CN-122021398-A - Cross-scale matrix flow modeling method combined with graph theory

CN122021398ACN 122021398 ACN122021398 ACN 122021398ACN-122021398-A

Abstract

The invention discloses a cross-scale matrix flow modeling method combined with graph theory, and relates to the field of composite material molding process simulation. The method comprises the steps of establishing a high-precision matrix shearing constitutive model through rheological experiments and symbolic regression, establishing a reinforced body pore wall surface rough model based on fractal theory, deriving a single horizontal circular tube flow formula considering rough effects by combining the two, performing binarization and coarsening treatment on a reinforced body CT image, establishing a graph network model, quantitatively defining edge resistance, identifying a minimum resistance path in the graph network to serve as a main flow channel by using Dijkstra algorithm, and finally, realizing flow prediction from nano rough scale and pore scale to macroscopic darcy scale based on main flow channel information and a serial calculation model. The method solves the problems of inaccurate rheological characterization, neglect of coarse effect, difficult cross-scale association and low recognition efficiency of the main channel in the traditional method, and remarkably improves the accuracy and efficiency of matrix flow prediction in the composite material forming process.

Inventors

LI YONG
XIE XINGYU
ZHANG TENGWEN
Miao yanan
CHEN LONG
HAN SHANLING

Assignees

山东科技大学

Dates

Publication Date: 20260512
Application Date: 20251226

Claims (8)

1. A method of cross-scale matrix flow modeling in combination with graph theory, comprising the steps of: s1, acquiring shear stress data of a matrix at different shear rates through a rheological experiment, and performing nonlinear fitting by adopting a symbolic regression algorithm based on the data to establish and determine a shear constitutive model of parameters, wherein the shear constitutive model is used for representing yield stress and shear thinning characteristics of the matrix; s2, acquiring a microscopic morphology image of a pore wall surface of the reinforcement, and constructing a fractal rough model of the wall surface by adopting a Weierstrass-Mandelbrot function based on a fractal theory to obtain a fractal self-imitated characteristic equation for representing a rough contour; s3, substituting the shear constitutive model determined in the step S1 into a circular tube flow equation considering yield stress correction, and deducing a single horizontal circular tube flow formula considering a rough effect by combining the parameters representing the roughness obtained in the step S2; S4, acquiring a three-dimensional pore structure image of the reinforcement, carrying out binarization and coarsening treatment on the image, and constructing a graph network model based on the treated image, wherein a pore area is defined as a node, and the connection between adjacent pore nodes is defined as an edge; S5, calculating edge resistance for each edge in the graph network model, wherein the edge resistance is a value calculated by a quantization formula based on the pore characteristics at the current node, the coarsening resolution of the image and the pressure difference direction between adjacent nodes; s6, searching a minimum resistance path from a specified inlet node to a specified outlet node in the graph network model by adopting a graph searching algorithm, and identifying the path as a main flow channel of the matrix flowing in the reinforcement; And S7, calculating the total flow prediction value of the inside of the reinforcement under the macroscopic pressure gradient through a serial flow calculation model based on the resistance information of each side on the main flow channel identified in the step S6 and the single horizontal circular tube flow formula considering the rough effect obtained in the step S3.
2. The graph-theory-combined cross-scale matrix flow modeling method according to claim 1, wherein in step S1, the shear constitutive model is a four-parameter rheological model, and the expression is: , wherein, In order for the shear stress to be a high shear stress, In order to achieve a shear rate, In order to be a yield stress, 、 As the coefficients of the model, Is a flow index; fitting experimental data by a symbolic regression algorithm to determine parameters 、、、 And the fitting variance is not less than 0.999.
3. The method of cross-scale matrix flow modeling in conjunction with graph theory of claim 1, wherein in step S2, The Weierstrass-Mandelbrot function is: ; Wherein, the Is the height of the rough profile, Is a coordinate of the horizontal position of the device, As a parameter of the characteristic dimension(s), For the fractal dimension, For a scale parameter greater than 1, In order to calculate the sum sequence number, Obtaining a fractal dimension D and a root mean square roughness sigma based on a scanning electron microscope image, and further solving a parameter G to generate a fractal rough wall surface model with statistical self-similar characteristics; is a coefficient; Controlling the decay rate of the amplitudes of the different frequency components.
4. A cross-scale matrix flow modeling method according to claim 3, wherein in step S3, the single horizontal tubular flow equation considering the coarse effect is obtained by: Firstly, introducing a yield stress correction term into a general circular tube flow equation, wherein the circular tube flow equation considering the yield stress correction is as follows: ; Wherein, the In order to be a flow rate, Is the radius of the capillary tube, For the shear stress of the pipe wall, In order to be a yield stress, Is the shear rate; then, the shear constitutive model is subjected to Substituting the above to carry out integral derivation and combining the relative roughness defined by the fractal rough model , Is the roughness of the root mean square, The single horizontal circular tube flow formula considering the coarse effect is obtained by taking the width of the characteristic channel as the following formula: wherein To take into account the flow after the coarse effect.
5. The graph-theory-combined cross-scale matrix flow modeling method according to claim 1, wherein in step S5, the calculation formula of the edge resistance is: ; Wherein, the Index for the current pore node; Is connected with pore nodes And Resistance associated with the edge between; is the minimum distance between the current aperture node and the entity node; to coarsen the image The number of aperture voxels of the original image in the block; the permeability of voxels with microporosity relative to the permeability of pore voxels, Representing the current pore node Move to the next pore node The weight due to the pressure differential component.
6. The graph theory-combined cross-scale matrix flow modeling method according to claim 1, wherein in step S6, the graph search algorithm is Dijkstra algorithm, and a binary heap data structure is adopted to optimize the algorithm, so as to improve the calculation efficiency of searching the minimum resistance path in the large graph network.
7. The graph-theory-combined cross-scale matrix flow modeling method according to claim 1, wherein in step S7, the series flow calculation model is: ; Wherein, the As a predicted value of the total flow rate, Calculating the flow rate for the ith flow unit according to the single horizontal circular tube flow rate formula considering the coarse effect, Is a series flow correction factor.
8. The graph-theory-combined cross-scale matrix flow modeling method of claim 7, wherein the series flow correction factor The value of (2) is set according to the geometric trend of the flow unit, the value of the horizontal serial section which is straight in the flow direction is 1, and the value of the bending serial section which is changed in the flow direction is 0.5.

