Equivalent physical performance prediction method of microstructure and computer equipment

Abstract

The invention relates to the technical field of performance analysis of a multi-scale curved surface structure, and discloses an equivalent physical performance prediction method of a microstructure, computer equipment, a computer readable storage medium and a computer program product. The microstructure is used for filling a multi-scale curved surface structure. The method comprises the following steps: acquiring a mapping relation between Cartesian coordinates and parameter coordinates of any three-dimensional microstructure unit in a physical space; according to the mapping relation and the microscopic balance condition, a microscopic balance equation corresponding to the microstructure unit is determined; and solving the microscopic balance equation, obtaining the equivalent physical performance of the microstructure unit, and completing the equivalent physical performance prediction of the microstructure unit. The method realizes the characterization of the equivalent physical performance of the internal filling microstructure of the multi-scale curved surface structure, and improves the characterization accuracy of the physical performance of the microstructure.

Description

Technical Field

[0001] The present application relates to the technical field of multi-scale complex surface structure performance analysis, and more specifically, to a method for predicting equivalent physical properties of a microstructure, a computer device, a computer-readable storage medium, and a computer program product. Background Art

[0002] With the continuous iterative development of high-end equipment in the fields of aviation, aerospace, navigation, etc., complex curved surface components represented by the tail section of launch vehicle boosters, aircraft engine blades, satellite antenna covers and fan blades have been widely used, and often have ultra-lightweight, high-load-bearing and impact-resistant structural performance and functional requirements.

[0003] Multi-scale complex curved surface components are hollow structures filled with lightweight porous microstructures that have significant scale differences from the macroscopic curved surface configuration. Compared with traditional solid curved surface components, carefully designed multi-scale curved surface components have significant advantages such as strong toughness, light weight, and impact resistance, and have important prospects in engineering applications.

[0004] Currently, performance analysis of microstructures filled inside multi-scale complex curved surface components is usually difficult to predict microstructure performance for different types of curved surface structures, and there is a problem of inaccurate characterization of the physical properties of the microstructure. Summary of the invention

[0005] In order to solve the above-mentioned problems, the present invention provides a method for predicting the equivalent physical properties of a microstructure, a computer device, a computer-readable storage medium and a computer program product, which realize the characterization of the equivalent physical properties of the internal filling microstructure of a multi-scale curved surface structure and improve the accuracy of the physical property characterization of the microstructure.

[0006] To achieve the above object, according to a first aspect of the present invention, a method for predicting equivalent physical properties of a microstructure is provided, wherein the microstructure is used to fill a multi-scale curved surface structure, and the method comprises:

[0007] Obtaining the mapping relationship between the Cartesian coordinates and the parameter coordinates of any three-dimensional microstructure unit in the physical space;

[0008] According to the mapping relationship and microscopic balance conditions, the microscopic balance equation corresponding to the microstructure unit is determined;

[0009] The microscopic equilibrium equation is solved to obtain the equivalent physical properties of the microstructure unit, and the equivalent physical properties of the microstructure unit are predicted.

[0010] According to a second aspect of the present invention, there is also provided a computer device, which includes a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to implement the steps of any one of the above methods.

[0011] According to a third aspect of the present invention, there is also provided a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps of any of the above methods are implemented.

[0012] According to a fourth aspect of the present invention, there is also provided a computer program product, comprising a computer program, which implements the steps of any of the above methods when executed by a processor.

[0013] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0014] (1) The present invention provides a method for predicting the equivalent physical properties of a microstructure, which is applied to a microstructure used to fill a multi-scale curved surface structure. The method obtains the mapping relationship between the Cartesian coordinates and the parameter coordinates of any three-dimensional microstructure unit in the physical space, and determines the micro-equilibrium equation corresponding to the microstructure unit according to the mapping relationship and the micro-equilibrium condition. The calculation result obtained by solving the micro-equilibrium equation represents the equivalent physical properties of the microstructure unit, thereby achieving the characterization of the equivalent physical properties of the internal filling microstructure of the multi-scale curved surface structure and improving the accuracy of the characterization of the equivalent physical properties of the microstructure.

