CN111881604A - Three-dimensional finite element model modeling method for Thiessen polygon subdivision - Google Patents
Three-dimensional finite element model modeling method for Thiessen polygon subdivision Download PDFInfo
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Abstract
The invention discloses a three-dimensional finite element model modeling method of Thiessen polygon subdivision, which comprises the following steps: (1) establishing a hexahedron finite element model; (2) the finite element model is divided into grids; (3) randomly generating Thiessen polygonal seeds; (4) dividing the finite element model into a plurality of unit sets according to the perpendicular bisector of two adjacent Thiessen polygonal seeds; (5) a collection is treated as a grain and grain properties such as grain orientation are imparted. The method is used for simulating the real microstructure of the polycrystalline material and randomly generating the Thiessen polygonal seeds, so that the contingency can be effectively avoided, the fault tolerance rate is improved, the batch processing is facilitated, the model is closer to the real, and the reliability of the mechanical calculation is higher.
Description
Technical Field
The invention relates to the field of material science crystallography, in particular to a three-dimensional finite element model modeling method for Thiessen polygon subdivision.
Background
The Thiessen polygons are a set of continuous polygons formed by perpendicular bisectors connecting two adjacent point line segments. The method is characterized in that the distance from any point in the Thiessen polygon to the control point forming the polygon is less than the distance from any point in the Thiessen polygon to the control point of other polygons.
The grains of the metal material or the polycrystalline material are actually different in size and shape. The traditional finite element model cannot truly describe the microstructure of the material and cannot reflect the uneven deformation in the crystal. And the three-dimensional finite element model is divided by using the Thiessen polygon, and the properties of each crystal grain are endowed to each crystal grain, so that the polycrystalline metal material can be better simulated.
The three-dimensional finite element model of the Thiessen polygon subdivision is used for researching a microscopic constitutive model of the polycrystalline material. Compared with the simulation of the material by adopting the macroscopic structure, the finite element model split by the Thiessen polygon can consider the anisotropy of the microstructure of the material caused by the difference of the grain orientation at the grain size during the simulation. Compared with other mesomechanics methods such as a self-consistent method for simulating the polycrystalline material, the method can reflect the nonuniformity of internal deformation, the interaction among crystal grains and the evolution of texture of the material in the loading process. Meanwhile, complicated boundary conditions are applied to a finite element model of the Thiessen polygon subdivision more easily, and the method is more suitable for simulating engineering problems.
In the prior art, when a finite element model is modeled, a Thiessen polygon is firstly divided, and then meshing is carried out. Although the geometric features at the grain boundaries can be preserved, only tetrahedral units can be used due to the irregularities of the Thiessen polygons and the shapes and sizes of the units vary greatly from grain shape to grain shape, and units of considerably poor quality are produced under some special geometries, causing singularity. The method needs a large amount of computing resources, the solving error of the tetrahedral unit is overlarge, and the solving result is overlarge in error and irrevocable due to the accumulation of a large amount of errors caused by maintaining the geometric characteristics of the interface.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a three-dimensional finite element model modeling method suitable for Thiessen polygon subdivision of a polycrystalline metal material.
In order to achieve the above object, the present invention provides a method for modeling a three-dimensional finite element model divided by a Thiessen polygon, comprising: the method comprises the following steps:
(1) establishing a hexahedron finite element model;
(2) the finite element model is divided into grids;
(3) randomly generating Thiessen polygonal seeds;
(4) dividing the finite element model into a plurality of unit sets according to the perpendicular bisector of two adjacent Thiessen polygonal seeds;
(5) a collection is treated as a grain and grain properties such as grain orientation are imparted.
Preferably, in the step (1), a hexahedral solid part is established by using finite element analysis software Abaqus;
in the step (2), the part is divided into grids by using finite element analysis software Abaqus; dispersing the component into a finite element model consisting of three-dimensional eight-node units;
in the step (3), a Python command line built in the finite element analysis software Abaqus is used, and random modules are used for randomly generating Thiessen polygon seeds with the number equal to the number of the polycrystalline material grains.
Further, the specific steps in the step (4) are as follows:
(4.1) averaging and calculating the coordinate of the geometric center of the unit according to the eight node coordinates of each unit;
(4.2) calculating the distance between the coordinates of the geometric center of each unit and all Thiessen polygon seeds;
(4.3) obtaining the nearest Thiessen polygon seeds from the geometric center of each unit through comparison;
(4.4) creating a set of cells for all cells closest to the same Thiessen polygon seed.
