Three-dimensional random field construction method and system for simulating mechanical properties of lunar soil bricks

Abstract

The invention belongs to the field of material mechanical property analysis, and particularly discloses a three-dimensional random field construction method and system for simulating the mechanical property of a lunar soil brick, and the method comprises the following steps: S1, obtaining hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick; s2, determining an edge distribution function F1 of the hardness based on the hardness distribution of all the sampling points, and determining an edge distribution function F2 of the elastic modulus based on the elastic modulus distribution of all the sampling points; s3, based on a Copula function, combining the edge distribution functions F1 and F2 into a joint distribution function; and S4, determining a cross correlation coefficient between the hardness and the elastic modulus based on the joint distribution function, forming a cross correlation coefficient covariance matrix R, and further determining the lunar soil brick mechanical property random field. According to the method, the random field for simulating the mechanical property of the lunar soil brick is accurately modeled, and a scientific basis can be provided for design and selection of lunar building materials.

Description

Technical Field

[0001] The present invention belongs to the field of material mechanical property analysis, and more specifically, relates to a three-dimensional random field construction method and system for simulating the mechanical properties of lunar soil bricks. Background Art

[0002] Against the backdrop of human exploration of the universe, lunar construction plans are gradually becoming a reality. Using in-situ resources - lunar soil as the main material for lunar construction has become an important research direction in lunar base construction. More and more scholars are using simulated lunar soil to make lunar soil bricks through sintering, melting, 3D printing, etc., and studying the molding process and its mechanical properties, aiming to provide higher strength and durability building materials for lunar construction.

[0003] However, due to the large randomness of molding process parameters, the materials of simulated lunar soil bricks often show spatial randomness. Most researchers explore their macroscopic mechanical properties while ignoring their microscopic properties, such as nanohardness and point domain elastic modulus. These microscopic properties may serve as weak points of lunar soil bricks and will directly affect their applicability and durability in the lunar environment. In-depth exploration of the microscopic mechanical properties and random characteristics of simulated lunar soil bricks can not only provide a material distribution basis for material simulation modeling, provide a comprehensive performance analysis for lunar base building materials, but also provide a theoretical basis for future improvements in the manufacturing process of lunar building materials.

[0004] Random fields are widely used in many fields, such as meteorology, geological exploration, image segmentation, etc. They can effectively analyze the spatial or temporal correlation in modeling data and help understand and predict the possible results of data changes. In terms of performance evaluation of spatial distribution of materials, random field theory can identify possible defects and inhomogeneities, which usually significantly affect the overall performance of the material.

[0005] At present, relevant studies have used random field theory to model the mechanical properties of materials. However, the analysis is only based on the independent random fields of a few distribution types, and does not fully consider the randomness and correlation characteristics between the surrounding rock parameters. For example, using Gaussian distribution to describe the hardness and elastic modulus of lunar soil bricks may fail to accurately reflect the performance changes of actual materials. In addition, due to the high sampling cost of nanoindentation experiments, the existing random field establishment work based on nanoindentation often lacks sufficient sample coverage, resulting in the data obtained not being able to truly represent the micromechanical properties of the entire material, affecting the understanding of the overall properties of the material. Summary of the invention

[0006] In response to the above defects or improvement needs of the prior art, the present invention provides a three-dimensional random field construction method and system for simulating the mechanical properties of lunar soil bricks, the purpose of which is to achieve accurate modeling of the random field of the mechanical properties of simulated lunar soil bricks.

[0007] To achieve the above object, according to one aspect of the present invention, a three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks is proposed, comprising the following steps:

[0008] S1. Obtain the hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick;

[0009] S2, determining the edge distribution function F1 of hardness based on the hardness distribution of all sampling points, and determining the edge distribution function F2 of elastic modulus based on the elastic modulus distribution of all sampling points;

[0010] S3, based on the Copula function, the marginal distribution functions F1 and F2 are combined into a joint distribution function;

[0011] S4. Determine the correlation coefficient between hardness and elastic modulus based on the joint distribution function, form the covariance matrix R of the correlation coefficient, and then determine the random field of the mechanical properties of the lunar soil brick.

