CN113722879A - Method and system for determining mechanical property of microstructure based on homogenization theory - Google Patents

Method and system for determining mechanical property of microstructure based on homogenization theory Download PDF

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CN113722879A
CN113722879A CN202110807357.0A CN202110807357A CN113722879A CN 113722879 A CN113722879 A CN 113722879A CN 202110807357 A CN202110807357 A CN 202110807357A CN 113722879 A CN113722879 A CN 113722879A
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吕琳
刘培庆
刘安
彭昊
田李昊
王忠仁
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Abstract

The invention belongs to the field of microstructure mechanical property analysis, and provides a method and a system for determining microstructure mechanical property based on a homogenization theory. Wherein the method comprises converting a mesh model of the microstructure into a voxel model; calculating linear elastic parameters of the microstructure based on the elastic performance parameters and the voxel model of the base material of the microstructure, wherein the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Misses stress distribution of the microstructure under the worst load working condition; calculating equivalent yield strength of the microstructure under different stresses based on the voxel model to obtain elastoplasticity parameters of the microstructure; and summarizing linear elastic parameters and elastic-plastic parameters of the microstructure, and drawing a microstructure physical property image for customized application and target property optimization of the microstructure.

Description

Method and system for determining mechanical property of microstructure based on homogenization theory
Technical Field
The invention belongs to the field of microstructure mechanical property analysis, and particularly relates to a microstructure mechanical property determination method and system based on a homogenization theory.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The microstructure refers to a geometric structure in a very small range with respect to the model as a whole. The metamaterial which is designed and manufactured by applying the microstructure in the material science greatly expands the physical property space of the original material, thereby realizing the physical property requirements which cannot be met by the uniform material, such as light weight and high strength requirements required by aerospace parts, energy absorption performance required by the automobile industry, negative poisson's ratio required by the biomedical field, material transmission performance and the like.
Additive manufacturing, commonly known as 3D printing, refers to a technique of forming a three-dimensional solid by accumulating and superimposing materials point by point layer by layer through discretization-accumulation, and parts of any complex shape can be rapidly and precisely manufactured on one device. With the increasing abundance of manufacturing materials and the increasing precision of machining, the manufacture of complex microstructures for a variety of applications is made possible. For example, Carbon corporation has manufactured a midsole of sports shoes carrying a lattice structure using digital optical synthesis technology, and the complicated lattice structure can disperse pressure of various sports while ensuring lightness of the midsole. Since the microstructure can bring excellent physical properties, in recent years, researchers have designed and manufactured microstructures of various forms and have been expanding the application range.
The microstructure can be formed into an integral model by periodically and densely paving basic units, and a regular hexahedral unit is mostly adopted. As an essential element constituting the microstructure, researchers have designed microstructure units of different forms, for example, a rod-like structure, a sheet-like structure, a foam structure, and the like. The microstructures in different forms have respective performance characteristics and applicable scenes.
Researchers analyze the mechanical properties of the microstructure through methods such as physical tests, structural analysis, finite element analysis and the like. The physical test method comprises the steps of carrying out compression or tensile test on the manufactured microstructure solid model, and acquiring the mechanical property of the microstructure according to the recorded force and displacement data; the structural analysis means that the microstructure units are decomposed into a plurality of basic components, and then an analysis model based on the basic components is established; finite element analysis refers to the simulation of the microstructure under a specific load working condition by using a mathematical approximation method, and the mechanical properties of the microstructure are obtained according to force and displacement data. However, the inventor finds that the physical test requires complicated equipment and test standards, the mechanical properties provided by structural analysis are limited, and the finite element analysis method has higher computational complexity.
Disclosure of Invention
In order to solve the technical problems in the background art, the invention provides a microstructure mechanical property determination method and a microstructure mechanical property determination system based on a homogenization theory, wherein in order to quickly, accurately and comprehensively obtain the mechanical property of a microstructure, on the basis of the homogenization theory, under the assumption of a periodic boundary, the microstructure units are analyzed to obtain the equivalent Young modulus, shear modulus, Poisson's ratio, compressive strength and shear strength of the microstructure, and the elastic anisotropy and stress distribution of the microstructure are displayed, so that the comprehensive analysis and comprehensive understanding of the microstructure mechanical property are realized, and a basis is provided for the customized application and target property optimization of the microstructure.
