CN109635391B - Simulation method of bicontinuous phase composite material - Google Patents
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Abstract
The invention relates to the technical field of simulation test of material performance, in particular to a simulation method of a bicontinuous phase composite material. The method comprises the following steps: simulating the structure of the bicontinuous phase composite material by adopting a Cahn-Hilliard equation to obtain a simulation equation of the structure of the bicontinuous phase composite material; step two, performing discrete processing on the simulation equation by adopting a central difference method to obtain a difference equation; acquiring phase coordinate position information of all components of the bicontinuous phase composite material according to the difference equation; and step four, embedding the coordinate position information of all the component phases into finite element software to obtain a simulation model of the bicontinuous phase composite material. According to the method, the calculation model capable of describing the mechanical behavior of the bicontinuous phase composite material can be obtained, the model can describe the spatial distribution of the bicontinuous structure, the mechanical property of the bicontinuous phase composite material can be predicted based on finite element analysis of the model, and the method is simple, high in efficiency and low in cost.
Description
Technical Field
The invention belongs to the technical field of simulation test of material performance, and particularly relates to a simulation method of a bicontinuous phase composite material.
Background
Because the bicontinuous phase composite material has a complex microstructure, the research on the mechanical properties of the bicontinuous phase composite material by adopting a numerical simulation method becomes a challenging work. With respect to the existing calculation model, the two-dimensional model is difficult to accurately describe the microstructure of the bicontinuous phase composite material, and actually, the components of the two-dimensional model are mutually communicated in a three-dimensional space, while the two components cannot maintain the connectivity in a two-dimensional space. Some three-dimensional models are regular in shape and greatly different from a real material microstructure, and the conventional three-dimensional random model has certain limitation because the connectivity is difficult to ensure due to the simple random mode. The finite element model is established based on the real microstructure of the experimental observation material, the process is complex, expensive instruments and equipment are needed, and the calculation efficiency is not high.
Accordingly, a technical solution is desired to overcome or at least alleviate at least one of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The invention aims to provide a simulation method of a bicontinuous phase composite material, which aims to solve at least one problem in the prior art.
The technical scheme of the invention is as follows:
a simulation method of a bicontinuous phase composite material comprises the following steps:
simulating the structure of the bicontinuous phase composite material by adopting a Cahn-Hilliard equation to obtain a simulation equation of the structure of the bicontinuous phase composite material;
step two, performing discrete processing on the simulation equation by adopting a central difference method to obtain a difference equation;
step three, acquiring phase coordinate position information of all components of the bicontinuous phase composite material according to the difference equation;
and step four, embedding the coordinate position information of all the component phases into finite element software to obtain a simulation model of the bicontinuous phase composite material.
Optionally, the simulation equation of the structure of the bicontinuous phase composite material in the first step is as follows:
wherein u (x, y, z, t) is a spatial position function of each component, x, y, z are spatial positions, t is evolution time, u t The derivative of u over t is taken as,
is a gradient operator, delta is a Laplace operator, f (u) is a free energy function, M (u) is a migration coefficient,
is the energy gradient coefficient.
Optionally, the free energy function f (u) is set to a twin-well potential function f (u) =1/4 (u) 2 -1) 2 。
Alternatively, the migration coefficient M (u) is set to a constant coefficient, and M (u) =1.
Optionally, coefficient of energy gradient
And will be
Is set as
Optionally, the difference equation in step two is:
wherein the content of the first and second substances,
τ is discrete time step, h is space step, and m, i, j, and k are different space position information.
Alternatively, the discrete time step is set to τ =0.01 and the spatial step is set to h =0.0001.
Optionally, the initial value of the spatial position function u in step two is a randomly generated set of numbers close to 0.
Optionally, before step three, the method further includes: setting a value u for distinguishing two-phase materials 0 If u > u 0 If u is less than or equal to u, the position is one phase material 0 Then the location is another phase of material.
Optionally, adjusting u 0 The volume fractions of the two different materials in the bicontinuous phase composite were varied.
The invention has at least the following beneficial technical effects:
according to the simulation method for the bicontinuous phase composite material, the calculation model capable of describing the mechanical behavior of the bicontinuous phase composite material can be easily obtained, the model can describe the spatial distribution of the bicontinuous structure, the mechanical property of the bicontinuous phase composite material can be predicted based on finite element analysis of the model, and the simulation method is simple, high in efficiency and low in cost.
Drawings
FIG. 1 is a flow chart of a simulation method for bicontinuous phase composite material of the present application;
FIG. 2 is a flow chart of a programmed simulation method for bicontinuous phase composite material according to the present application;
FIG. 3 is a schematic representation of a bicontinuous phase composite material in accordance with an embodiment of the present application;
FIG. 4 is a schematic view of a simulation model of a bicontinuous phase composite material in accordance with an embodiment of the present application.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are illustrative of some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention. 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. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate orientations or positional relationships based on those shown in the drawings, and are used merely for convenience in describing the present invention and for simplifying the description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore, should not be taken as limiting the scope of the present invention.
The present invention will be described in further detail with reference to fig. 1 to 2.
The application provides a simulation method of a bicontinuous phase composite material, which comprises the following steps:
simulating the structure of the bicontinuous phase composite material by adopting a Cahn-Hilliard equation to obtain a simulation equation of the structure of the bicontinuous phase composite material;
step two, performing discrete processing on the simulation equation by adopting a central difference method to obtain a difference equation;
acquiring phase coordinate position information of all components of the bicontinuous phase composite material according to the difference equation;
and step four, embedding the position information of all the component phase coordinates into finite element software to obtain a simulation model of the bicontinuous phase composite material.
