps of establishing a micro-geometric model of a representative volume unit of a composite material woven fabric, and outputting a surface triangular surface patch model after calculation; periodically mapping the triangular patch model into a composite material domain, and calculating surface intersection points of the triangular patches in a grid line domain; repairing the penetration and narrow gaps among different yarns along the direction of the grid lines; adjusting grid node coordinates to match the adjacent surface intersection points and setting grid node labels; judging the splitting mode of the surface according to the four nodes of the surface of the hexahedron unit; and splitting the hexahedral unit into a tetrahedron, a pyramid and a triangular prism unit again according to the splitting mode of the surface, setting a corresponding label set for the unit according to the label type of the unit, and simultaneously storing the material direction corresponding to the unit. The method can establish a finite element model of the high-fidelity woven composite material, and has a very wide application prospect.
Description
Technical Field
The invention relates to the field of woven composite material modeling, in particular to a finite element modeling method for a fabric composite material based on a microscopic geometric model.
Background
The woven composite material as a novel high-performance composite material has the characteristics of high specific modulus, high specific strength, good manufacturability and the like, and is widely applied to the fields of aerospace, military and the like. The woven fabric reinforcement in the woven composite material is woven by warp yarns, weft yarns and binding yarns according to a specific topological structure rule, has obvious multi-scale characteristics, and the microstructure and the microscopic structure of the woven fabric reinforcement directly influence the macroscopic performance of the composite material.
The woven composite material microscopic scale unit cell consists of yarn and matrix, wherein the yarn consists of fiber tows and the matrix infiltrated among the fibers. However, the mesoscopic yarns of the woven composite material have a complex geometry due to the mutual compression deformation of the fiber tows during the weaving process. In the past modeling research work, certain ideal assumptions are made on the section and the path of the mesoscopic yarn, but the section of the real mesoscopic yarn dynamically changes along with the path, and the ideal assumptions often have certain differences from the real structure, so that the deformation of the fabric needs to be fully considered during modeling in order to more truly reflect the mesoscopic yarn structure of the woven composite material.
For the mesoscopic modeling of the woven composite material, a common method is to perform certain section and path assumptions on yarns based on scanning electron microscope, optical microscope and Micro-CT scanning results, so as to create an ideal model of the mesoscopic structure of the woven composite material in a parameterized manner. However, the ideal geometric modeling method is mostly used for woven composite materials with low fiber volume content, and when the fiber volume content is higher, the yarns have different waviness and have certain asymmetry and torsion in the yarn section due to mutual extrusion deformation among the yarns. The difference between the regular yarn shape and track assumed by the ideal geometric model and the real model is large, even the yarn geometric model has certain interference, and the requirement of mechanical property analysis cannot be met.
Finite element based numerical calculation is an important and effective method for studying composite materials. The method needs to establish a finite element model of the material, and whether the model can effectively reflect the internal structure of the material and directly influence the precision of each mechanical property of the subsequently forecasted material; chinese patent CN 113987882A provides a digital modeling method for a woven composite material mesoscopic yarn structure, which realizes geometric modeling of a composite material reinforcement, but the method cannot realize matrix modeling and integral grid division of the composite material.
At present, the traditional meshing method is only suitable for meshing of an ideal woven composite material mesoscopic structure (the cross section of the yarn is oval, a runway shape, a lens shape and the like), meshing is only performed on each yarn and a matrix of the reinforcement respectively, and then the reinforcement and the matrix are combined into a composite material mesh, so that meshes between yarn-yarn interfaces and yarn-matrix interfaces have certain interference, and subsequent finite element simulation results are influenced.
Disclosure of Invention
Based on the problems in the prior art, the invention aims to provide a finite element modeling method for a fabric composite material based on a micro-geometric model. The method has the advantages that the composite material high-fidelity finite element model is quickly established based on the micro-scale woven fabric unit cell model, the prediction precision of the mechanical property of the finite element is improved, the method is suitable for developing two-dimensional and three-dimensional woven composite materials with various geometric structures, the development efficiency of the woven fabric composite materials is greatly improved, the development cost is reduced, and the method has a very good application prospect.