[0015] (2) The present invention provides a method for predicting the equivalent physical properties of a microstructure. According to the equivalent physical properties of the microstructure unit, fitting sample data is obtained to establish a gradient microstructure physical property prediction model with a variable volume ratio, thereby realizing a rapid prediction of the equivalent physical properties of the internal filling microstructure of a multi-scale curved surface structure and improving the accuracy of the prediction of the equivalent physical properties of the microstructure. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 A schematic diagram of a process for predicting equivalent physical properties of a microstructure provided in an embodiment of the present application;

[0018] Figure 2A schematic diagram of the steps of solving a microscopic equilibrium equation in a method for predicting equivalent physical properties of a microstructure provided in an embodiment of the present application;

[0019] Figure 3 A schematic diagram of the steps of establishing a gradient microstructure physical property prediction model in a microstructure equivalent physical property prediction method provided in an embodiment of the present application;

[0020] Figure 4A The elastic matrix coefficient of the microstructure type 1 provided in the embodiment of the present application is interpolated with the volume fraction by a cubic polynomial;

[0021] Figure 4B The standard deviation of the microstructure type 1 provided in the embodiment of the present application is interpolated with the volume fraction by a cubic polynomial;

[0022] Figure 5A The elastic matrix coefficient of the microstructure type 2 provided in the embodiment of the present application is interpolated with the volume fraction by a cubic polynomial;

[0023] Figure 5B The standard deviation of the microstructure type 2 provided in the embodiment of the present application is interpolated with the volume fraction by a cubic polynomial;

[0024] Fig. 6A The elastic matrix coefficient of the microstructure type 3 provided in the embodiment of the present application is interpolated with the volume fraction by a cubic polynomial;

[0025] Figure 6B The standard deviation of the microstructure type 3 provided in the embodiment of the present application is interpolated with the volume fraction by a cubic polynomial;

[0026] Fig. 7A A schematic diagram of a parallelepiped unit and its corresponding cuboid unit provided in an embodiment of the present application;

[0027] Figure 7B A schematic diagram of a BCC type microstructure filled in a parallelepiped unit provided in an embodiment of the present application;

[0028] Fig. 8A The coefficient matrix of the BCC type microstructure when the deflection angle combination provided in the embodiment of the present application is θ1=60°, θ2=60° The curves of various values ​​and microstructure volume fraction;

[0029] Figure 8B The coefficient matrix of the BCC type microstructure when the deflection angle combination provided in the embodiment of the present application is θ1=70°, θ2=60° The curves of various values ​​and microstructure volume fraction;

[0030] Figure 8CThe coefficient matrix of the BCC type microstructure when the deflection angle combination provided in the embodiment of the present application is θ1 = 90°, θ2 = 60° The curves of various values ​​and microstructure volume fraction;

[0031] Fig.8D The coefficient matrix of the BCC type microstructure when the deflection angle combination provided in the embodiment of the present application is θ1=90°, θ2=90° The curves of various values ​​and microstructure volume fraction;

[0032] Fig. 9 The elastic coefficient matrix cloud diagram of the BCC type microstructure provided in the embodiment of the present application at different volume fractions and different deflection angles;

[0033] Fig.10 A schematic diagram of the internal structure of a computer device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0035] The terms "first", "second", "third", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices.

[0036] The present embodiment provides a method for predicting the equivalent physical properties of a microstructure, wherein the microstructure is used to fill a multi-scale curved surface structure. The multi-scale curved surface structure may be a multi-scale thin shell curved surface structure, a multi-scale swept curved surface structure, or a multi-scale lofted curved surface structure. The multi-scale swept curved surface structure may be, for example, a parallelepiped, and the multi-scale lofted curved surface structure may be, for example, a special-shaped hexahedron. When the microstructure is used to fill a multi-scale thin shell curved surface structure or a multi-scale swept curved surface structure, the equivalent physical properties of the microstructure unit are calculated according to the numerical homogenization method; when the microstructure is used to fill a multi-scale lofted curved surface structure, the equivalent physical properties of the microstructure unit are calculated according to the generalized homogenization method or the extended homogenization method.

[0037] The method may be executed by a terminal or by a server communicating with the terminal through a network. The terminal may be, but is not limited to, various personal computers, laptops, smart phones, tablet computers, etc. The server may be an independent server or a server cluster consisting of multiple servers.

[0038] The following describes the method by taking application of the method to a terminal as an example.

[0039] like Figure 1 As shown, a method for predicting equivalent physical properties of a microstructure includes the following steps:

[0040] Step 101 : obtaining a mapping relationship between Cartesian coordinates and parameter coordinates of any three-dimensional microstructure unit in a physical space.