[0012] As a further preferred embodiment, step S4, determining the random field of mechanical properties of lunar soil bricks, specifically includes:

[0013] Perform Cholesky decomposition on the covariance matrix R of the mutual correlation coefficient to obtain the lower triangular matrix L1;

[0014] The autocorrelation coefficient covariance matrix C is determined according to the fluctuation parameter l, and the autocorrelation coefficient covariance matrix C is subjected to Cholesky decomposition to obtain a lower triangular matrix L2; the fluctuation parameter l represents the distance range in which the lunar soil mechanical parameters are correlated;

[0015] The random field Z of the mechanical properties of lunar soil bricks is obtained based on the lower triangular matrices L1 and L2.

[0016] As a further preferred embodiment, the fluctuation parameter l is determined by optimizing the gazelle algorithm. When the gazelle algorithm is iterated: a corresponding random field is obtained according to the current fluctuation parameter, and then a fitness function value is determined; and the fluctuation parameter is optimized based on the fitness function value;

[0017] The fitness function Fitness calculation formula is as follows:

[0018] Fitness=(SVF h -SVF h ′) 2 +(SVF m -SVF m ′) 2

[0019] Among them, SVF h , SVF mThey represent the semivariogram values ​​corresponding to the hardness and elastic modulus of the sampling points obtained by the indentation test, and SVF h ′、SVF m ′ respectively represent the semivariogram values ​​corresponding to the hardness and elastic modulus of the sampling points determined according to the current random field;

[0020] Repeat the above process until the termination condition is met, stop the iteration and output the fluctuation parameter l at this time; the random field corresponding to the fluctuation parameter l is used as the final random field Z of the mechanical properties of the lunar soil brick.

[0021] As further preferred, step S2 specifically includes:

[0022] Based on the hardness distribution of all sampling points, the best hardness edge distribution function F1 is determined from the candidate edge distribution functions through the KS test; based on the elastic modulus distribution of all sampling points, the best elastic modulus edge distribution function F2 is determined from the candidate edge distribution functions through the KS test.

[0023] As further preferred, the marginal distribution functions to be selected include Weibull distribution, Gamma distribution, Exp distribution, Normal distribution and lognormal distribution function.

[0024] As a further preferred embodiment, step S3 specifically includes:

[0025] Based on different Copula functions, the marginal distribution functions F1 and F2 are combined into a joint distribution function. Several joint distribution functions obtained are tested by AIC or BIC, and the optimal joint distribution function is selected.

[0026] As further preferred, the selection of the Copula function includes Gaussian Copula function, t-Copula function, Frank Copula function, Clyton Copula function and Gumbel Copula function.

[0027] As a further preferred method, the sampling points on the lunar soil bricks are determined as follows:

[0028] Slice the lunar soil brick in equal thickness along its height direction to obtain a sampling surface;

[0029] For the first layer of sampling surface, b sampling points are taken at equal intervals on the sampling line along the radius of the lunar soil brick; for each subsequent layer of sampling surface, b sampling points are taken at equal intervals on the sampling line along the radius of the lunar soil brick, and the sampling line of each layer of sampling surface is rotated 360 / a degrees in the same direction compared with the sampling line of the previous layer of sampling surface.

[0030] As a further preferred embodiment, in step S1, a nanoindentation rapid lattice experiment is performed on each sampling point on the lunar soil brick to obtain the hardness and elastic modulus corresponding to each sampling point.

[0031] According to another aspect of the present invention, a three-dimensional random field construction system for simulating the mechanical properties of lunar soil bricks is provided, comprising a processor, wherein the processor is used to execute the above-mentioned three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks.