In order to achieve the purpose, the invention provides the following technical scheme:
a finite element modeling method of a fabric composite material based on a microscopic geometric model comprises the following steps:
(1) Establishing a representative volume unit microscopic geometric model of the woven fabric;
(2) Calculating the axial direction of the yarn based on the representative volume unit micro-geometric model, and outputting a surface triangular patch model of the woven fabric yarn;
(3) Establishing a composite material domain, adding a matrix material and dispersing the composite material domain into hexahedral units;
(4) Mapping the surface triangular patch model of the yarns in the step (2) into a composite material domain, calculating the intersection points of the triangular patch and grid lines in the composite material domain, and storing the topological relation of the intersection points of the surfaces of the grid lines;
(5) Repairing the interpeave permeation and narrow gaps among different yarns caused by scale conversion along the direction of the grid lines;
(6) Adjusting the grid nodes of the composite material domain to the surface intersection points of the adjacent grid lines, and setting topological labels of the grid nodes;
(7) Traversing surfaces of the hexahedral unit, judging splitting modes of the corresponding six surfaces according to four grid nodes of each surface, and determining splitting lines;
(8) And splitting the hexahedral unit into a tetrahedron, a pyramid and a triangular prism again according to the splitting mode of six surfaces in the hexahedral unit, storing the hexahedral unit into a corresponding component unit set according to the label of each unit, and obtaining the material direction corresponding to each unit.
Compared with the prior art, the invention has the advantages that:
the invention can completely digitalize the development of woven composite material products without real fabrics. The product development period is greatly reduced. Meanwhile, the fidelity of the finite element model reconstructed based on the microscopic geometric structure can be effectively guaranteed, the penetration and narrow gaps among different yarns can be identified and repaired based on integral grid division, and all parts are perfectly meshed together by matching yarn-yarn and yarn-matrix interfaces. The method can improve the accuracy of mechanical property prediction of the composite woven composite material and well guide the development and verification of the woven composite material product.
Drawings
FIG. 1 is a flow chart of a finite element modeling method of a fabric composite material based on a micro-geometric model according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a three-dimensional orthogonal fabric representative volumetric cell topology according to an embodiment of the present invention;
FIG. 3 is a three-dimensional orthogonal fabric representative volumetric unit micro-geometric model of an embodiment of the present invention;
FIG. 4 is a schematic representation of a cross-sectional sliced fiber node of a three-dimensional orthogonal fabric weft according to an embodiment of the present invention;
FIG. 5 is a schematic representation of a three-dimensional orthogonal fabric weft cross-sectional boundary node according to an embodiment of the present invention;
FIG. 6 is a three-dimensional orthogonal fabric surface triangular patch model of an embodiment of the invention;
FIG. 7 is a schematic view of a triangular patch and composite domain mapping according to an embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating the calculation of intersection points on the grid line surface according to the embodiment of the present invention;
FIG. 9 is a schematic view of the adjustment of the penetration and narrow gap between yarns according to an embodiment of the present invention;
FIG. 10 is a schematic diagram of mesh node adjustment according to an embodiment of the present invention;
FIG. 11 is a schematic view of the hexahedral unit according to the embodiment of the present invention in a surface-resolved mode;
FIG. 12 is a schematic exploded view of a hexahedral unit according to an embodiment of the present invention;
FIG. 13 is a three-dimensional orthogonal fabric composite finite element mesh model according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; for a better explanation of the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
FIG. 1 is a flow chart of a finite element modeling method of a fabric composite material based on a micro-geometric model according to an embodiment of the invention; as shown in FIG. 1, the finite element modeling method of the fabric composite material based on the micro geometric model comprises the following steps:
(1) Establishing a representative volume unit microscopic geometric model of the woven fabric, which comprises the following steps:
(1.1) defining yarn parameters of all components of the woven fabric, the size of a representative volume unit and key nodes of the organization of the representative volume unit, and establishing a topological structure of the representative volume unit of the woven fabric;
in some embodiments of the present invention, the step (1.1) may further specifically include: the method comprises the steps of setting parameters such as initial cross-sectional area and modulus of yarns, setting the size of the fabric in the warp (length direction) and weft (width direction) directions, defining the coordinates of key points of the woven fabric and an initial path of the yarns, and establishing a topological structure of a representative volume unit of the fabric with a circular yarn section shape and broken lines of the yarn path, wherein the topological structure of the three-dimensional orthogonal fabric comprises three yarns, namely warp yarns, weft yarns and binding yarns, as shown in figure 2.