[0041] The microstructure is used to fill the multi-scale curved surface structure, and the multi-scale curved surface structure can be a multi-scale lofted curved surface structure. The microstructure unit is a component unit of the microstructure, and the microstructure unit is periodic under the parameter coordinate.

[0042] Exemplarily, the terminal uses a generalized homogenization method to obtain a mapping relationship between Cartesian coordinates and parameter coordinates of any three-dimensional microstructure unit in a physical space:

[0043] X=F(u), (1)

[0044] Among them, X is the Cartesian coordinate in the mapped physical space, and u is the parameter coordinate in the parameter domain.

[0045] Specifically, the expression of the mapping relationship is:

[0046]

[0047] In the above formula, X = [x1, x2, x3] T , u=(u,v,w) T .

[0048] Step 102: determining the microscopic balance equation corresponding to the microstructure unit according to the mapping relationship and the microscopic balance condition.

[0049] In one embodiment, the microscopic balance equation corresponding to the microstructure unit is expressed in a weak form of the microscopic balance equation.

[0050] Step 103, solving the microscopic equilibrium equation, obtaining the equivalent physical properties of the microstructure unit, and completing the prediction of the equivalent physical properties of the microstructure unit.

[0051] Among them, equivalent physical properties are also called equivalent mechanical properties.

[0052] The above-mentioned method for predicting the equivalent physical properties of microstructures is applied to microstructures used to fill multi-scale curved surface structures. By adopting the generalized homogenization method, the mapping relationship between the Cartesian coordinates and the parameter coordinates of any three-dimensional microstructure unit in the physical space is obtained. The micro-equilibrium equation corresponding to the microstructure unit is determined according to the mapping relationship and the micro-equilibrium condition. The calculation result obtained by solving the micro-equilibrium equation represents the equivalent physical properties of the microstructure unit, thereby realizing the equivalent physical performance characterization of the microstructure based on the equivalent physical performance of the microstructure unit, improving the accuracy of the physical performance characterization of the microstructure, and thus realizing the optimization design of the multi-scale lofted curved surface structure filled with the microstructure.

[0053] In one embodiment, the equivalent physical properties prediction method of the above-mentioned microstructure also includes obtaining a Jacobi matrix corresponding to the mapping relationship; expressing the microscopic equilibrium equation in a weak form according to the Jacobi matrix, the tensor components corresponding to the Jacobi matrix, and the generalized displacement corresponding to the Jacobi matrix.

[0054] The Jacobi matrix corresponding to the mapping relationship is:

[0055]

[0056] According to the Jacobi matrix, the tensor components of the inverse matrix of the Jacobi matrix and the generalized displacement corresponding to the Jacobi matrix are obtained, and the weak form of the microscopic equilibrium equation corresponding to the microstructure unit is calculated:

[0057]

[0058] in, is the inverse matrix of the Jacobian matrix, which represents the mapping from the parameter coordinate system u to the Cartesian coordinate system X. The tensor components representing the inverse of the Jacobian matrix, represents the generalized displacement in the parametric coordinate system, It shows periodicity in the microscopic parameter coordinate system, C ijkl is the flexibility tensor in the k and l directions.

[0059] The solution is that the flexibility tensor in the equivalent physical properties of the microstructure unit is:

[0060]

[0061] Among them, C ijpq is the flexibility tensor in the p-direction and the q-direction.

[0062] In one embodiment, the above-mentioned method for predicting equivalent physical properties of microstructures further includes reducing the order of tensor components in the microscopic equilibrium equation and the equivalent physical properties to obtain the reduced-order microscopic equilibrium equation and equivalent physical properties of the microstructure unit.

[0063] Specifically, for the tensor components of formula (4) Perform reduction processing:

[0064]

[0065] Among them, δ mj is the Kronecker symbol.

[0066] Taking the equivalent physical performance as the equivalent flexibility tensor as an example, the reduced-order microscopic equilibrium equation and equivalent physical performance of the microstructure unit are obtained:

[0067]

[0068] In one embodiment, Figure 2 As shown, the above step 103, solving the microscopic equilibrium equation to obtain the equivalent physical properties of the microstructure unit includes the following steps:

[0069] Step 201 : Obtain the strain transformation matrix, displacement vector and strain operator corresponding to the microstructure unit according to the Jacobian matrix.