[0032] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0033] 1. Based on the hardness and elastic modulus of a small number of sampling points on the simulated lunar soil bricks, the present invention uses the Copula function to construct the complex distribution relationship between hardness and elastic modulus, and then combines the generated Copula joint distribution function with the random field theory to determine the mutual correlation coefficient between hardness and elastic modulus, and then obtains the random field of mechanical properties of lunar soil bricks, successfully integrating the distribution of microscopic mechanical properties with spatial variation characteristics. Through this random field model, we can better understand the distribution of mechanical properties of lunar soil bricks at the microscopic scale, and provide a theoretical basis and support for the future modeling of mesoscopic physical models.

[0034] 2. For the uncertainty of parameter fluctuation range in the random field of micromechanical properties, the present invention introduces the gazelle algorithm and combines the semivariogram function to construct a fitness evaluation index to achieve efficient optimization of the parameter fluctuation range. The gazelle algorithm, due to its superior global search capability and computational efficiency, can effectively improve the description accuracy of the random field of micromechanical parameters, avoid the traditional costly experimental parameter search process, and ensure the high credibility of the characterization of micromechanical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of a mechanical property sampling method based on simulated lunar soil bricks according to an embodiment of the present invention;

[0036] Figure 2 A flowchart of constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to an embodiment of the present invention;

[0037] Figure 3 This is a flow chart of the gazelle algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] 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.

[0039] The embodiment of the present invention provides a three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks, such as Figure 2 As shown, the following steps are included:

[0040] S1. Determine the hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick.

[0041] Specifically, Figure 1 As shown, simulated lunar soil bricks are made in advance by powder-mold hot pressing and sintering, and the lunar soil brick samples are preferably cylindrical. According to the sample height, equal-height layered slicing is performed to determine the sampling surface, and sampling points are determined on each sampling surface to ensure the uniformity and representativeness of the sampling. Then, a nanoindentation fast lattice experiment is performed on each sampling point: a suitable indentation spacing and indentation load are selected, and a nanoindentation fast lattice experiment is performed at the sampling point along the radial direction using a nanoindentation tester to obtain the nanohardness and elastic modulus data of the material in the sampling point area, that is, each sampling point area corresponds to a lattice, and the lattice includes multiple indentation points; then, effective measurement data is screened according to the indentation depth, and the hardness and elastic modulus obtained from all indentation points in the lattice are averaged, which is the hardness and elastic modulus of the corresponding sampling point, thereby representing the mechanical properties of the sampling point.

[0042] Furthermore, the method for determining the sampling point is preferably:

[0043] The samples were sliced ​​using a linear cutting method. The height of each slice was the total height divided by the number of slices, and (a-1) slices of equal height were obtained. To obtain as many samples as possible, the sampling surface was determined as the upper surface of each slice and the upper and lower surfaces of the last slice, with a total of a sampling surfaces. Furthermore, to ensure that each sampling point on the sampling surface did not lose spatial representativeness, the radius formed by each layer of sampling points rotated a certain angle with the height of the sampling surface, and the rotation angle was 360 degrees divided by the number of sampling surfaces. That is, for the first layer of sampling surface, b sampling points were taken at equal intervals on the sampling line along the radius direction of the lunar soil brick; for each subsequent layer of sampling surface, b sampling points were taken at equal intervals on the sampling line along the radius direction of the lunar soil brick, and the sampling lines of each layer of sampling surface were rotated 360 / a degrees in the same direction compared with the sampling lines of the previous layer of sampling surface.

[0044] For example, a simulated lunar soil brick sample of 20 mm in height is cut into 4 slices, each slice is 5 mm in height, and the sampling surface is the upper surface of the first 3 slices and the upper and lower surfaces of the last slice, a total of 5 equally spaced surfaces. For the 5 sampling surfaces, the first sampling surface is at a height of 20 mm, and its sampling radius is set to 0 degrees. The second sampling surface is at a height of 15 mm, and its sampling radius is rotated 72 degrees clockwise relative to the radius of the first sampling surface, and so on.