And (1.2) setting boundary conditions of topological structure units, applying yarn tension, dispersing the yarns into micro-geometric units through yarn fiber discretization and fiber digital unit discretization, and performing numerical calculation on the dispersed yarns to obtain a micro-geometric unit model.
In some embodiments of the present invention, the step (1.2) may further specifically include: the periodic boundary conditions are set in the warp and weft directions, under the condition that the cross section area of the yarn is not changed, the warp yarn, the weft yarn and the binding yarn are respectively divided into 64 virtual fibers, 64 virtual fibers and 16 virtual fibers, the virtual fibers are discretized into digital units (rod units and fiber nodes), and the length of each digital unit is 0.5 time of the diameter of each virtual fiber. Constant tension is applied to the ends of the yarn, causing relative movement between the fibers, effecting changes in the path and cross-sectional shape of the yarn until approaching a true fabric structure. Fig. 3 shows a three-dimensional orthogonal fabric representative volume element micro-geometric model, with a representative volume element having a final dimension of 13.64 × 5.976 × 5.9753mm (length × width × thickness).
(2) Calculating the axial direction of the yarn based on the representative volume unit micro-geometric model, and outputting a triangular patch model of the surface of the woven fabric yarn, wherein the method specifically comprises the following steps:
(2.1) acquiring three-dimensional coordinate data of the fiber nodes of the model in the step (1) and recording corresponding topological relation;
it can be understood that, in the embodiment of the present invention, the virtual fibers belonging to the same yarn have the same number of fiber nodes, the fiber nodes of the same virtual fiber are sequentially ordered according to the yarn path direction, and the topological relationship of the fiber nodes can be formed according to the above relationship.
(2.2) calculating the path node of the middle shaft of the yarn through the three-dimensional coordinate of the node, uniformly slicing the section of the yarn along the path direction of each yarn, and obtaining the interpolation point of each fiber on the section of the yarn;
in some embodiments of the present invention, the step (2.2) may further specifically include: calculating the average value of the fiber nodes with the same yarn sequence number as the yarn path nodes, and sequentially connecting the yarn path nodes as the yarn path direction. Calculating a normal vector of a section plane along the yarn path direction, wherein the distance between two adjacent section planes is about 1-5 times of the length of the virtual fiber rod unit, and obtaining an interpolation point of the virtual fiber rod unit on the section plane, as shown in fig. 4, the interpolation point is a schematic diagram of the weft yarn along the yarn path direction.
(2.3) obtaining the boundary of the yarn section interpolation point in the step (2.2) in a self-adaptive manner by adopting a Delaunay triangularization algorithm and an Alpha-shape algorithm to obtain a polygonal boundary profile of the yarn section;
in some embodiments of the present invention, the step (2.3) may further specifically include: traversing the interpolation points of the truncation plane in the step (2.2), taking the interpolation points as the circle center, averagely adding 8-20 interpolation points on the truncation plane by taking the corresponding virtual fiber radius as the radius, and calculating the Delaunay triangulation network of all the interpolation points on the same truncation plane by utilizing a Delaunay triangulation algorithm. And deleting any triangle with one side larger than Alpha in the Delaunay triangulation to obtain the Alpha-shape of the triangulation, wherein the Alpha is 5-10 times of the diameter of the virtual fiber. Extracting the boundaries of the remaining Delaunay triangulation network to be the polygonal boundary contour of the yarn section, and performing homogenization interpolation along the contour to obtain the section boundary nodes, as shown in FIG. 5, which is a schematic diagram of the section boundary nodes of the weft yarns.
It should be noted that, in order to ensure the correct generation of the subsequent triangular patch, it is necessary to ensure that the number of boundary nodes of each section of the same yarn is the same.
And (2.4) carrying out homogenization interpolation on the section polygon in the step (2.3) to obtain the vertex of a triangular patch, and then generating a surface triangular patch model of the yarn according to a specific sequence.
In some embodiments, as shown in fig. 6, the boundary nodes on two adjacent cross-sectional planes are connected according to a specific boundary node sequence to obtain a surface triangular patch model of the yarn.