[0070] Specifically, for the tensor components of formula (4) Perform coordinate transformation and express it as three-dimensional second-order tensor coordinates:

[0071]

[0072] Among them, M jm and are all tensor components and satisfy

[0073] Define the displacement vector as Then we can deduce from formula (9):

[0074]

[0075] Writing the tensor form in matrix form gives:

[0076]

[0077] Where R is the strain transformation matrix, and the displacement vector It can be obtained through V, is the strain operator in the parameter coordinate system, R, and They are:

[0078]

[0079] Step 202, based on the strain transformation matrix, the displacement vector, the strain operator and the matrix form of the generalized displacement, the matrix form of the microscopic equilibrium equation and the matrix form of the equivalent physical performance are obtained.

[0080] Specifically, writing the tensor form into a matrix form gives:

[0081] C ijkl ε ij ε kl →ε T Cε. (15)

[0082] Define the generalized displacement vector as Where χ is the generalized displacement The matrix form of .

[0083] Therefore, by substituting the strain transformation matrix, displacement vector, strain operator and generalized displacement vector into formula (7) and formula (8), the matrix form of the microscopic equilibrium equation and equivalent physical performance corresponding to the microstructure unit is obtained as follows:

[0084]

[0085] Step 203, processing the matrix form of the microscopic balance equation and the matrix form of the equivalent physical performance to complete the solution of the microscopic balance equation.

[0086] Specifically, multiply both sides of formula (16) by the strain transformation matrix R to obtain:

[0087]

[0088] Multiply both sides of formula (17) by (R T ) -1 R T With RR -1 , after simplification, we get:

[0089]

[0090] In matrix form, C H =(D H ) -1 , D is the matrix form of the equivalent elastic tensor of the microstructure unit, also called the elastic matrix. So far, the equivalent physical properties of the microstructure filled in the multi-scale lofted surface structure have been calculated.

[0091] In one embodiment, Figure 3 As shown, the above-mentioned method for predicting equivalent physical properties of microstructures further includes the following steps:

[0092] Step 301, determining elastic matrix correction constants of microstructure units according to the inherent elastic matrix and the corrected elastic matrix of the solid material.

[0093] Specifically, the coefficients in the elastic matrix of the microstructure unit correspond to the volume fraction of the microstructure unit, and the coefficients in the elastic matrix are interpolated using a cubic polynomial to obtain the elastic matrix correction constant of the microstructure unit:

[0094]

[0095] Among them, D solid is the intrinsic elastic matrix of the solid material, that is, D solid =D pqrs , D pqrs is the intrinsic elasticity tensor of the solid material. is the modified elastic matrix. is the elastic matrix correction constant of the microstructure unit.

[0096] Step 302: Determine fitting sample data corresponding to the microstructure unit according to the elastic matrix correction constant and in combination with the equivalent physical properties.

[0097] Specifically, the elastic matrix of each microstructure unit is defined to satisfy:

[0098]

[0099] Among them, “⊙” represents the Hadamard product. is a matrix with 36 coefficients, when the microstructure filling domain is determined, It can be uniquely calculated by formula (21). And, when the deflection angle is fixed, will only be affected by the volume fraction Therefore, each item in the matrix can be constructed with respect to the volume fraction function and reassemble it into a coefficient matrix, namely:

[0100]

[0101] If we assume is a volume fraction If the polynomial function of is m, the highest term of the polynomial function is m, then the above relationship can be expressed as:

[0102]

[0103] Thus, the fitting sample data corresponding to the microstructure unit is obtained.

[0104] Step 303: Based on the fitting sample data, a physical property prediction model of a gradient microstructure with a variable volume ratio is established.

[0105] Among them, the gradient microstructure physical property prediction model is a mathematical model used to calculate the equivalent physical properties of the internal filling microstructure of any multi-scale curved surface structure.

[0106] In this embodiment, according to the equivalent physical properties of the microstructure unit, fitting sample data is obtained and a gradient microstructure physical property prediction model with variable volume ratio is established, which realizes the rapid prediction of the equivalent physical properties of the internal filling microstructure of the multi-scale curved surface structure and improves the accuracy of the prediction of the equivalent physical properties of the microstructure.

[0107] The following uses a multi-scale thin shell surface structure as an example to illustrate the method for predicting the equivalent physical properties of a microstructure.

