A hybrid method for crack growth
By combining physical information convolutional neural networks with the finite element method in an alternating iterative solution, the efficiency and accuracy problems in crack propagation calculation of large structures are solved, and efficient and accurate crack propagation simulation of complex curved surface structures is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA UNIV OF MINING & TECH
- Filing Date
- 2026-04-27
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies suffer from low computational efficiency, insufficient accuracy, and limited applicability in crack propagation calculations for large structures. In particular, the phase-field method consumes enormous computational resources and its predictions are prone to deviating from reality in large and complex structures.
A Physical Information Convolutional Neural Network (PICNN) and the Finite Element Method (FE) are used for iterative solution. By constructing the Physical Information Convolutional Neural Network (PICNN), the loss function is trained using the residuals of the phase field control equations. Combined with radial basis function interpolation and UV parameterization mapping, local fine-grained processing and global coarse-grid solution are achieved.
It improves computational efficiency, ensures that the prediction results are consistent with engineering practice, is applicable to complex curved surface structures, and achieves accurate calculation of crack propagation.
Smart Images
Figure CN122433508A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of numerical simulation technology, specifically a hybrid calculation method for crack propagation. Background Technology
[0002] During long-term service, engineering structures are prone to cracking due to factors such as load, material aging, and stress concentration. Cracks can develop and propagate, seriously threatening structural safety and service life. Therefore, achieving accurate and efficient calculation of crack initiation and propagation is a core problem that urgently needs to be solved in the engineering field.
[0003] Phase-field method, as one of the main techniques for crack prediction, can continuously describe the entire process of crack initiation and propagation by introducing a diffuse crack model, avoiding the problem of crack surface tracking in traditional fracture mechanics. It shows significant advantages in crack prediction of small components or local areas. However, in engineering applications of large structures, the phase-field method faces insurmountable technical bottlenecks. The computational accuracy of the phase-field method is highly dependent on fine mesh generation, requiring a match between the characteristic length and the mesh size. However, large structures have large spatial scales and complex surface morphologies. Fine mesh generation of the entire structure leads to an exponential increase in the number of nodes, resulting in huge computational power consumption, even exceeding the carrying capacity of conventional computing equipment.
[0004] To overcome the limitations of the phase-field method, existing technologies attempt to optimize it by combining traditional finite element (FE) coarse-grid solutions with local fine-grid phase-field calculations. However, the accuracy of boundary condition transfer during the transition between the two is insufficient, and the computational cost problem caused by fine-grid methods remains unresolved. While purely data-driven intelligent algorithms improve computational efficiency, they lack physical constraints such as phase-field control equations, making predictions prone to deviating from engineering realities. Furthermore, existing algorithms are mostly designed for planar structures and cannot adapt to the geometric and mechanical properties of large curved surfaces. Therefore, given the above situation, there is an urgent need to develop a hybrid calculation method for crack propagation to overcome the shortcomings in current practical applications. Summary of the Invention
[0005] The purpose of this invention is to provide a hybrid calculation method for crack propagation to solve the problems mentioned in the background art.
[0006] To achieve the above objectives, the present invention provides the following technical solution:
[0007] A hybrid calculation method for crack propagation includes the following steps:
[0008] S1. Construct a Physical Information Convolutional Neural Network (PICNN). The training process of the PICNN includes: obtaining the historical maximum tensile strain energy density matrix of a local region on the surface of the structure in the training samples as input, constructing a loss function with the residual of the phase field control equation, and training the PICNN.
[0009] S2. During the crack propagation calculation, the finite element method (FE) global solution and the PICNN local prediction are executed alternately, wherein:
[0010] The global FE solution includes: performing finite element analysis on the target structure using a coarse mesh to obtain global mechanical field data;
[0011] The PICNN local prediction includes: dividing a local region around the crack; extracting the boundary conditions of the local region through radial basis function interpolation based on the global mechanical field data; transforming the three-dimensional surface of the local region into a two-dimensional parametric plane through UV parametric mapping adapted to the geometry of the target structure, and generating the historical maximum tensile strain energy density matrix of the local region; and inputting the historical maximum tensile strain energy density matrix into the trained PICNN to obtain the predicted phase field of the local region.
[0012] S3. Determine the damage variables based on the predicted phase field, and update the global model in the FE global solution based on the damage variables.