[0045] Furthermore, in order to obtain as much indentation information as possible and make the calculated mechanical properties more general, the indentation load of the nanoindentation fast lattice experiment is 6000-10000 micronewtons, preferably 8000 micronewtons; the indentation points in the lattice are arranged in a 10*10 square, and the distance between each indentation point is 8 microns.

[0046] S2. Determine the edge distribution function F1 of hardness based on the hardness distribution of all sampling points, and determine the edge distribution function F2 of elastic modulus based on the elastic modulus distribution of all sampling points.

[0047] Specifically, the marginal distribution function suitable for nano-hardness and elastic modulus is pre-selected as a candidate, including but not limited to Weibull distribution, Gamma distribution, Exp distribution, Normal distribution and lognormal distribution. Then, according to the hardness and elastic modulus of the sampling point obtained in step S1, the KS test is used to test the pre-selected several marginal distribution functions to determine the best marginal distribution functions of hardness and elastic modulus respectively. Among them, the nano-hardness marginal distribution function is determined as F(x1), and the elastic modulus marginal distribution function is determined as F(x2), and x1 and x2 are random variables of nano-hardness and elastic modulus.

[0048] S3. Based on the Copula function, the marginal distribution functions F1 and F2 are combined into a joint distribution function.

[0049] Specifically, based on the determined marginal distribution function, different Copula functions are selected to generate the joint distribution density of elastic modulus and hardness, and the parameters in the Copula model are solved by semi-parametric maximum likelihood estimation; the selection of Copula functions includes but is not limited to Gaussian Copula function, t-Copula function, Frank Copula function, Clyton Copula function and Gumbel Copula function; finally, the optimal joint distribution function F(x1,x2) is determined by testing through AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion).

[0050] Furthermore, the Copula function is expressed as:

[0051] F(x1,x2)=C[F(x1),F(x2)]=C(F(x1),F(x2),θ)

[0052] Where F(x1,x2) is the joint probability distribution function of random variables x1 and x2, F(x1) and F(x2) are the marginal distribution function of hardness and elastic modulus, respectively, C[F(x1),F(x2)] represents the Copula function calculation operation on the two marginal distribution functions; θ is the model parameter in the Copula function, which is obtained by the semiparametric maximum likelihood estimation method.

[0053] Furthermore, the AIC and BIC criteria formulas are:

[0054]

[0055] where u 1i with u 2i is the empirical distribution function of the random variables x1 and x2, D is the probability density of the Copula function, N is the number of observations, and α is the number of model parameters.

[0056] S4. Based on the joint distribution function, the mechanical parameters of lunar soil bricks are simulated to obtain the correlation coefficient between hardness and elastic modulus, form the covariance matrix of the correlation coefficient, and then determine the random field of the mechanical properties of lunar soil bricks.

[0057] Specifically, a three-dimensional coordinate system is established in the random field research area, and the cross-correlation matrix between nanohardness and elastic modulus is calculated according to the joint distribution function obtained in step S3; the initial parameter fluctuation range values ​​related to the random field and the coordinates are set, and the autocorrelation matrix is ​​calculated in combination with the sampling point coordinate center, and the cross-correlation standard Gaussian random field of the two parameters of nanohardness and elastic modulus of the simulated lunar soil brick can be calculated according to the cross-correlation, autocorrelation matrix and random variable matrix; the standard Gaussian random field is converted into a cross-correlation uniform distribution random field through probability integral change. And based on the Gryphon Search Algorithm (GSA), the parameter fluctuation range values ​​are continuously optimized until the iteration is completed, and the mechanical parameters of the simulated lunar soil brick - nanohardness and elastic modulus spatial random field is obtained.