[0108] In one embodiment, for a multi-scale thin shell curved surface structure, the equivalent elastic tensor of its microstructure can be calculated by a numerical homogenization method. For the optimization design of a multi-scale thin shell curved surface structure, if the equivalent elastic tensor is recalculated for each microstructure in the design domain and the matrix is ​​assembled to realize the finite element analysis of the macroscopic overall structure, it will consume a lot of time. In order to reduce the calculation cost of the equivalent elastic tensor of the gradient microstructure in the optimization design, when the microstructure is used to fill the multi-scale thin shell curved surface structure, a method for predicting the equivalent physical properties of the microstructure is provided. The method is based on the continuous change of the microstructure and is a fast prediction method for the physical properties of the microstructure based on cubic polynomial fitting.

[0109] For a family of gradient microstructures that share the same set of feature lines, since their geometric features change continuously, their elastic matrices also have some similar features and their items change continuously. Each item is split and expressed in matrix form:

[0110]

[0111] Among them, D 11，soild , D 12，solid , D 21，solid , D 22，solid and D 33，solid They represent the values ​​of the corresponding positions of the equivalent stiffness matrix of the solid structure of the same material, and "⊙" represents the Hadamard product. Has the following form:

[0112]

[0113] In formula (25), is a matrix with 9 valid parameters, and Considering that the elastic matrix of the microstructure calculated by the numerical homogenization method has D 12，solid =D 21，solid and C 21 =C 12 , so the definition in formula (25) is Only four valid parameters are required {C 11 , C 12 , C 22 , C 33}. At the same time, in a family of microstructures, the volume fraction of the microstructure It is directly related to its equivalent physical properties, and in most cases it is a monotonically increasing function, so an m-order polynomial is selected to analyze and express this relationship, which is:

[0114]

[0115] In formula (26), represents the coefficient set of the r-th order polynomial {C 11，r , C 12，r , C 22，r , C 33，r}, Represented by the fitted polynomial and volume fraction The coefficient of the elastic matrix is ​​calculated. In the generated family of microstructures, appropriate M microstructures with different volume fractions are selected to be distributed as evenly as possible in the range of microstructure volume fraction, that is, The equivalent elastic matrix of each microstructure is calculated using the numerical homogenization method, and the corresponding coefficient matrix is ​​separated Determine the highest term m of the fitting polynomial, and ensure that the fitting is as accurate as possible without overfitting while satisfying m<<M.

[0116] This method uses an elastic matrix representation model similar to the solid isotropic material with penalty function (SIMP) method, which increases with the increase of penalty density, as shown in formula (27). If necessary, a penalty coefficient p can be applied to the volume fraction to obtain a volume fraction distribution closer to The predicted equivalent elastic matrix of a family of microstructures is:

[0117]

[0118] For a multi-scale thin shell surface structure established in an orthogonal curvilinear coordinate system, the parameterized generalized elastic matrix determined by the volume fraction on the shell mid-surface can be given by the following formula:

[0119]

[0120] Among them, T is a 6×6 diagonal matrix, and the last three items in T are given by the thickness calculation of the thin shell surface structure:

[0121] T = diag{1, 1, 1, t 2 / 12,t 2 / 12,t 2 / 12}. (29)

[0122] Therefore, substituting formula (27) into formula (28), the generalized elastic matrix of the microstructure of the thin shell structure in the mid-plane orthogonal curvilinear coordinate system can be calculated: for:

[0123]

[0124] Will Substituting it into the given elastic mechanics equation and writing it in matrix form, we can obtain the physical state of the multi-scale thin shell filled with a single type of gradient microstructure.

[0125] Taking three different types of gradient microstructures as examples, 51 microstructures with volume fractions between (0,1) were selected as samples for calculation, and a cubic polynomial function was used to fit the volume fraction as the independent variable. Tables 1.1, 1.2 and 1.3 respectively give the fitting coefficients of the three different microstructure configurations.

[0126] Table 1.1 Elastic matrix polynomial fitting coefficients of microstructure type 1

[0127]

[0128] Table 1.2 Elastic matrix polynomial fitting coefficients of microstructure type 2

[0129]

[0130] It should be noted that the microstructure described by the level set function may have certain numerical errors when the microstructure equivalent elastic matrix is ​​calculated by the numerical homogenization method. For example, the fitting coefficient of microstructure type 2 in Table 1.2 should theoretically have C 11，r =C 22，r , but the values ​​calculated in the table are slightly different. After testing, as the grid becomes denser, the numerical errors in the two directions will also decrease, C 11，r and C 22，r The calculated value will be closer.

