CN116227155B - Method for researching microscopic mechanical property of propellant - Google Patents
Method for researching microscopic mechanical property of propellant Download PDFInfo
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- CN116227155B CN116227155B CN202310032033.3A CN202310032033A CN116227155B CN 116227155 B CN116227155 B CN 116227155B CN 202310032033 A CN202310032033 A CN 202310032033A CN 116227155 B CN116227155 B CN 116227155B
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Abstract
The application discloses a method for researching the micro-mechanical property of a propellant, which belongs to the technical field of micro-mechanics and comprises the following steps: constructing a propellant microscopic particle filling model by using a molecular dynamics method; polygonal meshing is carried out on the propellant microscopic particle filling model by utilizing a meshing tool, and a propellant microscopic polygonal mesh model is obtained; designing a calculation scheme of the rigidity of the elastic particles of the propellant and the rigidity of the viscoelastic matrix; based on the propellant microscopic polygonal grid model, the propellant is subjected to stress relaxation simulation test by combining the propellant elastic particle rigidity and the viscoelastic matrix rigidity calculation scheme, so that the propellant microscopic mechanical property research is realized. The method can effectively cope with the complex microscopic geometric model of the propellant, and realizes the research on the microscopic mechanical properties of the propellant.
Description
Technical Field
The application relates to a method for researching the microscopic mechanical properties of a propellant, and belongs to the technical field of microscopic mechanics.
Background
The development direction of high loading, long service life and large range of solid missiles puts higher demands on the mechanical properties of solid propellants.
Currently, the development of solid propellant is still a semi-empirical semi-theoretical research method, and the development of the mechanical properties of propellant is difficult to develop. On the other hand, the prophetic mechanical property prophetic method of the propellant provides a research thought for the component design of the propellant. However, the conventional finite element method takes a lot of time to perform the meshing in terms of processing the prophetic mechanical property predictions of the propellant, and it is difficult to obtain a good meshing effect.
Disclosure of Invention
The application aims to provide a method for researching the micro-mechanical properties of a propellant, which can efficiently cope with a complex micro-geometric model of the propellant and realize the research on the micro-mechanical properties of the propellant.
In order to achieve the above purpose, the present application provides the following technical solutions:
a method for studying the microscopic mechanical properties of a propellant, comprising:
constructing a propellant microscopic particle filling model by using a molecular dynamics method;
polygonal meshing is carried out on the propellant microscopic particle filling model by utilizing a meshing tool, and a propellant microscopic polygonal mesh model is obtained;
calculating the rigidity of the elastic particles of the propellant and the rigidity of the viscoelastic matrix;
based on the propellant microscopic polygonal grid model, the propellant elastic particle rigidity and the viscoelasticity matrix rigidity are combined to perform stress relaxation simulation test on the propellant, so that the propellant microscopic mechanical property research is realized.
Further, using molecular dynamics methods, constructing a propellant fine particle filling model includes:
determining the number N of propellant grains according to the volume percentage of the propellant;
scattering N particles with initial radius of 0 in the coordinate range of the microscopic size of the propellant;
each of the particles is grown at a predetermined rate until its radius increases to a design value to construct a propellant fine particle filling model.
Further, constructing a space rectangular coordinate system by taking the center of the propellant microscopic particle filling model as an origin, wherein the dimensionless coordinate range of each particle is [ -1,1]Let the boundary vertex coordinates of the ith grain be eta i If eta i >1, let eta i ＝η i -2, if eta i <-1, let eta i ＝η i +2。
Further, performing polygonal meshing on the propellant microscopic particle filling model by using a meshing tool, wherein obtaining the propellant microscopic polygonal meshing model comprises:
stretching the propellant microscopic particle filling model from two dimensions to three dimensions to obtain a three-dimensional geometric model;
performing polygon meshing on the three-dimensional geometric model by adopting a ANASYS fluent meshing meshing tool;
and extracting surface information of the polyhedron from the three-dimensional geometric model divided by the polygonal mesh to obtain the propellant microscopic polygonal mesh model.
