A method for rapid identification of pore structure of a porous material and generation of a three-dimensional model

Abstract

The present application relates to the field of material science and engineering, in particular to a kind of porous material pore structure fast identification and three-dimensional model generation method.The present application is first to the two-dimensional micrograph of porous medium phase decoupling and feature extraction, obtains topological parameter set;Then through parameter space mapping establishes statistical feature matching model;Then generate geometric topological element in the feature space that satisfies the condition;Finally, the final continuous phase space domain is constructed using spatial domain topological mapping algorithm, for the digital reconstruction and performance simulation of porous material structure.The present application can effectively realize the identification and three-dimensional model construction of porous material pore structure, and the advantages of the model construction of the present application are verified through numerical simulation, which provides strong technical support for the research and application of porous materials.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of material science and engineering, in particular to a method for rapid identification of pore structure and generation of three-dimensional model of porous material. BACKGROUND

[0002] Porous materials have a wide range of applications in thermal insulation, energy absorption, filtration, etc. due to their unique pore structure. Accurate characterization of the pore structure and establishment of a three-dimensional model are key to studying material properties and optimizing design. Traditional methods usually analyze two-dimensional micrographs based on threshold segmentation to extract pore features, but existing phase decoupling techniques have insufficient recognition accuracy for complex pore boundaries, which can lead to deviations in porosity and size distribution parameters. In addition, existing statistical model matching methods rely on a single feature parameter, making it difficult to accurately reflect the multi-dimensional statistical characteristics of pore distribution and affecting the geometric fidelity of the three-dimensional reconstruction model.

[0003] In terms of three-dimensional reconstruction, conventional methods (such as continuous slice reconstruction) require a large amount of high-precision tomographic data, which is costly and inefficient. Methods based on random generation algorithms can quickly construct models, but often lack strict constraints on the statistical characteristics of actual materials, leading to significant differences between simulation results and real performance. Therefore, how to achieve efficient and accurate pore structure identification and three-dimensional model generation is still a technical problem to be solved in the field.

[0004] In view of the above problems, it is urgent to develop a method that can quickly identify pore structure characteristics and generate high-fidelity three-dimensional models, providing reliable technical support for performance prediction and structure design of porous materials. SUMMARY

[0005] The purpose of the present application is to provide a method for rapid identification of pore structure and generation of three-dimensional model of porous material.

[0006] The technical solution to achieve the purpose of the present application is: a method for rapid identification of pore structure and generation of three-dimensional model of porous material, comprising the following steps:

[0007] Step (1): Perform phase decoupling and feature extraction on the two-dimensional micrograph of the porous medium to obtain a set of topological parameters;

[0008] Step (2): Based on the set of topological parameters, establish a matching relationship between the feature size distribution function f and the candidate statistical model through parameter space mapping to determine the optimal matching model;

[0009] Step (3): Based on the optimal matching model of step (2), establish a feature space through dimensional constraint conditions and distribution constraint equations, and generate geometric topological primitives in the feature space that meet the statistical convergence conditions;

[0010] Step (4): Construct the final continuous phase space domain through the spatial domain topological mapping algorithm to achieve digital reconstruction and performance simulation of the porous material structure.

[0011] Furthermore, the phase decoupling in step (1) adopts a dynamic two-phase optimization algorithm, and the optimal phase decoupling threshold t * satisfy:

[0012]

[0013] Where: 、 is the dynamic weight operator in the two-phase region, 、 is the expected vector norm of the feature space, Represents the functional extreme value solving process.

[0014] Furthermore, the topological parameter set in step (1) includes a porosity parameter p, a characteristic scale distribution function f, and a characteristic scale cumulative distribution function F.

[0015] Furthermore, the candidate statistical model of step (2) includes at least one continuous probability distribution function.

[0016] Further candidate statistical models are GEV, Weibull or Logarithmic normal.