[0131] Table 1.3 Elastic matrix polynomial fitting coefficients of microstructure type 2

[0132]

[0133] refer to Figure 4A The discrete data points are the corresponding relationship between the equivalent elastic matrix coefficient and the microstructure volume fraction calculated by the numerical homogenization method for microstructure type 1. The curves of corresponding colors represent the continuous functions obtained by fitting the two by three polynomials. The standard deviation of the fitting is shown in Figure 4B As shown ( Figure 5A , Figure 5B , Fig. 6A , Figure 6B (same reason).

[0134] It can be seen that the standard deviation of the coefficients of the stiffness matrix of the first type of microstructure (also called microstructure type one) after cubic polynomial fitting does not exceed 0.008, the standard deviation of the coefficients of the second type of microstructure (also called microstructure type two) after cubic polynomial fitting does not exceed 0.024, and the standard deviation of the coefficients of the third type of microstructure (also called microstructure type three) after cubic polynomial fitting does not exceed 0.06, all of which can meet the requirements for microstructure performance evaluation in optimization design.

[0135] In summary, it can be concluded that in a family of microstructures, after sampling a finite number of units, analyzing through the numerical homogenization method, and fitting the coefficients of the calculated microstructure equivalent elastic matrix using polynomials, the generation of microstructure geometric characteristics and the prediction of their corresponding elastic properties can be achieved; correspondingly, in a family of microstructures, the solution of the microstructure volume fraction under known equivalent physical properties can also be achieved.

[0136] The following uses a multi-scale swept surface structure as an example to illustrate the method for predicting the equivalent physical properties of a microstructure.

[0137] In one embodiment, for a multi-scale swept surface structure, the equivalent elastic tensor of its microstructure can be calculated by a numerical homogenization method. When the microstructure is used to fill the multi-scale swept surface structure, a method for predicting the equivalent physical properties of the microstructure is provided. Since conformal mapping has angle-preserving and circular-preserving properties, the rectangular grid divided in the parameter domain can also be approximated as a rectangle when mapped to the isoparametric surface, so the microstructure design domain can be regarded as a parallelepiped with the same bottom and top surfaces and both are rectangular.

[0138] Fig. 7A is a parallelepiped unit and its corresponding cuboid unit, Figure 7B It is a body-centered cubic (BCC) microstructure filled in parallelepiped units. Fig. 7A and Figure 7BAs shown in the figure, for a pair of parallelepipeds with rectangular faces, after determining the three parameters of length 2a, width 2b and height 2c, it is necessary to further determine its shape by defining the deflection angle (θ1, θ2). And for the same level set function, changing the deflection angle (θ1, θ2) in the design domain of a parallelepiped with fixed length, width and height has an effect on the volume fraction of the filled microstructure. No impact.

[0139] Since for a parallelepiped, when the length, width, height and deflection angle are the same, the filled microstructure can still satisfy the geometric periodicity, that is, the displacement field vector function χ in the microstructure filled with a parallelepiped is [u, v, w] T satisfy:

[0140]

[0141] Therefore, the traditional numerical homogenization method in the cubic design domain can be generalized to solve the equivalent physical properties of the microstructure in the parallelepiped, and the vector field function χ = [u, v, w] T Expanding with ε as an infinitesimal quantity yields:

[0142] χ(x1, x2, x3) = ε 0 χ (0) (x1,x2,x3)+ε 1 χ (1) (x1, x2, x3)+…, (32)

[0143] In formula (32), χ (i) (x1, x2, x3) is X = [x1 ， x2 ， x3] T is a periodic smooth function (i=0, 1, 2, ...).