Description

Cross-scale matrix flow modeling method combined with graph theory Technical Field The invention relates to the technical field of simulation and optimization of composite material forming processes, in particular to a trans-scale modeling method for predicting matrix flow behavior of a reinforced body-based composite material (such as a resin matrix composite material) in processes of vacuum auxiliary resin transfer molding and the like, and particularly relates to a trans-scale matrix flow modeling algorithm combining rheology, fractal theory and graph theory. Background In the liquid forming process of reinforcement matrix composite materials (such as carbon fiber/resin composite materials), the precise prediction of the flow process of a matrix (usually a non-newtonian fluid such as resin) in a complex porous reinforcement is important for optimizing process parameters, avoiding defects such as dry spots and pores, improving product quality and reducing production cost. However, the prior art faces many challenges in realizing accurate flow prediction, firstly, a matrix often presents a non-Newtonian fluid with both yield stress and shear thinning characteristics, and a traditional bingham model, a power law model and other rheological models are difficult to simultaneously and accurately characterize the two characteristics, so that a flow constitutive relation is deviated. Secondly, the pore wall surface inside the reinforcement (such as fiber bundles) has a natural coarse structure on the nano scale, the existing modeling method is mostly characterized by adopting a simplified rule or a random curve, and the fractal self-similar statistical characteristics of the true coarse surface can not be reflected, so that the obvious influence of the micro-scale coarse effect on seepage is ignored. Furthermore, flow simulation needs to span a huge range from nano coarse scale, micro pore scale to macro product scale, the existing method lacks an efficient and accurate cross-scale correlation frame, and technical faults exist from microscopic permeability amplification to macroscopic darcy scale flow rules. Finally, in a complex porous medium network, the rapid and accurate identification of the path of least resistance (main flow channel) that dominates global flow is the key to flow prediction, and traditional methods rely on brute force searching or empirical determination, with low efficiency and large errors. Therefore, developing a modeling method capable of integrating a high-precision rheological model, a real rough effect, high-efficiency cross-scale correlation and intelligent flow path identification becomes a technical problem to be solved in the field. Disclosure of Invention The invention aims to solve the technical problem of overcoming the defects of the prior art and providing the cross-scale matrix flow modeling method which has high precision and good efficiency and can truly reflect the combination of graph theory from microscopic flow rule to macroscopic flow rule. . In order to achieve the above purpose, the present invention adopts the following technical scheme: a method of cross-scale matrix flow modeling in conjunction with graph theory, comprising the steps of: s1, acquiring shear stress data of a matrix at different shear rates through a rheological experiment, and performing nonlinear fitting by adopting a symbolic regression algorithm based on the data to establish and determine a shear constitutive model of parameters, wherein the shear constitutive model is used for representing yield stress and shear thinning characteristics of the matrix; s2, acquiring a microscopic morphology image of a pore wall surface of the reinforcement, and constructing a fractal rough model of the wall surface by adopting a Weierstrass-Mandelbrot function based on a fractal theory to obtain a fractal self-imitated characteristic equation for representing a rough contour; s3, substituting the shear constitutive model determined in the step S1 into a circular tube flow equation considering yield stress correction, and deducing a single horizontal circular tube flow formula considering a rough effect by combining the parameters representing the roughness obtained in the step S2; S4, acquiring a three-dimensional pore structure image of the reinforcement, carrying out binarization and coarsening treatment on the image, and constructing a graph network model based on the treated image, wherein a pore area is defined as a node, and the connection between adjacent pore nodes is defined as an edge; S5, calculating edge resistance for each edge in the graph network model, wherein the edge resistance is a value calculated by a quantization formula based on the pore characteristics at the current node, the coarsening resolution of the image and the pressure difference direction between adjacent nodes; s6, searching a minimum resistance path from a specified inlet node to a specified outlet node in the graph networ