[0017] Furthermore, step (2) specifically includes the following steps:

[0018] Step (21): Define the feature evaluation node set Q = {q1, q2, q3} and key statistical quantiles;

[0019] Step (22): Calculate the actual observation distribution F obs (q i ) and the theoretical distribution F calculated by the candidate statistical model th (q ᵢ ) difference matrix;

[0020] Step (23): Construct a composite matching function:

[0021]

[0022] Where: is the composite matching score;

[0023] Step (24): Select The candidate statistical model with the smallest value is taken as the optimal matching model of the characteristic scale distribution function f.

[0024] Furthermore, the dimensional constraints in step (3) are as follows:

[0025] L / D ≥ 5

[0026] where: L is the eigen dimension of the feature space, D is the median of the feature dimension;

[0027] The distribution constraint equation in step (3) is as follows:

[0028]

[0029] where: x i , y i , z i are the center coordinates of the geometric topology primitive; Φ(D) is the optimal matching model of the feature dimension distribution function f; D i is the equivalent feature dimension of the geometric topology primitive, satisfying D min ≤ D i ≤ D max ; δ() is the Dirac Delta function.

[0030] Further, the number N of the geometric topology primitives in step (3) satisfies:

[0031] .

[0032] Further, the spatial position of the geometric topology primitive in step (3) satisfies the following boundary constraint condition:

[0033] .

[0034] Further, any two geometric topology primitives in step (3) need to satisfy the spatial non-inclusion criterion:

[0035]

[0036] where: (x a , y a , z a ) and (x b , y b , z b ) are the spatial coordinates of any two geometric topology primitives, R a and R b are the feature radii of the corresponding geometric topology primitives.

[0037] Further, the final continuous phase space domain in step (4) is generated by the following formula:

[0038]

[0039] where: Ω final is the final continuous phase space domain, Ω0 is the initial continuous phase space domain, B kis the space domain difference set operation for the kth geometric topological primitive to occupy the space.

[0040] Compared with the prior art, the present application has the following beneficial effects:

[0041] The present application determines the optimal matching model through the characteristic scale distribution function, and establishes the geometric topological primitive and the continuous space domain based on the geometric topological primitive; the recognition and three-dimensional model construction of the pore structure of the porous material can be effectively realized, and the influence of the pore structure on the mechanical properties of the material is revealed through numerical simulation, thereby providing strong technical support for the research and application of the porous material. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The figure is a method flowchart of the present application.

[0043] Figure 2 The figure is an example porous material original image.

[0044] Figure 3 The figure is an image processed by a dynamic two-phase optimization algorithm.

[0045] Figure 4 The figure is a characteristic scale distribution function f.

[0046] Figure 5 The figures are three-dimensional models generated according to the optimal probability distribution function of different porosity parameters p and different pore diameter cumulative curves; wherein (a) the porosity parameter p is 49.18%, (b) the porosity parameter p is 61.04%, and (c) the porosity parameter p is 72.81%.

[0047] Figure 6 The figures are the maximum principal stresses of three-dimensional models with different porosity parameters p under compression in ABAQUS; wherein (a) the porosity parameter p is 49.18%, (b) the porosity parameter p is 61.04%, and (c) the porosity parameter p is 72.81%.

[0048] Figure 7 The figures are the damage states of three-dimensional models with different porosity parameters p under compression in ABAQUS; wherein (a) the porosity parameter p is 49.18%, (b) the porosity parameter p is 61.04%, and (c) the porosity parameter p is 72.81%.

[0049] Figure 8 The figures are the stress changes of a three-dimensional model with a porosity parameter p of 49.18% under compression in ABAQUS; wherein (a) is the initial stage of uniform stress distribution, (b) is the initial stage of stress aggregation to the dense pore area, (c) is the final stage of stress aggregation to the dense pore area, and (d) is the fracture at the intersection of pores. DETAILED DESCRIPTION

[0050] The application will be further described in detail below in combination with the drawings and specific embodiments.