[0013] As a further aspect of the present invention, the training process of the PICNN further includes: transforming the historical maximum tensile strain energy density matrix according to the rule of corresponding Gaussian points for each pixel, and inputting it into the PICNN with a 4-layer symmetric convolutional structure; the output of the PICNN is the phase field prediction matrix; the loss function is constructed based on the global average residual L2 norm of the strong form of the phase field control equation.
[0014] As a further aspect of the present invention: the generation method of the historical maximum tensile strain energy density matrix includes: calculating the tensile strain energy density of the current load step, traversing the historical load steps, and taking the maximum value of the tensile strain energy density as the historical maximum tensile strain energy density; wherein, the tensile strain energy density is calculated based on the strain field and material elastic parameters of the local region.
[0015] As a further aspect of the present invention: the step of extracting the boundary conditions of the local region by radial basis function interpolation includes: expanding outward from the boundary of the local region to form an interpolation domain, selecting global nodes as sample points within the interpolation domain, and using composite interpolation of radial basis functions and linear polynomials to calculate the stress and displacement on the boundary of the local region.
[0016] As a further aspect of the present invention, the UV parameterization mapping includes: for planar structures, a rectangular coordinate translation mapping; for conical structures, a polar coordinate to rectangular coordinate conversion mapping; and for hyperbolic paraboloid structures, a conformal correction mapping.
[0017] As a further aspect of the present invention: generating the historical maximum tensile strain energy density matrix of the local region includes: discretizing the two-dimensional parameter plane obtained by the UV parameterization mapping into a pixel matrix, extracting the strain value corresponding to each pixel point from the strain field of the local region by bilinear interpolation, and then calculating the historical maximum tensile strain energy density of each pixel point.
[0018] As a further aspect of the present invention: updating the global model in the global solution of the FE based on the damage variable includes: obtaining the damage variable according to the predicted phase field mapping, updating the elastic modulus of the local element according to the rule that the elastic modulus decreases monotonically with the damage variable, and integrating the updated local element stiffness matrix into the global stiffness matrix.
[0019] The present invention also provides a hybrid computing device, electronic device, and computer-readable storage medium for crack propagation, for performing the above-described method, wherein the hybrid computing device for crack propagation includes:
[0020] The model building module is used to build a Physical Information Convolutional Neural Network (PICNN). The training process of the PICNN includes: obtaining the historical maximum tensile strain energy density matrix of a local region on the surface of the structure in the training samples as input, constructing a loss function with the residual of the phase field control equation, and training the PICNN.
[0021] The staggered solution module is used to alternately execute the global solution of finite element method (FE) and the local prediction of PICNN during the crack propagation calculation process;
[0022] The interleaved solution module includes:
[0023] The FE solver element is used to perform finite element analysis on the target structure using a coarse mesh to obtain global mechanical field data.
[0024] The PICNN prediction unit is used to divide a local region around the crack. Based on the global mechanical field data, it extracts the boundary conditions of the local region through radial basis function interpolation. By using UV parameterized mapping adapted to the geometry of the target structure, it transforms the three-dimensional surface of the local region into a two-dimensional parametric plane and generates the historical maximum tensile strain energy density matrix of the local region. The historical maximum tensile strain energy density matrix is input into the trained PICNN to obtain the predicted phase field of the local region.
[0025] The update unit is used to determine the damage variable based on the predicted phase field and update the global model in the FE global solution based on the damage variable.
[0026] Compared with the prior art, the beneficial effects of the present invention are:
[0027] 1. High computational efficiency: This invention uses a coarse FE mesh for global solution and only performs fine processing on the local area around the crack. The phase field is quickly predicted by the PICNN surrogate model, which avoids the huge computational power consumption caused by the fine mesh division of the entire structure in the traditional phase field method and greatly improves the computational efficiency.
[0028] 2. Strong physical constraints: This invention uses the residuals of the phase field control equations to construct a loss function to train PICNN, embedding the physical laws of fracture mechanics into the intelligent prediction model, ensuring that the prediction results conform to engineering practice, and overcoming the defect that pure data-driven models are prone to deviating from the physical essence.
[0029] 3. Wide range of applicability: This invention proposes a UV parameterized mapping method that is suitable for different geometric structures such as planes, conical surfaces, and hyperbolic paraboloids. Combined with radial basis function interpolation to accurately transfer boundary conditions, it realizes accurate calculation of crack propagation in complex curved surface structures.