Further, calculating the propellant elastane particle stiffness and the viscoelastic matrix stiffness comprises:
defining a mapping operator from the virtual cell space to the cell polynomial space;
acquiring an expression of a basis function and a unit stiffness matrix by using the mapping operator;
and calculating the rigidity of the elastic particles of the propellant and the rigidity of the visco-elastic matrix according to the basic function and the expression of the unit rigidity matrix.
Further, the mapping operator has an orthogonal relationship as shown in formula (1) for each function in the virtual cell space:
in the formula (1), P k (E) Is a unit polynomial space, p k Is a unit polynomial space P k (E) Is selected from the group consisting of,to map operator, v h Is a virtual unit space V k (E) E is a cell region.
Further, the expression of the basis function is shown in formula (2):
in the formula (2),as a basis function, i is the ordinal number of the basis function;
the expression of the rigidity matrix is shown in formula (3):
in the formula (3), K E Is a rigidity matrix, I is an identity matrix,g is the second auxiliary matrix.
Further, performing a stress relaxation simulation test on the propellant includes:
restraining the longitudinal displacement and left lateral displacement of the bottom of the propellant microscopic polygonal grid model, applying 5% of longitudinal step strain on the top of the propellant microscopic polygonal grid model, and keeping for 1000s;
calculating the average stress and average strain of the propellant microscopic polygonal grid model according to the rigidity of the propellant elastic particles and the rigidity of the visco-elastic matrix;
calculating the loose modulus of the propellant under different representative volume unit sizes according to the average stress and the average strain of the propellant microscopic polygonal grid model;
reducing the size of the representative volume element until the relative error of the relaxed modulus exceeds 5%;
and according to each relaxation modulus, realizing the research on the microscopic mechanical properties of the propellant.
Further, the average stress of the propellant microscopic polygonal mesh model is the average stress of each node of the propellant microscopic polygonal mesh model, and the average strain of the propellant microscopic polygonal mesh model is the average strain of each node of the propellant microscopic polygonal mesh model.
Further, the representative volume units are micro structures extracted from the composite material as a whole for studying the performance of the composite material.
Compared with the prior art, the application has the beneficial effects that:
compared with the traditional finite element method, the method can effectively cope with the complex microscopic geometric model of the propellant. Under the condition that the total number of degrees of freedom is the same, the application can construct more entity units for propellant microscopic geometric modeling.
Drawings
FIG. 1 is a flow chart of a method for researching the microscopic mechanical properties of a propellant, which is provided by the embodiment of the application;
FIG. 2 is a schematic illustration of a particle according to an embodiment of the present application when a "wire-pressing" event occurs;
FIG. 3 is a schematic illustration of a propellant fine particle filling model provided by an embodiment of the present application;
FIG. 4 is a schematic view of a three-dimensional geometric model provided by an embodiment of the present application;
FIG. 5 is a schematic diagram of a three-dimensional geometric model polygon meshing provided by an embodiment of the present application;
FIG. 6 is a schematic diagram of a propellant microscopic polygon mesh model provided by an embodiment of the present application;
fig. 7 is an axial stress cloud of a propellant mesostructure according to an embodiment of the present application relaxed to a time of 1000 s.
Detailed Description
The technical scheme of the patent is further described in detail below with reference to the specific embodiments.
Embodiments of the present patent are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present patent and are not to be construed as limiting the present patent. The embodiments of the present application and technical features in the embodiments may be combined with each other without collision.
Embodiment one:
fig. 1 is a flowchart of a method for researching the micro-mechanical properties of a propellant, which is provided in the first embodiment of the present application, and the flowchart merely shows the logic sequence of the method in this embodiment, and on the premise of not conflicting with each other, in other possible embodiments of the present application, the steps shown or described can be completed in a different sequence from that shown in fig. 1.