[0051] The application proposes a method for rapid identification of pore structure of porous materials and generation of three-dimensional model. The specific technical scheme adopted by the application is as follows:

[0052] Step (1): the two-dimensional microscopic image of the porous medium is subjected to phase decoupling and feature extraction, and a topological parameter set containing a porosity parameter p, a feature scale distribution and an evolution law thereof is obtained;

[0053] A high-resolution microscopic camera is used to shoot the surface morphology of the porous foam. Figure 2 An annular LED light source is used to compensate for imaging shadows, so as to ensure uniformity of the image gray scale. Subsequently, a dynamic two-phase optimization algorithm is applied to phase decoupling, so as to obtain an optimal phase decoupling threshold t * :

[0054]

[0055] In the formula, t * is the optimal phase decoupling threshold, , is a dynamic weight operator of the two-phase region, , is a norm of an expected vector of a feature space, represents a functional extreme value solving process, and the processed picture is shown in Figure 3 .

[0056] Based on the optimal phase decoupling image, a topological parameter set including a porosity parameter p, a feature scale distribution function f and a cumulative distribution function F is extracted. A matching relationship between the feature scale distribution function f and a candidate statistical model is established through parameter space mapping, and the candidate statistical model includes at least one continuous probability distribution function. In this example, three continuous probability distribution functions meeting the conditions are selected, as shown in Table 1.

[0057] Table 1 Topological parameter set information

[0058] Step (2): based on the topological parameter set, a matching relationship between the feature scale distribution function f and a candidate statistical model is established through parameter space mapping, and an optimal matching model is determined.

[0059] Step (2) specific implementation process:

[0060] A feature evaluation node set Q={q1, q2, q3} is defined, wherein the key statistical quantiles are set to 0.25, 0.5 and 0.75;

[0061] When the porosity parameter p is 49.18%, the characteristic evaluation node set has three elements, q 0.25 = 0.173 mm, q 0.50 = 0.193 mm, q 0.75 = 0.231 mm, F obs (q 0.25 ) = 0.530, F obs (q 0.50 ) = 0.640, F obs (q 0.75 ) = 0.730,

[0062] The GEV distribution theoretical cumulative probability is calculated :

[0063]

[0064] When the porosity parameter p is 49.18%, the characteristic evaluation node set has three elements:

[0065] , , ,

[0066] Similarly, the Weibull distribution theoretical cumulative probability is calculated

[0067]

[0068] , , ,

[0069] and the Logarithmic normal distribution theoretical cumulative probability is calculated :

[0070]

[0071] , , ,

[0072] The difference matrix between the actual observed distribution F obs (q i ) and the theoretical distribution P th (q i ) is calculated, and a composite matching degree function is constructed:

[0073]

[0074] In the formula: is the composite matching degree score value, F obs is the observed cumulative probability, Pth is the theoretical cumulative probability. It is calculated as GEV = 0.09, Weibull = 0.434, Logarithmic normal = 0.508, GEV Weibull Logarithmic normal

[0075] Similarly, when the porosity parameter p is 61.04% and when the porosity parameter p is 72.81%, similar results are also obtained.

[0076] From the above scoring results, it can be seen that GEV is the optimal matching model of the cumulative curve of the distribution pore diameter as the characteristic scale distribution function f.

[0077] Step (3): Based on the optimal matching model of step (2), a characteristic space is established by the dimensional constraint condition L / D≥5 and the distribution constraint equation, and a geometric topological element that meets the statistical convergence condition is generated in the space;

[0078] The characteristic space needs to meet the dimensional constraint condition:

[0079] L / D≥5

[0080] In the formula: L is the intrinsic scale of the characteristic space, and D is the median of the characteristic scale.

[0081] The spatial distribution of the geometric topological element meets the constraint equation:

[0082]

[0083] In the formula: x i , y i , z i are the coordinates of the center of the geometric topological element; Φ(D) is the optimal matching model of the characteristic scale distribution function f; D i is the equivalent characteristic scale of the geometric topological element, which satisfies D min ≤D i ≤D max ; δ() is the Dirac Delta function.