[0030] 4. Accurate closed-loop feedback: This invention establishes a quantitative mapping relationship between phase field values and damage variables, and feeds the prediction results back to the FE global model in a closed loop through the elastic modulus degradation mechanism, so as to realize the dynamic update of the stiffness matrix and fully simulate the entire process of crack initiation to fracture. Attached Figure Description
[0031] Figure 1 This is a flowchart illustrating the crack propagation hybrid calculation method provided in an embodiment of the present invention.
[0032] Figure 2 This is a schematic diagram of the structure of PICNN in an embodiment of the present invention.
[0033] Figure 3 This is a schematic diagram of the symmetry constraint of the 5×5 convolution kernel in an embodiment of the present invention.
[0034] Figure 4 This is a schematic diagram of the local interpolation domain in an embodiment of the present invention. Detailed Implementation
[0035] The technical solution of this application will be further described in detail below with reference to specific embodiments.
[0036] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.
[0037] This invention provides a hybrid calculation method for crack propagation, the core of which lies in the interleaved iterative solution of Physical Information Convolutional Neural Network (PICNN) and Finite Element Method (FE). For example... Figure 1 As shown, this method mainly includes the PICNN training stage and the FE-PICNN interleaved iterative solution stage.
[0038] I. PICNN Training Phase:
[0039] The goal of this phase is to build a surrogate model that can quickly and accurately predict the phase field based on the local mechanical state.
[0040] First, prepare the training dataset. Typical engineering structures such as planar structures, conical structures, and hyperbolic paraboloid structures are selected as training samples. For each structure, a coarse mesh is discretized, and material properties, loads, and boundary conditions are input. The global strain field, stress field, and displacement field are output through finite element analysis.
[0041] For each training sample, a square local fine-mesh region with a side length three times the crack length is defined centered on the crack. Radial basis function interpolation is used to extract the mechanical and displacement boundaries of the local region from the global coarse-mesh data. An appropriate UV parametric mapping method is selected based on the structural geometry type to convert the local 3D geometric surface into a 2D parametric plane. Specifically:
[0042] (1) Dataset preparation
[0043] It represents the maximum tensile strain energy density at a point on the surface of the structure from the initial moment to the current moment, and is the physical quantity that drives crack propagation.
[0044] First, calculate the tensile strain energy density of the current load step. :
[0045] (1);
[0046] in, and These are the elastic moduli of the material in two directions, respectively. and The principal strain at Gaussian points in a local fine mesh (output by FE solution); For Macaulay brackets, defined as .
[0047] Traversing historical load steps, taking The maximum value is used as :
[0048] (2);
[0049] in, Represents the time from the initial moment to the current moment. All historical loading steps, ensure The load decreases monotonically, which is consistent with the physical law that once a crack initiates, it cannot heal itself.
[0050] The local fine mesh uses structured square cells, each containing one Gaussian point (GP), and is transformed according to the rule that one Gaussian point corresponds to one pixel:
[0051] (3);
[0052] in, For pixel matrix index, the pixel matrix size is . ( This represents the side length of a local fine-mesh square region. (for unit size)
[0053] (2) PICNN architecture design
[0054] The PICNN network architecture design aims to balance the accuracy of physical feature extraction with computational efficiency, while ensuring generalization ability for cracks in different directions. It employs a four-layer symmetrical convolutional structure. The input is a single-channel... Pixel matrix (size is The output is a phase field prediction matrix of the same size. Detailed model structure as follows Figure 2 As shown.
[0055] The first three layers are feature convolutional layers, each using a 5×5 kernel with a stride of 1 and padding of 2. To avoid the model becoming dependent on the crack propagation direction, each kernel is subject to four symmetry constraints: left-right mirroring and top-bottom mirroring. This kernel has six independently trainable parameters, reducing model complexity and accelerating training convergence. The kernel is as follows... Figure 3 As shown in the figure. The activation function used is the Tanh function, and the calculation formula is shown in equation (4).
[0056] (4);
[0057] The fourth layer is the output convolutional layer, with the same parameter settings as the first three layers, but the activation function is replaced by the Sigmoid function (Equation (5)). The output range of this function is limited to [0, 1], which is to conform to the phase field. The physical definition of phase field. =0 indicates that the material is intact and undamaged. =1 indicates that the material is completely broken, while the range (0,1) indicates different degrees of damage.