[0144] Similarly, expanding the displacement field in the periodic domain yields:

[0145] u(x1, x2, x3) = ε0u (0) (x1,x2,x3)+ε 1 u (1) (x1, x2, x3)+…, (33)

[0146] By substituting the expanded displacement field into the equilibrium equation and solving it, the elastic tensor of the microstructure is obtained as:

[0147]

[0148] Among them, D pqrs is the intrinsic elastic tensor of the solid material, |V| represents the volume of the microstructure unit, is the strain field under periodic boundary conditions. It can be obtained by solving the equation:

[0149]

[0150] Among them, u ij and v kl are the real displacement and virtual displacement of the microstructure, is the allowable displacement space. By numerical homogenization method, the equivalent elastic matrix D of a family of three-dimensional microstructures with continuously changing volume fractions at different deflection angles can be calculated. mic The elastic matrix is ​​transformed into a form of 6×6=36 parameters, namely:

[0151]

[0152] Due to the effect of the deflection angle, the isotropic properties of the microstructure in the cube may not be effectively maintained after it is filled into the parallelepiped. Therefore, it is necessary to assign the zero item in the elastic matrix of the solid material to 1 so that when the coefficient at the corresponding position The value obtained when multiplied by it is accurate, namely:

[0153]

[0154] Among them, D solid is the elastic matrix of the solid material, that is, D solid =D pqrs ,and

[0155]

[0156] Assume that the elastic matrix of each microstructure satisfies:

[0157]

[0158] Wherein, “⊙” represents the Hadamard product, E represents the Young's modulus of the solid, v is the Poisson's ratio of the solid material, and G is the shear modulus of the solid material. is a matrix with 36 coefficients, when the parallelepiped deflection angle (θ1, θ2) and the microstructure volume fraction When confirmed, It can be uniquely calculated using formula (39).

[0159] In the swept surface structure parameterization method, once the surface structure and its mesh are determined, the deflection angle of the parallelepiped mesh (i.e., microstructure design domain) used to design each infill microstructure is also uniquely determined. When the deflection angle is fixed, It is only affected by the volume fraction, that is, the gradient microstructure that needs to be designed is also only controlled by its volume fraction. Therefore, each item in the matrix can be constructed with respect to the volume fraction function and reassemble it into a coefficient matrix:

[0160]

[0161] Assumptions Each value in It is a The polynomial function, the highest degree of the polynomial is m, the above relationship can be expressed as:

[0162]

[0163] For example, when θ1=π / 2, θ2=π / 2, and m=2, we have:

[0164]

[0165] In formula (43), the independent variable satisfy i = 1, 2, 3, ..., N, and the polynomial coefficient m satisfies m<<N. On this basis, a set can be constructed Satisfy the following formula:

[0166]

[0167] At this time, let the coefficients of the elastic matrix of the microstructure constitute the set Right now:

[0168]

[0169] Therefore, we can define an operator Γ to represent arrive The mapping:

[0170]

[0171] When the deflection angle (θ1, θ2) of the filling microstructure is determined, any coefficient in the elastic matrix can be fitted into a continuously differentiable function relative to the volume fraction by a polynomial. In this embodiment, 10,000 groups of sample microstructures with different volume fractions and deflection angles are generated equidistantly according to control parameters for typical three-dimensional filling microstructures (such as BCC, etc.), and their equivalent physical properties are directly calculated by the homogenization method facing the parallelepiped. Finally, the obtained data is processed by polynomial fitting to obtain a continuous mapping of the deflection angle / volume fraction set to the equivalent elastic matrix coefficient set. This method can be used to quickly predict the equivalent physical properties of the filling microstructure configuration (and vice versa), which provides the possibility for the subsequent multi-scale swept surface structure optimization design and sensitivity analysis of the gradient filling microstructure.

[0172] The mapping relationship between the microstructure volume fraction and the values ​​in the equivalent elastic coefficient matrix established by polynomial fitting. Taking the BCC type microstructure as an example, FIG. 8A to FIG. 8D is the coefficient matrix of the BCC microstructure under different deflection angle combinations The curves of the various values ​​and the volume fraction of the microstructure show that the change in the volume fraction of the BCC type microstructure under different deflection angle combinations leads to the change in the elastic matrix coefficient.

[0173] from FIG. 8A to FIG. 8D It can be seen that the coefficient curves of the elastic matrix are smooth and continuous, and are continuously differentiable for the volume fraction of the microstructure, which shows that the microstructure performance fitting method proposed in this embodiment is very conducive to calculating sensitivity and is convenient for subsequent multi-scale swept surface structure optimization design. Some typical gradient microstructure physical performance prediction models and the predicted equivalent elastic matrices are shown in Table 2.1.