[0084] The number of geometric topological elements N meets:

[0085]

[0086] In the formula: L is the intrinsic scale of the characteristic space; D is the median of the characteristic scale, and p is the porosity parameter. ​​​

[0087] According to the parameters in Table 1, the number of geometric topological primitives deployed is 117, 145, and 173.

[0088] The spatial position of geometric topological primitives must satisfy boundary constraints:

[0089]

[0090] Where L is the intrinsic scale of the feature space, x i , y i , z i are the center coordinates of the geometric topological primitive.

[0091] Any two geometric topological primitives must satisfy the space non-containment criterion:

[0092]

[0093] Where: (x a ,y a ,z a ) and (x b ,y b ,z b ) are the spatial coordinates R of any two geometric topological primitives a 、R b is the characteristic radius of the corresponding geometric topological primitive.

[0094] In step (4), the spatial domain topological mapping algorithm generates the final continuous phase space domain by the following formula:

[0095]

[0096] Where: Ω final is the final continuous phase space domain, Ω0 is the initial continuous phase space domain, B k The kth geometric topological primitive occupies space, and \ represents the difference operation in the spatial domain.

[0097] The completed three-dimensional model of the porous material is shown in the figure ( Figure 5 (a)-(c))

[0098] Step (5): Perform numerical simulation based on the constructed three-dimensional geometric model of the porous material.

[0099] The three-dimensional geometric model generated in step (4) ( Figure 5 ) is imported into finite element analysis software (such as ABAQUS) to assign linear elastic material properties to the matrix phase in the final continuous phase space domain. Adaptive tetrahedral meshing is used to ensure that the mesh density at the pore interface meets the calculation accuracy requirements.

[0100] Fixed constraints (restricting x, y, z direction displacement) were applied on the bottom surface of the model; axial displacement load was applied on the top (simulating quasi-static compression condition); lateral surface kept free boundary condition, allowing lateral deformation.

[0101] After running the simulation, the following key results were extracted:

[0102] The maximum principal stress distribution of different porosity parameter models shows that the low porosity parameter model (49.18%, (a)) has a significant stress concentration phenomenon, the high porosity parameter model (72.81%, (c)) has a relatively dispersed stress distribution, indicating that the pore structure plays a leading role in the spatial distribution characteristics of the load transfer path. Figure 6 Figure 6 The maximum principal stress distribution of different porosity parameter models shows that the low porosity parameter model (49.18%, (a)) has a significant stress concentration phenomenon, the high porosity parameter model (72.81%, (c)) has a relatively dispersed stress distribution, indicating that the pore structure plays a leading role in the spatial distribution characteristics of the load transfer path.

[0103] The maximum principal stress distribution of different porosity parameter models shows that the low porosity parameter model (49.18%, (a)) has a significant stress concentration phenomenon, the high porosity parameter model (72.81%, (c)) has a relatively dispersed stress distribution, indicating that the pore structure plays a leading role in the spatial distribution characteristics of the load transfer path. Figure 7 Figure 7 The maximum principal stress distribution of different porosity parameter models shows that the low porosity parameter model (49.18%, (a)) has a significant stress concentration phenomenon, the high porosity parameter model (72.81%, (c)) has a relatively dispersed stress distribution, indicating that the pore structure plays a leading role in the spatial distribution characteristics of the load transfer path.