Further, in the step (4.1), the coordinates of the geometric center of the unit are calculated by averaging the coordinates of the eight nodes of each unit, specifically:
(4.1.1) using a Python language command mdb.models [ 'model name' ]. parts [ 'part name' ] provided by the Abaqus command line to read all the part information of the part to be processed and to assign a variable part to represent the part to be processed;
(4.1.2) reading all node information of the current part using the command part.nodes and giving list nodes; each element in nodes represents a node; each node stores the coordinates of the node;
(4.1.3) reading all the unit information of the current part using the command part. each element in the elements represents a unit; the connection attribute in each element stores the node numbers of the eight nodes forming the element;
(4.1.4) reading each node number constituting each cell by the connectivity attribute of the cell, and calculating the coordinates of the geometric center of the cell by combining the coordinates of each node number in the nodes list.
Still further, the step (4.2) calculates the distances of the coordinates of the geometric center of each cell from all the Thiessen polygon seeds: and traversing all the component units, and calculating the distance between each unit and each Thiessen polygon seed.
Further, in the step (4.4), each unit is put into the unit set of the Thiessen polygonal seed nearest to the unit set, specifically:
(4.4.1) establishing a dictionary, wherein the key is a Thiessen polygon seed number, and the value is a list for recording the unit numbers of the units belonging to the key; traversing all the units, and putting the unit numbers into a list of Thiessen polygon seed numbers belonging to the units;
(4.4.2) creating a Unit set: set () method is used to create a set of units for each Thiessen polygon seed, read the list of values in the dictionary that belong to it, and put all units in the list into the set of units.
The invention has the following advantages and beneficial effects:
in the invention, meshes are divided firstly and then Thiessen polygon subdivision is carried out. In the modeling process of the finite element model, regular eight-node hexahedron units are divided first, and then all the crystal grains are put into unit sets. The finished hexahedron unit does not need to worry about grid quality, and the consumption of computing resources is far lower than that of the existing scheme. Although the edges of the crystal grains generate jagged edges and surfaces, the calculation accuracy of the model is not greatly influenced under the condition of sufficient grid density. Even if the scheme uses more units, the consumption of computing resources is far smaller than that of the existing scheme, and the computing error is smaller than that of the existing scheme caused by overlarge unit shape and size difference.
Drawings
FIG. 1 is a flow chart of a three-dimensional finite element model modeling method of Thiessen polygon subdivision of the present invention.
FIG. 2 is a three-dimensional finite element model of the Thiessen polygon subdivision of the present invention.
Detailed Description
The invention is further described below with reference to specific embodiments and the accompanying drawings.
The invention discloses a finite element model modeling method suitable for an amplitude modulation decomposition tissue of a nano porous material, the flow of the method is shown in figure 1, and the method comprises the following concrete implementation steps:
step 1: establishing a hexahedron finite element model:
an initial model-1 was used to build a three-dimensional deformable solid element with dimensions 60X 60, part name part-1.
Step 2: grid division of the finite element model:
for a grid-divided cell, the approximate global size is 1. The part has 60 × 60 × 60 units of 216000 units.
And step 3: randomly generating Thiessen polygonal seeds:
an Abaqus command line import random module was used to generate 20 random three-dimensional coordinate points as seeds of the Thiessen polygon of 20 grains.
And 4, step 4: dividing the finite element model into a plurality of unit sets according to the perpendicular bisector of two adjacent Thiessen polygonal seeds:
1. and averaging the coordinates of the geometric center of the calculation unit according to the eight node coordinates of each unit:
1) the model [ 'model-1' ]. part [ 'part-1' ]. elements command is used to read all the elements of the part-1 of the model-1 and to assign the variables elements.
2) The node numbers of the eight nodes constituting each cell are read using elements [0]. connection-elements [215999]. connection command.
3) The mdb.model [ 'model-1' ]. part [ 'part-1' ]. nodes command is used to read all the nodes of the part-1 of the model-1 and to assign the variable nodes.
4) The node numbers of the respective units are read according to the elements of the respective units and the node coordinates of the respective nodes are read through nodes.
5) The coordinates of the cell center are calculated from the node coordinates of the eight nodes of each cell.
2. Calculating the distance between the coordinates of the geometric center of each unit and all Thiessen polygon seeds and establishing a dictionary:
1) a dictionary is created with keys of Thiessen polygon seed numbers 1-20 and a null list.