[0058] Further, the following steps are included:

[0059] Calculate the random field cross-correlation triangular matrix L1: Use the joint probability distribution function F(x1,x2) to calculate the mechanical parameters of the simulated lunar soil brick and obtain the correlation coefficient r between nanohardness and elastic modulus 12 、r 21 , and form the cross-correlation coefficient covariance matrix R 2×2 =(r 12 ) 2×2 :

[0060]

[0061] The Cholesky decomposition of the above correlation coefficient matrix gives the lower triangular matrix L1:

[0062] satisfy,

[0063] Calculate the random field autocorrelation triangular matrix L2: Calculate the autocorrelation coefficient ρ of the random field based on the fluctuation parameter l. The fluctuation parameter l is a property of rock soil, which refers to the range within which its mechanical parameters (hardness, elastic modulus, etc.) are related. For example, the density of the soil is related within a range of 2 meters in the horizontal direction, and the properties of the soil particles outside the range of 2 meters are independent, that is, the fluctuation parameter in the horizontal direction is 2, which is generally determined by experience; and the present invention proposes a fluctuation parameter l optimization method based on the gazelle algorithm for lunar soil, which will be described later for details.

[0064] The fluctuation parameters l include l r , l θ , l z , respectively represent the fluctuation range of the mechanical parameters in the radial direction, azimuth direction, and height direction. A three-dimensional coordinate system is established in the random field research area, and cylindrical coordinate grid division is performed as needed; the autocorrelation coefficient ρ of the random field is calculated as follows:

[0065]

[0066] in, (r i ,θ i ,z i ) is the coordinate of the center point of the i-th column coordinate grid, (r j ,θ j ,z j ) is the coordinate of the center point of the j-th column coordinate grid. If the number of grid divisions is k, then the covariance matrix C composed of the autocorrelation coefficients corresponding to any two grid center coordinates is k×k for:

[0067]

[0068] For the above covariance matrix C k×k Perform Cholesky decomposition to obtain the lower triangular covariance matrix L2:

[0069] satisfy

[0070] For a matrix Y consisting of a set of normal random numbers m×2, then the standard normal random field Z = L2·Y·L1 can be calculated, and the cross-correlated uniform distribution random field can be obtained by performing probability integral transformation on Z The final random field is a matrix, in which each row represents a point in the random field coordinate system, the first column of each row represents the hardness random field calculated value, and the second column represents the elastic modulus random field calculated value.

[0071] Furthermore, the gazelle algorithm is selected as the parameter fluctuation range optimization algorithm, such as Figure 3 As shown, specifically including:

[0072] Initial position fitness evaluation, number of iterations, initialization based on Brownian motion random number vector and Levy distribution random number vector; global search for fitness and optimal solution matrix of the updated position; local search for fitness and optimal solution matrix of the updated position; output the optimal solution matrix after reaching the number of iterations.

[0073] Among them, the optimal solution matrix refers to the fluctuation parameter l, and the fitness value is determined according to the random field Z corresponding to the current fluctuation parameter l during iteration; the initial fluctuation parameter during iteration is given according to the size of the study area. The fitness function Fitness is preferably composed of the sum of the squares of the semivariogram estimate (SVF) calculated from the sampling point test data and the semivariogram calculated from the random field corresponding point data, and the expression is:

[0074] Fitness=(SVF h -SVF h ′) 2 +(SVF m -SVF m ′) 2

[0075] Among them, SVF h , SVF m Respectively represent the semi-variance estimates of hardness and elastic modulus at equally spaced sampling points based on indentation tests, Where m represents the sampling surface number, n represents the sampling point number, a and b are the number of sampling surfaces and the number of sampling points in the radial direction of each sampling surface, that is, h m,n Indicates the hardness value of the nth sampling point on the mth sampling surface, e m,n Indicates the elastic modulus value of the nth sampling point on the mth sampling surface; SVF h ′、SVF m ′ is calculated in a similar way, and represents the semi-variance estimate of the hardness and elastic modulus of the corresponding sampling point obtained according to the current random field.