In order to achieve the purpose, the invention adopts the following technical scheme:
the first aspect of the invention provides a method for determining the mechanical property of a microstructure based on homogenization theory.
A method for determining the mechanical property of a microstructure based on homogenization theory comprises the following steps:
converting the grid model of the microstructure into a voxel model;
calculating linear elastic parameters of the microstructure based on the elastic performance parameters and the voxel model of the base material of the microstructure, wherein the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Misses stress distribution of the microstructure under the worst load working condition;
calculating equivalent yield strength of the microstructure under different stresses based on the voxel model to obtain elastoplasticity parameters of the microstructure;
and summarizing linear elastic parameters and elastic-plastic parameters of the microstructure, and drawing a microstructure physical property image for customized application and target property optimization of the microstructure.
A second aspect of the invention provides a system for determining mechanical properties of a microstructure based on homogenization theory.
A homogenization theory based microstructure mechanical property determination system, comprising:
a voxel model conversion module for converting the grid model of the microstructure into a voxel model;
the linear elastic parameter calculation module is used for calculating linear elastic parameters of the microstructure based on the elastic performance parameters and the voxel model of the base material of the microstructure, and the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Misses stress distribution of the microstructure under the worst load working condition;
the elastic-plastic parameter calculation module is used for calculating the equivalent yield strength of the microstructure under different stresses based on the voxel model to obtain the elastic-plastic parameters of the microstructure;
and the physical performance portrait drawing module is used for summarizing linear elastic parameters and elastic-plastic parameters of the microstructure and drawing a microstructure physical performance portrait so as to be used for customization application and target performance optimization of the microstructure.
A third aspect of the invention provides a computer-readable storage medium.
A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method for determining a mechanical property of a microstructure based on homogenization theory as described above.
A fourth aspect of the invention provides a computer apparatus.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the homogenization theory based microstructure mechanical property determination method as described above when executing the program.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method is characterized in that a grid model of the microstructure is converted into a voxel model based on a homogenization theory, the mechanical property of the microstructure is rapidly, accurately and comprehensively obtained, the mechanical property comprises linear elastic parameters and elastoplasticity parameters of the microstructure, the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Missels stress distribution of the microstructure under the worst load working condition, the elastoplasticity parameters are equivalent yield strengths of the microstructure under different stresses calculated based on the voxel model, the Young modulus, the shear modulus, the Poisson ratio and the Young modulus surface describe the elastic property of the microstructure, and the compressive yield strength, the shear strength and the Von-Missels stress distribution under the worst load working condition describe the strength property of the microstructure.
(2) The invention draws the physical property image of the microstructure, visually displays the mechanical property of the microstructure, can visually display the property difference among various types of microstructures, assists a user to summarize the corresponding relation between the structure and the property, and can provide corresponding guidance for the user to select and improve the microstructure.
Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a flow chart of a method for determining mechanical properties of a microstructure based on homogenization theory according to example 1 of the present invention;
fig. 2(a) is a schematic diagram of a mesh model 1 and a voxel model provided in embodiment 1 of the present invention;
fig. 2(b) is a schematic diagram of a mesh model 2 and a voxel model provided in embodiment 1 of the present invention;
FIG. 3 is a schematic diagram of a Young's modulus provided in example 1 of the present invention;
FIG. 4 is a schematic diagram of von mises stress distribution under worst load condition according to embodiment 1 of the present invention;
FIG. 5 is a flow chart of the microstructure elastoplasticity analysis method provided in embodiment 1 of the present invention;
FIG. 6 is a mechanical property image of the microstructure provided in example 1 of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Example one
As shown in fig. 1, the present embodiment provides a method for determining mechanical properties of a microstructure based on a homogenization theory, which specifically includes the following steps:
step 1: the mesh model of the microstructure is converted into a voxel model.
In a specific implementation, the mesh model of the microstructure shown in fig. 2(a) is converted into a voxel model shown in fig. 2 (b). The specific process comprises the following steps:
uniformly dividing the bounding box space of the grid model along the x, y and z axes, and generally dividing the bounding box space into cubic units with the resolution of 60 × 60;
initializing a three-dimensional matrix voxel with a space of 60 × 60, judging the position of each cubic unit, if the cubic unit is positioned inside or on the boundary of the grid, the cubic unit is an entity unit, the position corresponding to the voxel is recorded as 1, if the cubic unit is positioned outside the grid, the cubic unit is a non-entity unit, and the position corresponding to the voxel is recorded as 0.