2) And traversing all the units, calculating the distance between one unit and all the Thiessen polygon seeds, finding the Thiessen polygon seed closest to the unit, and recording the unit number in a list of the Thiessen polygon seed numbers with the key of the dictionary as the key closest to the unit.
3. Each cell is placed into the set of cells of the Thiessen polygon seed that is closest to it.
1) A unit list set elements is created for each thiessen polygon seed.
2) Adding units into a unit list in an index mode:
set _ elements + elements [ element number: element number +1]
3) Set () method creates a set of units for all units belonging to the same grain (i.e. nearest to the same thieson polygon seed):
set (elements set _ elements, name unit set name)
And 5: a collection is treated as a grain and grain properties such as grain orientation are imparted.
Claims (6)
1. A three-dimensional finite element model modeling method of Thiessen polygon subdivision is characterized in that: the method comprises the following steps:
(1) establishing a hexahedron finite element model;
(2) the finite element model is divided into grids;
(3) randomly generating Thiessen polygonal seeds;
(4) dividing the finite element model into a plurality of unit sets according to the perpendicular bisector of two adjacent Thiessen polygonal seeds;
(5) a collection is treated as a grain and grain properties such as grain orientation are imparted.
2. The method of modeling a three-dimensional finite element model of a Thiessen polygon subdivision of claim 1, wherein: in the step (1), establishing a hexahedral solid part by using finite element analysis software Abaqus;
in the step (2), the part is divided into grids by using finite element analysis software Abaqus; dispersing the component into a finite element model consisting of three-dimensional eight-node units;
in the step (3), a Python command line built in the finite element analysis software Abaqus is used, and random modules are used for randomly generating Thiessen polygon seeds with the number equal to the number of the polycrystalline material grains.
3. The method of modeling a three-dimensional finite element model of a Thiessen polygon subdivision according to claim 1 or 2, characterized in that: the specific steps in the step (4) are as follows:
(4.1) averaging and calculating the coordinate of the geometric center of the unit according to the eight node coordinates of each unit;
(4.2) calculating the distance between the coordinates of the geometric center of each unit and all Thiessen polygon seeds;
(4.3) obtaining the nearest Thiessen polygon seeds from the geometric center of each unit through comparison;
(4.4) creating a set of cells for all cells closest to the same Thiessen polygon seed.
4. The method of modeling a three-dimensional finite element model of a Thiessen polygon subdivision of claim 3, wherein:
in the step (4.1), the coordinates of the geometric center of the computing unit are averaged according to the coordinates of the eight nodes of each unit, specifically:
(4.1.1) using a Python language command mdb.models [ 'model name' ]. parts [ 'part name' ] provided by the Abaqus command line to read all the part information of the part to be processed and to assign a variable part to represent the part to be processed;
(4.1.2) reading all node information of the current part using the command part.nodes and giving list nodes; each element in nodes represents a node; each node stores the coordinates of the node;
(4.1.3) reading all the unit information of the current part using the command part. each element in the elements represents a unit; the connection attribute in each element stores the node numbers of the eight nodes forming the element;
(4.1.4) reading each node number constituting each cell by the connectivity attribute of the cell, and calculating the coordinates of the geometric center of the cell by combining the coordinates of each node number in the nodes list.
5. The method of modeling a three-dimensional finite element model of a Thiessen polygon subdivision of claim 4, wherein:
the step (4.2) calculates the distance between the coordinates of the geometric center of each unit and all Thiessen polygon seeds: and traversing all the component units, and calculating the distance between each unit and each Thiessen polygon seed.
6. The method of modeling a three-dimensional finite element model of a Thiessen polygon subdivision of claim 5, wherein:
in the step (4.4), each unit is placed in the unit set of the Thiessen polygonal seeds closest to the unit set, specifically:
(4.4.1) establishing a dictionary, wherein the key is a Thiessen polygon seed number, and the value is a list for recording the unit numbers of the units belonging to the key; traversing all the units, and putting the unit numbers into a list of Thiessen polygon seed numbers belonging to the units;
(4.4.2) creating a Unit set: set () method is used to create a set of units for each Thiessen polygon seed, read the list of values in the dictionary that belong to it, and put all units in the list into the set of units.
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| CN113221416A (en) * | 2021-05-14 | 2021-08-06 | 上海工程技术大学 | Method for constructing two-dimensional microstructure of particle-reinforced composite material |
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