(3) Establishing a composite material domain, adding a matrix material and dispersing the composite material domain into hexahedral units, which specifically comprises the following steps:
(3.1) reading the size of a representative volume unit of the fabric, and setting two key nodes of min and max of a composite material domain;
in some embodiments of the present invention, the step (3.1) may further specifically include: let the composite material have a midpoint P cmid (x cmid ,y cmid ,z cmid ) The midpoint of all fiber nodes of the representative volume unit microscopic geometric model of the woven fabric is P tmid (x tmid ,y tmid ,z tmid ) Then there is x cmid ＝x tmid +x off ，y cmid ＝y tmid +y off ，z cmid ＝z tmid Wherein x is off And y off The composite material domain midpoint is offset in the x and y directions (the warp and weft directions) by a distance (the x direction is +/-1/2 length, the y direction is +/-1/2 width). Defining a composite material domain minimum point P cmin (x cmin ,y cmin ,z cmin ) And a maximum point P cmax (x cmax ,y cmax ,z cmax ) Has x cmin ＝x cmid -1/2*length，y cmin ＝y cmid -1/2*width，z cmin ＝z cmid -1/2*thickness*(1+z inc )，x cmax ＝x cmid +1/2*length，y cmax ＝y cmid +1/2*width，z cmax ＝z cmid +1/2*thickness*(1+z inc ) Wherein z is inc Increasing the thickness percentage for the z-direction (according to different composite structures z) inc 0 or more). P cmin And P cmax The cuboid region formed by the two points in the x, y and z positive directions is the composite material region containing the woven fabric reinforcement and the matrix material.
(3.2) setting the size of a proper hexahedral unit according to the fiber size and the cross-section parameter of the fabric, and uniformly dispersing the material domain in the step (3.1) into hexahedral units with corresponding sizes.
In some embodiments of the present invention, the step (3.2) may further specifically include: the sizes of the hexahedral units in the x, y and z directions can be set according to the average diameter of all virtual fibers of the fabric, and the number of grids is increased sharply due to the excessively small unit size, so that the consumption of computing resources is increased. Excessive cell size can result in partial loss of detail of the fabric, affecting subsequent simulation accuracy. The cell size is typically set to 1-5 times the mean diameter of the virtual fiber. Adding P in step (3.1) cmin And P cmax The composite material domain surrounded by two points is uniformly dispersed into hexahedral units, and the cuboid region is the composite material domain after offset as shown in fig. 7.
(4) Mapping the yarn surface triangular patch model in the step (2) into a composite material domain, calculating the intersection points of the triangular patch and grid lines in the composite material domain, and storing the topological relation of the intersection points of the surfaces of the grid lines, wherein the topological relation is as follows:
(4.1) mapping the triangular surface patch on the surface of the yarn to a composite material domain, calculating surface intersection points of the triangular surface patch and grid lines in the x direction, the y direction and the z direction, and recording topological information of the intersection points;
in some embodiments of the present invention, the step (4.1) may further specifically include: mapping the yarn surface triangle patch into the composite material domain as shown in fig. 7, since the composite material domain may be shifted along the warp and weft directions in step (3), the part of the triangle patch is not in the composite material domain, periodically mapping the triangle surface not in the composite material domain to the other side of the representative volume unit, calculating surface intersections of the triangle patch with grid lines in the x, y and z directions, and recording topology information of the intersections as a schematic diagram of the calculated intersections shown in fig. 8, wherein the triangle abc is a yarn surface triangle patch, and the triangles a ' b ' c ', a ' b ' c ' and a ' "b '" c ' "are vertical projections of the triangle abc on the xoy plane, the xoz plane and the zoy plane, respectively. Taking the xoy plane as an example, firstly, judging whether a mesh node exists in a triangle a ' b ' c ' of the xoy plane, if the mesh node exists, calculating a corresponding node coordinate, and reversely projecting the corresponding node coordinate onto a triangular patch abc to calculate a projection point coordinate; if not, the calculation is not carried out, and the projection point is the surface intersection point of the yarn and the grid line. And sequentially judging the vertical projection conditions of the triangle abc on the xoz plane and the zoy plane, wherein the points 1,2 and 3 are the intersection points of the triangle abc on the yarn surface and the grid line surfaces in the x direction, the y direction and the z direction.
And (4.2) periodically mapping the grid line surface intersection points on the boundaries of the six surfaces of the composite material domain, so that the grid line surface intersection points meet the periodic boundary conditions of the representative volume units.