[0104] For the model with porosity parameter p = 49.18%, Figure 8 (a)-(d) show the complete process from initial uniform loading to local instability: at the initial stage, the stress is uniformly distributed ( (a)), as the deformation increases, the stress gradually concentrates in the pore-intensive area ( (b)-(c)), and finally, fracture occurs at the pore intersection ( (d)), which is consistent with the actual material compression failure pattern. Figure 8 (a)-(d) show the complete process from initial uniform loading to local instability: at the initial stage, the stress is uniformly distributed ( (a)), as the deformation increases, the stress gradually concentrates in the pore-intensive area ( (b)-(c)), and finally, fracture occurs at the pore intersection ( (d)), which is consistent with the actual material compression failure pattern. Figure 8 (a)-(d) show the complete process from initial uniform loading to local instability: at the initial stage, the stress is uniformly distributed ( (a)), as the deformation increases, the stress gradually concentrates in the pore-intensive area ( (b)-(c)), and finally, fracture occurs at the pore intersection ( (d)), which is consistent with the actual material compression failure pattern. Figure 8 (a)-(d) show the complete process from initial uniform loading to local instability: at the initial stage, the stress is uniformly distributed ( (a)), as the deformation increases, the stress gradually concentrates in the pore-intensive area ( (b)-(c)), and finally, fracture occurs at the pore intersection ( (d)), which is consistent with the actual material compression failure pattern.​​

Claims

1. A method for rapidly identifying the pore structure of porous materials and generating a three-dimensional model, characterized by: The following steps are involved: Step (1): performing phase decoupling and feature extraction on the two-dimensional microscopic image of the porous medium to obtain a set of topological parameters; The topological parameter set includes the porosity parameter p, the characteristic scale distribution function f and the characteristic scale cumulative distribution function F; Step (2): Based on the topological parameter set, the matching relationship between the characteristic scale distribution function f and the candidate statistical model is established through parameter space mapping to determine the optimal matching model; Step (3): Based on the optimal matching model in step (2), a feature space is established through dimensional constraints and distribution constraint equations, and geometric topological primitives that meet statistical convergence conditions are generated in the feature space; Step (4): constructing the final continuous phase space domain through the spatial domain topological mapping algorithm to realize the digital reconstruction and performance simulation of the porous material structure; The dimensional constraints in step (3) are as follows: L / D≥5, Where: L is the intrinsic scale of the feature space, D is the median of the feature scale; The distribution constraint equation in step (3) is as follows: Where: x i ,y i ,z i is the center coordinate of the geometric topological primitive; Φ(D) is the optimal matching model of the characteristic scale distribution function f; D i is the equivalent characteristic scale of geometric topological primitives, satisfying D min ≤D i ≤D max ;δ() is the Dirac Delta function; The number N of geometric topological primitives in step (3) satisfies: The spatial position of the geometric topological primitives in step (3) satisfies the following boundary constraints: In step (3), any two geometric topological primitives must satisfy the space non-containment criterion: Where: (x a ,y a ,z a ) and (x b ,y b ,z b ) are the spatial coordinates of any two geometric topological primitives, R a 、R b is the characteristic radius of the corresponding geometric topological primitive; In step (4), the final continuous phase space domain is generated by the following formula: Where: Ω final is the final continuous phase space domain, Ω0 is the initial continuous phase space domain, B k The kth geometric topological primitive occupies space, and \ represents the difference operation in the spatial domain.

2. The method according to claim 1, wherein: The phase decoupling in step (1) adopts a dynamic two-phase optimization algorithm, and the optimal phase decoupling threshold t * satisfy: Where Λ0(t) and Λ1(t) are the dynamic weight operators in the two-phase region, μ0(t) and μ1(t) are the expected vector norms of the feature space, and argmax represents the functional extreme value solution process.

3. The method according to claim 1, wherein: The candidate statistical model of step (2) includes at least one continuous probability distribution function.

4. The method according to claim 3, wherein: Step (2) specifically includes the following steps: Step (21): define the feature evaluation node set Q = {q1, q2, q3} and key statistical quantiles; Step (22): Calculate the actual observation distribution F obs (q i ) and the theoretical distribution F calculated by the candidate statistical model th (q i ) difference matrix; Step (23): Construct a composite matching function: Where: is the composite matching score; Step (24): Select The candidate statistical model with the smallest value is taken as the optimal matching model of the characteristic scale distribution function f.

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