[0174] Table 2.1 Equivalent elastic matrix of BCC microstructures with 9 different deflection angles at the same volume fraction

[0175]

[0176] Fig. 9 It is the elastic coefficient matrix cloud diagram of BCC type microstructure at different volume fractions and different deflection angles. It can be seen from Table 2.1 and Figure 7 that the stiffness matrix of the microstructure with different deflection angles and the coefficient cube cloud diagram drawn have a certain symmetry relationship both in the whole and in the part. Fig. 9 There are: d 11 With d 22 Symmetric about the plane θ1-θ2=0, d 44 It is symmetric about θ1=θ2, and all coefficient cubes satisfy d ij =d jiHowever, these symmetries are not applicable to all microstructures. For microstructures that do not have symmetry, the symmetry of the elastic matrix / elastic tensor calculated with respect to angles will not exist.

[0177] The present application also provides a computer device, the internal structure diagram of which can be as follows: Fig.10 As shown. The computer device includes a processor, a memory, an input / output interface, a communication interface, a display unit and an input device. Wherein, the processor, the memory and the input / output interface are connected via a system bus, and the communication interface, the display unit and the input device are connected to the system bus via the input / output interface. Wherein, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be implemented through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, a method for predicting equivalent physical properties of a microstructure is implemented.

[0178] Those skilled in the art will understand that Fig.10 The structure shown in is merely a block diagram of a portion of the structure related to the present application solution and does not constitute a limitation on the computer device to which the present application solution is applied.

[0179] The present application also provides a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented. The computer-readable storage medium may include, but is not limited to, any type of disk, including a floppy disk, an optical disk, a DVD, a CD-ROM, a micro drive, and a magneto-optical disk, a ROM, a RAM, an EPROM, an EEPROM, a DRAM, a VRAM, a flash memory device, a magnetic card or an optical card, a nanosystem (including a molecular memory IC), or any type of medium or device suitable for storing instructions and / or data.

[0180] The present application also provides a computer program product, including a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.

[0181] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0182] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting equivalent physical properties of a microstructure, characterized in that: The microstructure is used to fill a multi-scale curved surface structure, and the method comprises: Obtaining a mapping relationship between the Cartesian coordinates of any three-dimensional microstructure unit in the physical space and the parameter coordinates; Determining a microscopic balance equation corresponding to the microstructure unit according to the mapping relationship and the microscopic balance condition; The microscopic equilibrium equation is solved to obtain the equivalent physical properties of the microstructure unit, and the equivalent physical properties prediction of the microstructure unit is completed.

2. The method according to claim 1, characterized in that The microscopic equilibrium equation corresponding to the microstructure unit is expressed in a weak form of the microscopic equilibrium equation.

3. The method according to claim 2, characterized in that The method further comprises: Obtaining a Jacobi matrix corresponding to the mapping relationship; The microscopic equilibrium equation is expressed in a weak form according to the Jacobi matrix, the tensor components corresponding to the Jacobi matrix, and the generalized displacement corresponding to the Jacobi matrix.

4. The method according to any one of claims 1 to 3, characterized in that: The microstructure units present periodicity under the parameter coordinates.

5. The method according to claim 3 or 4, characterized in that: The method further comprises: The tensor components in the microscopic balance equation and the equivalent physical properties are reduced in order to obtain the reduced-order microscopic balance equation and the equivalent physical properties of the microstructure unit.

6. The method according to claim 5, characterized in that The step of solving the microscopic equilibrium equation comprises: According to the Jacobi matrix, a strain transformation matrix, a displacement vector and a strain operator corresponding to the microstructure unit are obtained; Based on the strain transformation matrix, the displacement vector, the strain operator and the matrix form of the generalized displacement, obtaining the matrix form of the microscopic equilibrium equation and the matrix form of the equivalent physical performance; The matrix form of the microscopic balance equation and the matrix form of the equivalent physical performance are processed to complete the solution of the microscopic balance equation.

7. The method according to any one of claims 1 to 6, characterized in that: The method further comprises: Determining elastic matrix correction constants of the microstructure unit according to the inherent elastic matrix and the modified elastic matrix of the entity material; Determine fitting sample data corresponding to the microstructure unit according to the elastic matrix correction constant and in combination with the equivalent physical properties; Based on the fitting sample data, a physical property prediction model of a gradient microstructure with variable volume ratio is established.

8. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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