[0058] (5);
[0059] To construct physical constraints, the Laplace operator of the phase field needs to be calculated during network training. It employs a 9-point finite difference scheme to improve computational accuracy, and uses a custom convolution kernel. The result is achieved as shown in equation (6).
[0060] (6);
[0061] final, The calculation formula is as follows:
[0062] (7);
[0063] in, For pixel spacing, the value is the same as... equal, These are the spatial coordinates of the pixel matrix.
[0064] (3) Loss Function
[0065] The loss function is crucial; it ensures that the PICNN prediction results conform to the physical laws of crack fracture. The strong form of the phase-field governing equation (AT2 model) is:
[0066] (8);
[0067] in, For fracture energy, The characteristic length is denoted as .
[0068] Based on the definition of the residual term in the phase field control equation (Equation (8)) :
[0069] (9);
[0070] The smaller the residual, the closer the predicted phase field is to the actual physical laws.
[0071] The loss function uses the global average residual L2 norm of the pixel matrix, i.e.:
[0072] (10);
[0073] (4) Training process
[0074] The training process of PICNN follows the standard deep learning training paradigm of initialization, forward propagation, loss calculation, back propagation, and parameter update. First, the weights of each layer of the network are initialized, followed by batch input of training samples. The pixel matrix is used to calculate the predicted phase field through forward propagation of 4 convolutional layers. Calculate the Laplace operator based on the predicted phase field With residual Then calculate the loss function. Then, the gradient of the loss function with respect to the weights of each layer is calculated using the backpropagation algorithm, and the network weights are updated using the Adam optimizer. Finally, the above process of forward propagation to weight update is repeated until the convergence criterion is met, and the model training is completed.
[0075] II. FE-PICNN Interleaved Iterative Solution Stage
[0076] In this stage, the trained PICNN is embedded into the finite element analysis process to achieve efficient and accurate crack propagation simulation.
[0077] (1) Global mechanical solution of FE
[0078] The use of a coarse mesh in the FE global mechanics solution is to quickly obtain the mechanical data of the structure and output the global strain field. Global stress field Global displacement field Surface curvature field And Gaussian point coordinates; this data will be used for local region partitioning, boundary condition transfer, and... calculate.
[0079] (2) Localized fine processing
[0080] The core of the local refinement module is to generate data that meets the input requirements of PICNN based on the global FE data. The pixel matrix involves specific steps including region division, boundary transfer, and coordinate mapping. Calculation, pixel conversion.
[0081] The local computational domain is a square, and its boundary is denoted as . Side length 3 times the crack length Local unit size for .
[0082] To ensure the continuity of the local and global mechanical fields, radial basis function interpolation is used to extract local boundary conditions, avoiding the accuracy loss caused by directly using the global coarse mesh boundary. This is achieved by using the local computational domain boundary... Based on the baseline, expand outward by 0.2 times. To avoid abrupt changes in the difference results, it is denoted as the local interpolation domain, such as... Figure 4 As shown. The geometric definition of sample points within the local interpolation domain is... , and These are the indices of the sample point in the x and y directions of the global grid, respectively. Each Includes spatial coordinates ,stress (Perpendicular to the crack direction), displacement (Perpendicular to the crack direction) and weighting markers .
[0083] Using a composite interpolation of radial basis functions and linear polynomials, interpolation functions are constructed for the stress and displacement of arbitrary nodes on the boundary of the local computational domain:
[0084] (11);
[0085] (12);
[0086] In the formula: and Let be the target stress value and target displacement value of the ij-th node on the local boundary; The Euclidean distance between local boundary node ij and sample point kl is defined as follows: ; For multiple quadratic radial basis functions, defined as ,in This is a shape parameter, and its value is the side length of the local computational domain. 0.1 times; and These are the radial basis function coefficients corresponding to sample points kl in stress and displacement interpolation, respectively, used to control the contribution weight of sample points to local boundary nodes; , , , These are the coefficients of the linear polynomial.
[0087] Will Substitute the coordinates of all nodes into equations (11) and (12) respectively to calculate the boundary stress and boundary displacement of each node, and use them as the mechanical boundary conditions and displacement boundary conditions of the local computational domain.
[0088] To address the characteristics of complex curved surfaces, UV parametric mapping is used to establish a one-to-one correspondence between the local 3D spatial coordinates and the 2D parametric plane coordinates of the structure.