It can be understood that, by periodically mapping the triangular patch mesh in the grid line surface intersection points on the six plane boundaries of the review material domain, the topological relation of the grid line surface intersection points can be reflected, so that the grid line surface intersection points satisfy the representative volume unit periodic boundary condition.
(5) Repairing the interpeak permeation and narrow gaps between different yarns caused by scale conversion along the direction of the grid lines, which is specifically as follows:
(5.1) respectively extracting intersection points of the yarns on the grid line surfaces in the x direction, the y direction and the z direction and sequencing the intersection points according to the x coordinate value, the y coordinate value or the z coordinate value of the intersection points; as shown in fig. 9 (a) - (b), there are 2-4 unequal grid line surface intersections on the grid lines in the vertical direction;
and (5.2) adjusting the intersection point of the surfaces of two mutually-penetrated different yarns into the midpoint of two points according to the x, y or z value of the intersection point of the grid lines and the topological relation of the intersection point, and simultaneously interchanging the topological labels of the two nodes. And adjusting the intersection point of the surfaces of two different yarns with the distance smaller than the set threshold value to the midpoint of the two points.
In some embodiments of the present invention, the step (5.2) may further specifically include: according to the x, y or z values of the grid line surface intersection points and the topological relation thereof, like Yarn1 and Yarn2 in FIG. 9 (a), two interlaced yarns are provided, wherein i 1 And i 2 The intersection points of the grid line surfaces of the Yarn1 and the Yarn2 are respectively, and the Yarn1 and the Yarn2 have penetration, and similarly, as shown in fig. 9 (b), narrow gaps (the narrow gap judgment threshold is less than 1/3 times of the grid size) appear between the Yarn1 and the Yarn 2. The intersection point of the surface of the two grid lines where the penetration or narrow gap occurs is adjusted to the midpoint of the two points, as shown in fig. 9 (a) - (b), the hollow node is the adjusted surface intersection point, and the dotted line is the material boundary of the two yarns.
(6) Adjusting the intersection point of the grid node of the composite material domain to the surface of the adjacent grid line, and setting a topological label of the grid node, wherein the method specifically comprises the following steps:
(6.1) reading the grid line surface intersection points adjusted in the step (5), judging the grid line surface intersection points adjacent to the grid nodes and storing the grid line surface intersection points in the corresponding grid node adjacent linked list, as shown in fig. 10 (a), taking a plane as an example, the grid nodes N 1 In the adjacency linked list is S 1 、S 2 And S 3 Three surface intersections.
And (6.2) traversing all the grid nodes, if the grid node adjacency list is zero, not adjusting the grid nodes, and simultaneously setting the labels of the grid nodes as the corresponding single component labels. Otherwise, adjusting the coordinates of the grid nodes to the middle points of the intersection points of all the adjacent surfaces, and setting the grid node labels as corresponding multi-component labels.
In some embodiments of the present invention, the step (6.2) may further specifically include: traversing all mesh nodes, e.g. N in FIG. 10 (a) 1 Three adjacent grid surface intersection points are provided, and N is adjusted 1 To S 1 、S 2 And S 3 At the midpoint, set N 1 The label of (a) is a multicomponent label; as shown by N in FIG. 10 (a) 2 Only S 4 One adjacent grid surface intersection, adjust N 2 Node to S 4 Where is set up N 2 The label of (a) is a multicomponent label; such as mesh node N in FIG. 10 (a) 3 Setting N without adjusting grid node when the adjacent linked list is zero 3 The label of the grid node is a label corresponding to a single component. Fig. 10 (b) is a schematic diagram of adjusted mesh nodes, wherein the unadjusted mesh nodes are all single component tags.
(7) Traversing surfaces of the hexahedral unit, judging splitting modes of the corresponding six surfaces according to four grid nodes of each surface, and determining splitting lines, wherein the splitting lines are as follows:
reading four vertex labels corresponding to the quadrangle, judging whether the quadrangle needs to be divided into two triangles according to the number of the labels and the type of the labels, if so, adding adjacent grid nodes of grid nodes, as shown in fig. 9, wherein the adjacent grid nodes are 6 surface splitting modes, m grid nodes belong to two or more materials, and s grid nodes belong to a single material. 4 mesh nodes s mesh nodes in fig. 11 (a), without adding dividing lines to the surface; in fig. 11 (b) - (c), 1 node or 2 nodes on the same side are m nodes, so m nodes and s nodes must contain the same label, and the surface does not need to be marked with dividing lines; fig. 11 (d) - (f) include 2 or more m nodes, and the labels of the m nodes including the s node are such that the surface is a material, and no dividing line needs to be added, otherwise, dividing lines need to be added at 2 m nodes.