Referring to fig. 1, the method of this embodiment specifically includes the following steps:
step one: constructing a propellant microscopic particle filling model by using a molecular dynamics method;
the construction of the propellant microscopic particle filling model by using a molecular dynamics method comprises the following steps:
step A: determining the number N of propellant grains according to the volume percentage of the propellant;
and (B) step (B): scattering N particles with initial radius of 0 in the coordinate range of the microscopic size of the propellant;
the coordinates of the microscopic dimensions of the propellant range from: in the two-dimensional plane, point a (0, 0), point B (L, 0), point C (L, L), and point D (0, L) are four-point lines, where L is the propellant mesoscopic size.
Step C: growing each particle at a predetermined rate until its radius increases to a design value to form a propellant fine particle filling model;
during the radius becoming larger, when particles collide, the particles spring in the opposite direction, and so on, until the radius increases to the design value.
In order to describe the mechanical response of a true mesostructure, the propellant mesogranule filling model must meet the requirements of the periodic geometry and the periodic boundary conditions. For the periodic geometry, if a particle "line-up" event occurs during particle loading, as shown in fig. 2, there is a corresponding particle on the corresponding geometric side (or face in the three-dimensional model) to satisfy the constraint of the periodic geometry. Furthermore, the number of particles and the corresponding geometry are fixed values calculated according to the formulation of the material and cannot be changed by the filling process before the particle filling is carried out.
In order to solve the problems of periodic geometry and periodic boundary conditions, a space rectangular coordinate system is constructed by taking the center of a propellant microscopic particle filling model as an origin, and the dimensionless coordinate range of each particle is [ -1,1]Let the boundary vertex coordinates of the ith grain be eta i If eta i >1, let eta i ＝η i -2, if eta i <-1, let eta i ＝η i +2。
By this method, it is possible to have all the particles "pressed" symmetrically on the corresponding geometric border of the model, while the number of particles is increased compared to the number initially calculated, without affecting the total packing fraction. As shown in fig. 3, a propellant fine particle filling model is generated by filling propellant particles by a molecular dynamics method, in fig. 3, circles are particles, and the rest is a matrix.
Step two: polygonal mesh division is carried out on the propellant microscopic particle filling model by utilizing a mesh division tool, and a propellant microscopic polygonal mesh model is obtained;
polygonal meshing is carried out on the propellant microscopic particle filling model by utilizing a meshing tool, and the propellant microscopic polygonal meshing model is obtained, wherein the method comprises the following steps of:
step a: stretching the propellant microscopic particle filling model from two dimensions to three dimensions to obtain a three-dimensional geometric model;
step b: adopting a ANASYS fluent meshing mesh dividing tool to carry out polygonal mesh division on the three-dimensional geometric model;
step c: extracting surface information of a polyhedron from the three-dimensional geometric model divided by the polygonal mesh to obtain a propellant microscopic polygonal mesh model;
at present, polygon meshing is relatively more software, but is a ANASYS fluent meshing meshing tool relatively mature. Since the meshing tool now only supports meshing of three-dimensional geometry, the propellant microscopic particle filling model in fig. 3 needs to be stretched to obtain the three-dimensional geometry model shown in fig. 4, then the obtained three-dimensional geometry model is imported into the ANASYS fluent meshing meshing tool, the three-dimensional geometry model is subjected to polygonal meshing by the ANASYS fluent meshing meshing tool, finally the propellant microscopic polygonal meshing model is obtained by extracting polyhedral surface information, and the obtained propellant microscopic polygonal meshing model is shown in fig. 6.