[0089] 1. Planar structure
[0090] The z-axis coordinate of the planar structure is 0, so no complex transformation is needed; a direct Cartesian coordinate translation mapping can be used.
[0091] (13);
[0092] In the formula, and Let x and y be the spatial coordinates of the ij-th node in the local 3D region; and Let be the 2D parametric plane coordinates corresponding to the ij-th node; and These are the x and y coordinates of the lower left vertex of the local 3D region.
[0093] 2. Conical surface structure
[0094] The local 3D region of the conical structure is a segment of the conical surface, satisfying the following spatial coordinate relationship:
[0095] (14);
[0096] In the formula, , and Let x, y, z be the x, y, z coordinates of the ij-th node in the local 3D region of the structure. The radius of the bottom of the conical structure is... This represents the height of the conical structure.
[0097] Using polar coordinates to rectangular coordinates conversion mapping:
[0098] (15);
[0099] In the formula, Let be the distance from the ij-th node to the z-axis; Let be the polar angle of the ij-th node; It represents the minimum polar angle within a local 3D region.
[0100] 3. Hyperbolic parabolic structure
[0101] The local 3D region of a hyperbolic paraboloid structure is a hyperbolic paraboloid, which generally satisfies the following spatial coordinate relationships:
[0102] (16);
[0103] In the formula, , and Let x, y, z be the x, y, z coordinates of the ij-th node in the local 3D region of the hyperbolic paraboloid structure; Let be the curvature coefficient at the ij-th node.
[0104] Conformal mapping is used, and the mapping relationship is as follows:
[0105] (17);
[0106] and These are the 2D parametric plane coordinates after curvature correction.
[0107] After UV mapping, all three structures mentioned above require normalization of their final 2D parameter coordinates to ensure that the parameter plane dimensions input to PICNN are standardized.
[0108] (18);
[0109] and The coordinates are the result of mapping various structures. , , , These represent the minimum and maximum values of the corresponding coordinates within the local area.
[0110] (3) Pixel matrix calculation and calling PICNN
[0111] FE global solver outputs the strain tensor of each node within the local 3D region. Then, it is mapped to UV and transformed into a strain field in a 2D parametric plane. Taking plane stress problems as an example, the 3D strain tensor contains only in-plane components:
[0112] (19);
[0113] The strain value is directly transferred through coordinate mapping, that is:
[0114] (20);
[0115] This equation shows that the in-plane strain of the 3D node (i, j) is completely consistent with the strain value of the corresponding 2D pixel (p, q), only the spatial coordinate dimension is changed from 3D to 2D.
[0116] Let the range of the 2D parameter plane after UV mapping be... , Preset pixel size = Then the pixel matrix size is:
[0117] (twenty one);
[0118] In the formula, This is the floor operator.
[0119] For pixel (p, q), its center coordinates are:
[0120] (twenty two);
[0121] The corresponding strain values are extracted from the 2D strain field using bilinear interpolation:
[0122] (twenty three);
[0123] (twenty four);
[0124] In the formula, These are the interpolation weights.
[0125] Under unconstrained conditions, the in-plane strain energy density of an orthotropic material is:
[0126] (25);
[0127] In the formula, For cross-modulus of elasticity, Shear modulus This is the shear modulus.
[0128] Crack propagation is irreversible; that is, once the tensile strain energy density at a certain point reaches its peak, the damage driving energy at that point will not decrease even if the subsequent load is reduced. It needs to be defined as the maximum value of tensile strain energy density from the initial moment to the current moment.
[0129] Then The matrix is normalized to the interval [0, 1]. Let the current... The minimum value of the matrix is The maximum value is Then the normalization formula is:
[0130] (26);
[0131] Normalized Inputting into PICNN, it is processed through 4 convolutional layers to obtain... To feed back to the FE global model, the 2D phase field prediction matrix is converted into a 3D phase field distribution through UV inverse mapping:
[0132] (27);
[0133] (28);
[0134] in, The 3D phase field value is obtained through UV inverse mapping.
[0135] (4) Damage feedback and global update
[0136] Phase ,in =0 indicates that the material is intact. =1 indicates complete fracture, therefore the damage variable It can be directly obtained from the phase field values, and the formula is:
[0137] (29);
[0138] In the formula, Let be the damage variable of the ij-th node in the 3D local region.