It should be noted that the regular quadrilateral shown in fig. 11, the m-node and s-node sequences are schematic diagrams, a non-regular quadrilateral surface shown in fig. 10 may appear, and the corresponding node distribution sequence in fig. 11 can be obtained by rotating different node distribution sequences.
(8) Splitting the hexahedral unit into a tetrahedron, a pyramid and a triangular prism unit again according to the splitting mode of six surfaces in the hexahedral unit, storing the hexahedral unit into corresponding component unit sets according to the topological labels of the grid intersections of each unit, and obtaining the material direction corresponding to each unit, specifically as follows:
(8.1) reading adjacent points of nodes of the hexahedral unit, dividing the hexahedral unit into one component, two components or three components according to the node labels, splitting each component into a tetrahedron, pyramid or triangular prism unit, and adding nodes in the hexahedral unit for splitting if necessary. As shown in fig. 12 (a), two dividing lines exist on two surfaces of the hexahedral unit, and the unit is divided into 2 triangular prism units; as shown in fig. 12 (b), the hexahedral cell belongs to two or three components, and the cell is divided into 1 tetrahedral cell, 1 pyramidal cell, and 1 triangular prism cell. Fig. 13 (a) - (c) are respectively a composite finite element mesh, a composite reinforcement woven fabric mesh and a matrix mesh.
(8.2) judging the path node of each unit corresponding to the adjacent yarn path in the step (2) of each unit set, and setting the material direction of each unit as the path direction of the node.
In conclusion, the finite element modeling method for the fabric composite material provided by the invention realizes full-digital finite element model modeling without an idealized assumption and an accurate real model; the accurate conversion of the fabric model from microscopic scale to microscopic scale can be completed; realizing the penetration and narrow gap repair among yarns, and the adjustment and attribute distribution of grid nodes; perfect engagement between yarn-to-yarn and yarn-to-substrate interfaces; obtaining a composite material grid model with material attribute information, and providing a basis for defining the isotropic attribute of the material; meanwhile, the grid model meets the periodic boundary of the representative volume unit; greatly improves the development efficiency and the simulation precision of the fabric composite material and reduces the development period of the fabric composite material.
Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by associated hardware instructed by a program, which may be stored in a computer-readable storage medium, and the storage medium may include: ROM, RAM, magnetic or optical disks, and the like.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (10)
1. A finite element modeling method of a fabric composite material based on a microscopic geometric model comprises the following steps:
(1) Establishing a representative volume unit microscopic geometric model of the woven fabric;
(2) Calculating the axial direction of the yarn based on the representative volume unit micro-geometric model, and outputting a surface triangular patch model of the woven fabric yarn;
(3) Establishing a composite material domain, adding a matrix material and dispersing the composite material domain into hexahedral units;
(4) Mapping the surface triangular patch model of the yarns in the step (2) into a composite material domain, calculating the intersection points of the triangular patches and grid lines in the composite material domain, and storing the topological relation of the intersection points of the surfaces of the grid lines;
(5) Repairing the interpeak permeation and narrow gaps between different yarns caused by scale conversion along the direction of the grid lines;
(6) Adjusting the grid nodes of the composite material domain to the surface intersection points of the adjacent grid lines, and setting topological labels of the grid nodes;
(7) Traversing surfaces of the hexahedral unit, judging splitting modes of corresponding six surfaces according to four grid nodes of each surface, and determining a splitting line;
(8) And splitting the hexahedral unit into a tetrahedron, a pyramid and a triangular prism again according to the splitting mode of six surfaces in the hexahedral unit, storing the hexahedral unit into a corresponding component unit set according to the label of each unit, and obtaining the material direction corresponding to each unit.
2. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1, wherein: the step (1) is specifically as follows:
(1.1) defining yarn parameters of all components of the woven fabric, the size of a representative volume unit and key nodes of the organization of the representative volume unit, and establishing a topological structure of the representative volume unit of the woven fabric;
and (1.2) setting boundary conditions of a topological structure and applying yarn tension, dispersing the yarns into micro-geometric units through yarn fiber discretization and fiber digital unit discretization, and performing numerical calculation on the dispersed yarns to obtain a micro-geometric unit model.
3. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1, wherein: the step (2) is specifically as follows:
(2.1) acquiring the three-dimensional coordinate data of the fiber nodes of the model in the step (1) and recording the corresponding topological relation;
(2.2) calculating the path node of the middle shaft of the yarn through the three-dimensional coordinate of the node, uniformly slicing the section of the yarn along the path direction of each yarn, and obtaining the interpolation point of each fiber on the section of the yarn;
(2.3) self-adaptively acquiring the boundary of the yarn section interpolation point in the step (2.2) by adopting a Delaunay triangularization algorithm and an Alpha-shape algorithm to obtain a polygonal boundary profile of the yarn section;
and (2.4) carrying out homogenization interpolation on the section polygon in the step (2.3) to obtain the vertex of a triangular patch, and then generating a surface triangular patch model of the yarn according to a specific sequence.
4. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1 wherein: the step (3) is specifically as follows:
(3.1) reading the size of a representative volume unit of the fabric, and setting two key nodes of min and max of a composite material domain;
(3.2) setting the size of a proper hexahedral unit according to the fiber size and the cross-section parameter of the fabric, and uniformly dispersing the material domain in the step (3.1) into hexahedral units with corresponding sizes.
5. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1, wherein: the step (4) is specifically as follows:
(4.1) mapping the triangular surface patch on the surface of the yarn to a composite material domain, calculating surface intersection points of the triangular surface patch and grid lines in the x direction, the y direction and the z direction, and recording topological information of the intersection points;
and (4.2) periodically mapping the grid line surface intersection points on the boundaries of the six surfaces of the composite material domain, so that the grid line surface intersection points meet the periodic boundary conditions of the representative volume units.
6. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1 wherein: the step (5) is specifically as follows:
(5.1) respectively extracting intersection points of the yarns on the grid line surfaces in the x direction, the y direction and the z direction and sequencing the intersection points according to the x coordinate value, the y coordinate value or the z coordinate value of the intersection points;
(5.2) adjusting the intersection point of the surfaces of two mutually-permeated different yarns into the middle point of two points according to the x, y or z value of the intersection point of the grid lines and the topological relation of the intersection point, and simultaneously interchanging the topological labels of the two nodes; and adjusting the intersection point of the surfaces of two different yarns with the distance smaller than the set threshold value to the midpoint of the two points.
7. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1 wherein: the step (6) is specifically as follows:
(6.1) reading the grid line surface intersection points adjusted in the step (5), judging adjacent grid nodes of the grid line surface intersection points, and storing the grid line surface intersection points in corresponding grid node adjacent linked lists;
(6.2) traversing all grid nodes, if the grid node adjacency linked list is zero, not adjusting the grid nodes, and simultaneously setting the labels of the grid nodes as corresponding single component labels; otherwise, adjusting the coordinates of the grid nodes to the middle points of the intersection points of all the adjacent surfaces, and setting the grid node labels as corresponding multi-component labels.
8. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1 wherein: the step (7) is specifically as follows:
reading four grid node labels corresponding to a quadrangle on the surface of the hexahedron unit, judging whether the quadrangle needs to be divided into two triangles or not according to the number of the labels and the types of the labels, and adding adjacent nodes of the nodes if the quadrangle needs to be divided.
9. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 1 wherein: the step (8) is specifically as follows:
(8.1) reading adjacent points of nodes of the hexahedral unit, dividing the hexahedral unit into one component, two components or three components according to the node labels, and dividing each corresponding component into a tetrahedron, pyramid or triangular prism unit;
(8.2) judging the path node of each unit corresponding to the adjacent yarn path in the step (2) of each unit set, and setting the material direction of each unit as the path direction of the node.
10. A method of finite element modeling of a fabric composite based on a micro-geometric model as claimed in claim 9 wherein: in the step (8.1), the splitting of the components includes adding nodes in the hexahedral unit for splitting.
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