Step 2: and calculating the linear elastic parameters of the microstructure based on the elastic performance parameters and the voxel model of the base material of the microstructure, wherein the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Misses stress distribution of the microstructure under the worst load working condition.
In particular implementations, this step also initializes the elastic performance parameters of the base material, including Young's modulus E(e)Poisson ratio
Figure BDA0003166844170000061
Yield strength
Figure BDA0003166844170000062
Initializing a constitutive matrix C of base material(e)：
Figure BDA0003166844170000063
Wherein λ(e)，μ(e)For the first and second parameters of lami, the following are defined:
Figure BDA0003166844170000064
in the specific implementation, in the process of calculating the linear elastic parameters of the microstructure, a unit stiffness matrix of a voxel model is initialized, the microstructure is assembled into a whole stiffness matrix according to the voxel model and periodic boundary conditions, a microstructure whole stiffness equation is solved, disturbance unit disturbance displacement is solved, an equivalent constitutive matrix and an equivalent compliance matrix are calculated according to the unit disturbance displacement, and an equivalent Young modulus, a shear modulus and a Poisson's ratio are extracted from the compliance matrix.
Calculating an equivalent Young modulus surface according to the equivalent constitutive matrix, and displaying elastic anisotropy of the microstructure; and calculating von mises stress of each unit according to the unit disturbance displacement, solving the worst load working condition from a tensor characteristic value problem defined by the von mises stress, and displaying the structure-mieses stress distribution of the microstructure under the worst load working condition.
The specific process for calculating the linear elastic parameters of the microstructure comprises the following steps:
step 2-1: initializing a cell stiffness matrix K(e)And unit load
Figure BDA0003166844170000071
K(e)＝∫Ω(e)BTC(e)BdΩe，
Figure BDA0003166844170000072
Wherein omega(e)Is a voxel unit, B is a unit geometric function matrix,
Figure BDA0003166844170000073
is the ith macroscopic strain component, defined as:
Figure BDA0003166844170000074
Figure BDA0003166844170000075
step 2-2: assembling the overall stiffness matrix K and the overall load f according to the periodic boundary conditionsi(ii) a Solving the integral rigidity equation:
Kχi＝fi
obtaining the node displacement x corresponding to the ith macroscopic strain componenti；
Step 2-3: calculating an equivalent constitutive matrix C according to node displacement xH：
Figure BDA0003166844170000076
Wherein | Ω | is the microstructure unit volume, Ω(e)Is a unit of a voxel, and is,
Figure BDA0003166844170000077
for unit node virtual displacement, from node displacement matrix χiThe method comprises the steps of extracting according to the node index,
Figure BDA0003166844170000078
is macroscopic strain epsiloniThe corresponding unit initial displacement is calculated by a unit stiffness equation to obtain:
Figure BDA0003166844170000079
wherein K(e)In the form of a matrix of cell stiffness,
Figure BDA00031668441700000710
the unit load is calculated and obtained in the step 2-1;
to CHInversion is carried out to obtain an equivalent compliance matrix SH；
Step 2-4: from SHExtracted Young's modulus EiShear modulus GijPoisson ratio vij：
Figure BDA0003166844170000081
Step 2-5: the edge [ i, j, k ] is calculated according to the following formula]Young's modulus of orientation Eijk：
Figure BDA0003166844170000082
Wherein SHIn the form of a compliance matrix, the compliance matrix,
Figure BDA0003166844170000083
is [ i, j, k ]]The direction cosine of the direction;
for space [ i, j, k]Sampling direction, calculating EijkDrawing a Young modulus surface according to sampling points, wherein FIG. 3 is a schematic diagram of the Young modulus surface, and the distance from the center of the Young modulus surface to any point on the Young modulus surface represents the magnitude of the Young modulus in the direction;
step 2-6: calculating the micro stress sigmai：
Figure BDA0003166844170000084
Wherein C is(e)Is a constitutive matrix of a base material,
Figure BDA0003166844170000085
is the ith macroscopic strain component, B is the matrix of the cell geometry function, χiThe node virtual displacement corresponding to the ith macroscopic strain component;
macroscopic strain
Figure BDA0003166844170000086
And macroscopic stress
Figure BDA0003166844170000087
There is a relationship:
Figure BDA0003166844170000088
wherein SHIs a compliance matrix;
the microscopic stress σ can therefore be expressed as:
Figure BDA0003166844170000091
wherein C is(e)Is a constitutive matrix of base material, SHIn the form of a compliance matrix, the compliance matrix,
Figure BDA0003166844170000092
for macroscopic stress, B is a matrix of cell geometry functions, XeIs a unit displacement;
is simply written as
Figure BDA0003166844170000093
Calculating the unit maximum von mises stress:
Figure BDA0003166844170000094
wherein
Figure BDA0003166844170000095
The unit von mises stress was calculated:
Figure BDA0003166844170000096
f is obtainedTVTThe characteristic vector corresponding to the maximum characteristic value of the characteristic values of VF is the worst load working condition sigma*；
According to σ*And calculating the von mises stress of the unit, and drawing von mises stress distribution, wherein fig. 4 is a schematic view of the von mises stress distribution of the microstructure under the worst load working condition, the gray value represents the von mises value, and the upper right-corner schematic view represents the worst load working condition.