Step three: calculating the rigidity of the elastic particles of the propellant and the rigidity of the viscoelastic matrix;
the calculation of the propellant elastane particle stiffness and viscoelastic matrix stiffness comprises the steps of:
step I: defining a slave virtual cell space V k (E) To the unit polynomial space P k (E) Mapping operator of (a)
Step II: using mapping operatorsAcquiring a basis function->And cell stiffness matrix K E Is an expression of (2);
step III: root of Chinese characterAccording to the basis functionAnd cell stiffness matrix K E Calculating the propellant elastane particle stiffness and viscoelastic matrix stiffness;
wherein the mapping operatorFor the virtual cell space V k (E) Is a function v h There is an orthogonal relationship as shown in equation (1):
in the formula (1), P k (E) Is a unit polynomial space, p k Is a unit polynomial space P k (E) Is selected from the group consisting of,to map operator, v h Is a virtual unit space V k (E) E is a cell region.
The expression of the basis function is shown in formula (2):
in the formula (2),as a basis function, i is the ordinal number of the basis function;
the expression of the stiffness matrix is shown in formula (3):
in the formula (3), K E Is a rigidity matrix, I is an identity matrix,g is the second auxiliary matrix.
Substituting the elasticity and the viscoelasticity of the propellant into the formula (3), and obtaining the rigidity of the elastic particles and the rigidity of the viscoelasticity matrix of the propellant through calculation.
Step four: based on a propellant microscopic polygonal grid model, combining the rigidity of elastic particles of the propellant and the rigidity of a viscoelastic matrix, performing stress relaxation simulation test on the propellant, and realizing the research on the microscopic mechanical properties of the propellant;
based on a propellant microscopic polygonal grid model, combining the rigidity of propellant elastic particles and the rigidity of a visco-elastic matrix, carrying out stress relaxation simulation test on the propellant, and realizing the research on the microscopic mechanical properties of the propellant, wherein the method comprises the following steps:
step i: restraining longitudinal displacement of the bottom and left lateral displacement of the propellant microscopic polygonal grid model, applying 5% of longitudinal step strain on the top of the propellant microscopic polygonal grid model, and keeping the top of the propellant microscopic polygonal grid model for 1000s;
step ii: calculating average stress and average strain of the propellant microscopic polygonal grid model according to the rigidity of the propellant elastic particles and the rigidity of the visco-elastic matrix;
step iii: calculating the loose modulus of the propellant under different representative volume unit sizes according to the average stress and the average strain of the propellant microscopic polygonal grid model;
step iv: decreasing the size of the representative volume unit until the relative error in the relaxed modulus exceeds 5%;
step v: according to each relaxation modulus, the research on the microscopic mechanical properties of the propellant is realized;
the average stress of the propellant microscopic polygonal mesh model is the average stress of each node of the propellant microscopic polygonal mesh model, and the average strain of the propellant microscopic polygonal mesh model is the average strain of each node of the propellant microscopic polygonal mesh model.
The representative volume units are micro structures extracted from the composite material as a whole for studying the properties of the composite material. The loose moduli of the propellant under different sizes of the representative volume units are calculated respectively, the sizes of the representative volume units are reduced until the relative error of the loose moduli exceeds 5%, and the loose moduli are the loose moduli of the propellant under the components, and as shown in fig. 7, are axial stress cloud diagrams of the mesoscopic structure of the propellant when the loose to 1000 s.
Compared with the traditional finite element method, the method for researching the micro-mechanical properties of the propellant can efficiently cope with complex micro-geometric models of the propellant and realize the research on the micro-mechanical properties of the propellant. Under the condition that the total number of degrees of freedom is the same, the application can construct more entity units for propellant microscopic geometric modeling.
The foregoing is merely a preferred embodiment of the present application, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present application, and such modifications and variations should also be regarded as being within the scope of the application.