In one embodiment of the present application, the Cahn-Hilliard equation is used to simulate the structure of the bicontinuous phase composite material, and the obtained simulation equation of the structure of the bicontinuous phase composite material is:
wherein u (x, y, z, t) is a spatial position function of each component, x, y, z are spatial positions, t is evolution time, u t The derivative of u over t is taken as,
is a gradient operator, delta is a Laplace operator, f (u) is a free energy function, M (u) is a migration coefficient,
is the energy gradient coefficient.
In this embodiment, a twin-well potential function f (u) =1/4 (u) is selected 2 -1) 2 And, setting the transfer function as a constant coefficient, taking M (u) =1, and then setting the energy gradient coefficient
In the step (1), the first step,
is set as
The value does not affect the calculation result of the application.
Further, the equation (1) is subjected to discrete processing by using a central difference method, and the following form is obtained:
wherein the content of the first and second substances,
τ is discrete time step, h is space step, and m, i, j, and k are different space position information.
When the nonlinear differential equation is solved by adopting a numerical method, it is particularly important to select a proper time step τ and a proper space step h. If the time step τ is too large, the convergence and stability of the result are not ideal, however, if the time step τ is too small, the calculation time is greatly increased, and the calculation efficiency is reduced. In the application, a time step τ =0.01 and a space step h =0.0001 are adopted, and the time step and the space step are suitable after a large number of attempts.
Before calculation, the initial value of the equation needs to be set, and since the random model has no quantitative requirement on the initial value, the initial value of the spatial position function u is taken as a set of randomly generated numbers close to 0. The setting of the equation boundary conditions is to adopt periodic boundary conditions in three directions, and the size of the model can be determined by the size of a calculation domain and is generally adjusted according to needs.
Before the third step, the method also comprises the following steps: setting a value u for distinguishing two-phase materials 0 If u is greater than or equal to u 0 That position is one of the phase materials, if u<u 0 Then the location is another phase of material. Therefore, the spatial information of each component phase in the bicontinuous phase composite material can be obtained, and the size of the model can be adjusted according to the calculation requirement. By adjusting u 0 The value of (c) can vary the volume fraction of the two different materials in the bicontinuous phase composite.
After all component phase coordinate position information of the bicontinuous phase composite material is collected, embedding the component phase coordinate position information into finite element software through a writing program, realizing the complete butt joint of a phase field equation and the finite element software, and finally obtaining a simulation model of the bicontinuous phase composite material.
According to the simulation method for the bicontinuous phase composite material, a program calculation flow chart is shown in fig. 2, and different model information can be obtained by changing the initial value and the evolution time of an equation. As shown in FIG. 3, in one embodiment of the present application, the Volume Fraction (VF) of both component phases in the simulation model of the bicontinuous phase composite is 50%. As can be seen from the figure, the two component phases have good connectivity in three-dimensional space and periodicity in all three directions. In this embodiment, the model size is 40 × 40 × 40, one voxel is placed on each position coordinate, different material attributes are given to the voxel at different position coordinates according to different component phase information, a perfect interface is considered between the two materials, and finally, the establishment of the three-dimensional random interpenetrating finite element model is completed, as shown in fig. 4.
According to the simulation method of the bicontinuous phase composite material, the calculation model for describing the mechanical behavior of the bicontinuous phase composite material can be obtained, the model can describe the spatial distribution of the bicontinuous structure, and the mechanical property of the bicontinuous phase composite material can be predicted based on finite element analysis of the model. The method is simple, high in efficiency and low in cost.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (10)
1. A simulation method of a bicontinuous phase composite material is characterized by comprising the following steps:
simulating the structure of the bicontinuous phase composite material by adopting a Cahn-Hilliard equation to obtain a simulation equation of the structure of the bicontinuous phase composite material;
step two, performing discrete processing on the simulation equation by adopting a central difference method to obtain a difference equation;
acquiring phase coordinate position information of all components of the bicontinuous phase composite material according to the difference equation;
and step four, embedding the coordinate position information of all the component phases into finite element software to obtain a simulation model of the bicontinuous phase composite material.
2. The method for simulation of a bicontinuous phase composite material as claimed in claim 1, characterized in that the simulation equation of the structure of the bicontinuous phase composite material in step one is:
wherein u (x, y, z, t) is a spatial position function of each component, x, y, z are spatial positions, t is evolution time, u t The derivative of u over t is taken as,
is a gradient operator, delta is a Laplace operator, f (u) is a free energy function, M (u) is a migration coefficient,
is the energy gradient coefficient.
3. The method for simulation of a bicontinuous phase composite material according to claim 2, characterized in that the free energy function f (u) is set as a twin-well potential function f (u) =1/4 (u) 2 -1) 2 。
4. The simulation method of a bicontinuous phase composite material according to claim 3, characterized in that the mobility coefficient M (u) is set to a constant coefficient, and M (u) =1.
5. The simulation method of the bicontinuous phase composite material of claim 4,characterised by an energy gradient coefficient
And will be provided with
Is set as
6. The method for simulation of a bicontinuous phase composite material according to claim 5, characterized in that in step two said difference equation is:
wherein the content of the first and second substances,
τ is discrete time step, h is space step, and m, i, j, and k are different space position information.
7. The method of claim 6, wherein the discrete time step is set at τ =0.01 and the spatial step is set at h =0.0001.
8. The method for simulation of a bicontinuous phase composite material in accordance with claim 7, characterized in that the initial value of spatial position function u in step two is a randomly generated set of numbers close to 0.
9. The simulation method of the bicontinuous phase composite material according to claim 8, further comprising, before step three: setting a value u for distinguishing between two phase materials 0 If u is greater than or equal to u 0 Then the position is one of the phase materials, if u<u 0 Then the location is another phase material.
10. The method of claim 9, wherein u is adjusted 0 The volume fractions of the two different materials in the bicontinuous phase composite were varied.
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