And step 3: and calculating the equivalent yield strength of the microstructure under different stresses based on the voxel model to obtain the elastoplasticity parameters of the microstructure.
In the specific implementation, in the process of calculating the equivalent yield strength of the microstructure under different stresses, the initial macroscopic strain is updated incrementally, the overall stiffness matrix is updated according to the initial macroscopic strain, the stiffness equation is solved, the unit with the von mises stress exceeding the yield strength of the base material is set as a yield unit, the macroscopic stress is calculated, a macroscopic stress-strain curve is drawn, and the equivalent yield strength of the microstructure is obtained according to the stress-strain curve.
The specific process of the step 3 is as follows:
step 3-1: the microstructure is subjected to elasto-plastic analysis, and the calculation flow is shown in fig. 5; incrementally updating macroscopic strain
Figure BDA0003166844170000097
Figure BDA0003166844170000101
Wherein
Figure BDA0003166844170000102
Is the incremental change of macroscopic strain;
step 3-2: calculating the unit micro stress sigma and von mises stress svS according to von mises yield criterionvExceeding the yield strength of the base material
Figure BDA0003166844170000103
Is arranged as a yield unit, having its Young's modulus E(e)Set to 0;
step 3-3: calculating macroscopic stress
Figure BDA0003166844170000104
And drawing a stress-strain curve, and taking the maximum stress on the curve as the yield strength of the microstructure.
And 4, step 4: and summarizing linear elastic parameters and elastic-plastic parameters of the microstructure, and drawing a microstructure physical property image for customized application and target property optimization of the microstructure.
Specifically, five common mechanical property indexes of Young modulus, shear modulus, Poisson's ratio, compressive yield strength and shear strength are drawn in a radar chart form; the distribution of von mises stress under the Young modulus surface and the worst load working condition is used as the supplement of a radar map, and a microstructure mechanical property image is drawn, as shown in FIG. 6.
Example two
The embodiment provides a system for determining mechanical properties of a microstructure based on a homogenization theory, which specifically comprises the following modules:
a voxel model conversion module for converting the grid model of the microstructure into a voxel model;
the linear elastic parameter calculation module is used for calculating linear elastic parameters of the microstructure based on the elastic performance parameters and the voxel model of the base material of the microstructure, and the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Misses stress distribution of the microstructure under the worst load working condition;
the elastic-plastic parameter calculation module is used for calculating the equivalent yield strength of the microstructure under different stresses based on the voxel model to obtain the elastic-plastic parameters of the microstructure;
and the physical performance portrait drawing module is used for summarizing linear elastic parameters and elastic-plastic parameters of the microstructure and drawing a microstructure physical performance portrait so as to be used for customization application and target performance optimization of the microstructure.
It should be noted that, each module in the microstructure mechanical property determination system based on the homogenization theory of the present embodiment corresponds to each step in the microstructure mechanical property determination method based on the homogenization theory of the first embodiment one by one, and the specific implementation process is the same, and will not be described again here.
EXAMPLE III
The present embodiment provides a computer readable storage medium having stored thereon a computer program which, when being executed by a processor, carries out the steps of the method for determining mechanical properties of a microstructure based on homogenization theory as described above.