Claims (6)
1. A method for studying the microscopic mechanical properties of a propellant, comprising:
constructing a propellant microscopic particle filling model by using a molecular dynamics method;
polygonal meshing is carried out on the propellant microscopic particle filling model by utilizing a meshing tool, and a propellant microscopic polygonal mesh model is obtained;
calculating the rigidity of the elastic particles of the propellant and the rigidity of the viscoelastic matrix;
based on the propellant microscopic polygonal grid model, combining the propellant elastic particle rigidity and the viscoelasticity matrix rigidity, performing stress relaxation simulation test on the propellant to realize propellant microscopic mechanical property research;
calculating the propellant elastane particle stiffness and viscoelastic matrix stiffness includes:
defining a mapping operator from the virtual cell space to the cell polynomial space;
acquiring an expression of a basis function and a unit stiffness matrix by using the mapping operator;
calculating the rigidity of elastic particles of the propellant and the rigidity of the viscoelastic matrix according to the basic function and the expression of the unit rigidity matrix;
the mapping operator has an orthogonal relationship for each function in the virtual cell space as shown in equation (1):
in the formula (1), P k (E) Is a unit polynomial space, p k Is a unit polynomial space P k (E) Is selected from the group consisting of,to map operator, v h Is a virtual unit space V k (E) E is a unit area;
the expression of the basis function is shown in formula (2):
in the formula (2),as a basis function, i is the ordinal number of the basis function;
the expression of the rigidity matrix is shown in formula (3):
in the formula (3), K E Is a rigidity matrix, I is an identity matrix,g is the second auxiliary matrix.
2. The method of claim 1, wherein constructing a model of propellant microscopic particle packing using molecular dynamics methods comprises:
determining the number N of propellant grains according to the volume percentage of the propellant;
scattering N particles with initial radius of 0 in the coordinate range of the microscopic size of the propellant;
each of the particles is grown at a predetermined rate until its radius increases to a design value to construct a propellant fine particle filling model.
3. The method for studying the microscopic mechanical properties of a propellant according to claim 2, wherein a space rectangular coordinate system is constructed with the center of the propellant microscopic particle filling model as an origin, and the dimensionless coordinate range of each particle is [ -1,1]Let the boundary vertex coordinates of the ith grain be eta i If eta i >1, let eta i ＝η i -2, if eta i <-1, let eta i ＝η i +2。
4. The method of claim 1, wherein performing polygonal meshing of the propellant microscopic particle filling model with a meshing tool to obtain a propellant microscopic polygonal mesh model comprises:
stretching the propellant microscopic particle filling model from two dimensions to three dimensions to obtain a three-dimensional geometric model;
performing polygon meshing on the three-dimensional geometric model by adopting a ANASYS fluent meshing meshing tool;
and extracting surface information of the polyhedron from the three-dimensional geometric model divided by the polygonal mesh to obtain the propellant microscopic polygonal mesh model.
5. The method of claim 1, wherein performing a stress relaxation simulation test on the propellant based on the propellant microscopic polygonal mesh model in combination with the propellant elastic particle stiffness and the viscoelastic matrix stiffness, the performing the propellant microscopic mechanical property study comprises:
restraining the longitudinal displacement and left lateral displacement of the bottom of the propellant microscopic polygonal grid model, applying 5% of longitudinal step strain on the top of the propellant microscopic polygonal grid model, and keeping for 1000s;
calculating the average stress and average strain of the propellant microscopic polygonal grid model according to the rigidity of the propellant elastic particles and the rigidity of the visco-elastic matrix;
calculating the loose modulus of the propellant under different representative volume unit sizes according to the average stress and the average strain of the propellant microscopic polygonal grid model;
reducing the size of the representative volume element until the relative error of the relaxed modulus exceeds 5%;
according to each relaxation modulus, realizing the research on the microscopic mechanical properties of the propellant;
the representative volume units are micro structures extracted from the composite material as a whole for studying the performance of the composite material.
6. The method for studying the microscopic mechanical properties of a propellant according to claim 5, wherein the average stress of the microscopic polygonal mesh model of the propellant is an average value of the stress of each node of the microscopic polygonal mesh model of the propellant, and the average strain of the microscopic polygonal mesh model of the propellant is an average value of the strain of each node of the microscopic polygonal mesh model of the propellant.
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