[0076] 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 three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks, characterized in that: The steps include: S1. Obtain the hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick; S2, determining the edge distribution function F1 of hardness based on the hardness distribution of all sampling points, and determining the edge distribution function F2 of elastic modulus based on the elastic modulus distribution of all sampling points; S3, based on the Copula function, the marginal distribution functions F1 and F2 are combined into a joint distribution function; S4. Determine the correlation coefficient between hardness and elastic modulus based on the joint distribution function, form the covariance matrix R of the correlation coefficient, and then determine the random field of the mechanical properties of the lunar soil brick.

2. The three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks according to claim 1, characterized in that: Step S4, determining the random field of mechanical properties of lunar soil bricks, specifically includes: Perform Cholesky decomposition on the covariance matrix R of the mutual correlation coefficient to obtain the lower triangular matrix L1; The autocorrelation coefficient covariance matrix C is determined according to the fluctuation parameter l, and the autocorrelation coefficient covariance matrix C is subjected to Cholesky decomposition to obtain a lower triangular matrix L2; the fluctuation parameter l represents the distance range in which the lunar soil mechanical parameters are correlated; The random field Z of the mechanical properties of lunar soil bricks is obtained based on the lower triangular matrices L1 and L2.

3. The three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks according to claim 2, characterized in that: The fluctuation parameter l is determined by optimizing the Gazelle algorithm. When the Gazelle algorithm iterates: the corresponding random field is obtained according to the current fluctuation parameter, and then the fitness function value is determined; the fluctuation parameter is optimized based on the fitness function value; The fitness function Fitness calculation formula is as follows: Fitness=(SVF h -SVF h ′) 2 +(SVF m -SVF m ′) 2 Among them, SVF h , SVF m They represent the semivariogram values ​​corresponding to the hardness and elastic modulus of the sampling points obtained by the indentation test, and SVF h ′、SVF m ′ respectively represent the semivariogram values ​​corresponding to the hardness and elastic modulus of the sampling points determined according to the current random field; Repeat the above process until the termination condition is met, stop the iteration and output the fluctuation parameter l at this time; the random field corresponding to the fluctuation parameter l is used as the final random field Z of the mechanical properties of the lunar soil brick.

4. The three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks according to claim 1, characterized in that: Step S2 specifically includes: Based on the hardness distribution of all sampling points, the best hardness edge distribution function F1 is determined from the candidate edge distribution functions through the KS test; based on the elastic modulus distribution of all sampling points, the best elastic modulus edge distribution function F2 is determined from the candidate edge distribution functions through the KS test.

5. The three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks according to claim 4, characterized in that: The marginal distribution functions to be selected include Weibull distribution, Gamma distribution, Exp distribution, Normal distribution and lognormal distribution function.

6. The three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks according to claim 1, characterized in that: Step S3 specifically includes: Based on different Copula functions, the marginal distribution functions F1 and F2 are combined into a joint distribution function. Several joint distribution functions obtained are tested by AIC or BIC, and the optimal joint distribution function is selected.

7. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to claim 6, characterized in that: The selection of the Copula function includes Gaussian Copula function, t-Copula function, Frank Copula function, Clyton Copula function and Gumbel Copula function.

8. The three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks according to claim 1, characterized in that: The method for determining the sampling points on the lunar soil brick is: Slice the lunar soil brick in equal thickness along its height direction to obtain a sampling surface; For the first layer of sampling surface, b sampling points are taken at equal intervals on the sampling line along the radius of the lunar soil brick; for each subsequent layer of sampling surface, b sampling points are taken at equal intervals on the sampling line along the radius of the lunar soil brick, and the sampling line of each layer of sampling surface is rotated 360 / a degrees in the same direction compared with the sampling line of the previous layer of sampling surface.

9. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to any one of claims 1 to 8, characterized in that: Step S1, performing a nanoindentation rapid dot matrix experiment on each sampling point on the lunar soil brick, so as to obtain the hardness and elastic modulus corresponding to each sampling point.

10. A three-dimensional random field construction system for simulating the mechanical properties of lunar soil bricks, characterized in that: It includes a processor, which is used to execute the three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks as described in any one of claims 1-9.

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