Example four
The embodiment provides a computer device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the homogenization theory based microstructure mechanical property determination method.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A microstructure mechanical property determination method based on homogenization theory is characterized by comprising the following steps:
converting the grid model of the microstructure into a voxel model;
calculating linear elastic parameters of the microstructure based on the elastic performance parameters and the voxel model of the base material of the microstructure, wherein the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Misses stress distribution of the microstructure under the worst load working condition;
calculating equivalent yield strength of the microstructure under different stresses based on the voxel model to obtain elastoplasticity parameters of the microstructure;
and summarizing linear elastic parameters and elastic-plastic parameters of the microstructure, and drawing a microstructure physical property image for customized application and target property optimization of the microstructure.
2. The method for determining the mechanical property of the microstructure based on the homogenization theory as claimed in claim 1, wherein five common mechanical property indexes of young's modulus, shear modulus, poisson's ratio, compressive yield strength and shear strength are plotted in a radar chart form; and drawing the microstructure mechanical property image by taking the Von.Misses stress distribution under the Young modulus surface and the worst load working condition as the supplement of a radar map.
3. The method for determining mechanical properties of a microstructure based on the homogenization theory as claimed in claim 1, wherein in the process of calculating the linear elastic parameters of the microstructure, a unit stiffness matrix of a voxel model is initialized, the integral stiffness matrix is assembled according to the voxel model and periodic boundary conditions, a microstructure integral stiffness equation is solved, disturbance unit disturbance displacement is solved, an equivalent constitutive matrix and an equivalent compliance matrix are calculated according to the unit disturbance displacement, and an equivalent Young modulus, a shear modulus and a Poisson's ratio are extracted from the compliance matrix.
4. The method for determining the mechanical property of the microstructure based on the homogenization theory as claimed in claim 3, wherein the elastic anisotropy of the microstructure is demonstrated by calculating an equivalent Young modulus surface according to an equivalent constitutive matrix; and calculating von mises stress of each unit according to the unit disturbance displacement, solving the worst load working condition from a tensor characteristic value problem defined by the von mises stress, and displaying the structure-mieses stress distribution of the microstructure under the worst load working condition.
5. The method for determining the mechanical properties of a microstructure based on the homogenization theory as claimed in claim 1, wherein in the process of calculating the equivalent yield strengths of the microstructures under different stresses, the initial macroscopic strain is updated incrementally, the overall stiffness matrix is updated and stiffness equations are solved according to the initial macroscopic strain, the units of von mises stress exceeding the yield strength of the base material are set as yield units, the macroscopic stress is calculated, a macroscopic stress-strain curve is drawn, and the equivalent yield strengths of the microstructures are obtained according to the stress-strain curve.
6. The method of claim 1, wherein the elastic property parameters of the base material include Young's modulus, Poisson's ratio and yield strength.
7. The method for determining the mechanical property of the microstructure based on the homogenization theory as claimed in claim 1, wherein the process of converting the mesh model of the microstructure into the voxel model is as follows: and uniformly dividing the bounding box space of the grid model along the x, y and z axes to form a matrix model.
8. A microstructure mechanical property determination system based on homogenization theory is characterized by comprising:
a voxel model conversion module for converting the grid model of the microstructure into a voxel model;
the linear elastic parameter calculation module is used for calculating linear elastic parameters of the microstructure based on the elastic performance parameters and the voxel model of the base material of the microstructure, and the linear elastic parameters comprise Young modulus, shear modulus, Poisson ratio, equivalent Young modulus surface and Von-Misses stress distribution of the microstructure under the worst load working condition;
the elastic-plastic parameter calculation module is used for calculating the equivalent yield strength of the microstructure under different stresses based on the voxel model to obtain the elastic-plastic parameters of the microstructure;
and the physical performance portrait drawing module is used for summarizing linear elastic parameters and elastic-plastic parameters of the microstructure and drawing a microstructure physical performance portrait so as to be used for customization application and target performance optimization of the microstructure.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method for determining a mechanical property of a microstructure based on homogenization theory according to any of claims 1-7.
10. Computer arrangement comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor when executing the program performs the steps of the method for determining a mechanical property of a microstructure based on homogenization theory according to any one of claims 1-7.
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CN110210103A (en) * 2019-05-27 2019-09-06 北京工业大学 A kind of multi-dimension analogy method of heterogeneous composite material mechanical behavior
CN112395746A (en) * 2020-11-03 2021-02-23 山东大学 Method for calculating property of equivalent material of microstructure family, microstructure, system and medium

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CN116882239B (en) * 2023-07-10 2024-01-23 哈尔滨工业大学 Composite material attribute analysis method based on component space distribution, electronic equipment and storage medium

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