[0139] The elastic modulus decreases monotonically with respect to the damage variable, satisfying:
[0140] (30);
[0141] In the formula, The initial elastic modulus of the material. The elastic modulus after damage. Damage variable
[0142] Based on the degraded material properties, the element stiffness matrix of the global FE model is updated, and a load step is added to continue solving the displacement and strain fields.
[0143] (5) Iteration terminated
[0144] The entire process proceeds in stages according to the load coefficient. Each stage completes a cycle of "damage feedback → stiffness update → mechanical resolution → PICNN prediction" until the external load reaches the preset maximum value, at which point the iteration terminates.
[0145] Specific examples
[0146] The method of the present invention will now be described using an umbrella-shaped membrane structure with a diameter of 8m and a height of 3m as an example.
[0147] Step 1: Umbrella-shaped membrane structure modeling and FE solution
[0148] Step 1-1: Establish a 3D model of the umbrella-shaped membrane in the finite element software. The bottom radius R=4m, the umbrella height H=3m, the membrane thickness t=0.7mm, and the material parameters are orthogonal elastic modulus (E1=1000MPa, E2=900MPa, G12=40MPa, Poisson's ratio ν0=0.3, fracture energy Gc=40kJ / m2). Pre-fabricate a crack with a length of 10mm on the membrane surface.
[0149] Steps 1-2: Use triangular shell elements to generate a global coarse mesh, constrain the degrees of freedom of the top nodes of the umbrella-shaped membrane, and apply a uniformly distributed load along the meridional direction of the membrane surface. The load step t starts from 0 and is applied in increments of 0.01.
[0150] Steps 1-3: Start the FE static mechanics solution and output the global node data of the first loading step (t=0.01), including 3D spatial coordinates, strain field, and stress field.
[0151] Step 2: Determining the local computational domain and extracting the mechanical boundary
[0152] Step 2-1: Determine the local computational domain, such that the adjacent edges of the local computational domain are parallel and perpendicular to the crack, and the crack is located at the center of the local computational domain. The side length of the local computational domain is 30mm.
[0153] Step 2-2: Based on the conical surface geometric characteristics of the umbrella-shaped membrane structure, the 3D coordinates of the local computational domain are converted into 2D coordinates according to Equation (15).
[0154] Steps 2-3: Using the boundary of the local computational domain as a reference, expand outward by 0.2 times the length to form a sample region. Select 20 global nodes in the sample region as sample points. Use multiple quadratic radial basis functions to construct an interpolation function and calculate the boundary stress of all nodes on the boundary.
[0155] Step 3: H-pixel matrix calculation and PICNN phase field prediction
[0156] Step 3-1: Determine the size of the H pixel matrix based on the 2D parameter plane size and pixel size after UV mapping, and discretize the 2D strain field after UV mapping into a pixelated strain matrix through bilinear interpolation.
[0157] Step 3-2: Call the pre-trained PICNN model, input H into the network, and output the predicted phase field matrix.
[0158] Step 3-3: Convert the 2D phase field matrix into a 3D local domain phase field distribution using the UV inverse mapping function.
[0159] Step 4: Damage Feedback and Global Model Update Iteration
[0160] Step 4-1: Using the 3D phase field value as the damage variable, correct the element elastic modulus for each FE element in the local domain.
[0161] Step 4-2: Integrate the degraded local element stiffness matrix into the global stiffness matrix, perform FE solution, and output the global strain field updated at load step t=0.01.
[0162] Step 4-3: Add a load step, use the updated strain field as the input for the next round of calculation, repeat steps 2 to 4 until the external load reaches the preset maximum value, and the iteration terminates.
[0163] By following the steps above, efficient and accurate simulation of crack propagation in large and complex structures can be achieved.
[0164] This hybrid computational method for crack propagation avoids the high computational cost of the phase-field method by iteratively combining FE (Fractional Equation) and PICNN (Physical Intensity-Conjecture-CNN) phase field prediction. This achieves efficient computation of crack propagation at the structural scale, and the entire method can be completed using only a computer equipped with conventional FE software and a deep learning framework. By constructing the PICNN loss function from the residuals of the phase-field governing equations, physical laws are embedded into the intelligent prediction model, avoiding the pitfalls of purely data-driven models that easily deviate from the essence of fracture mechanics. This method ensures computational efficiency while outputting crack paths and damage distribution results that conform to actual engineering laws. For structures with different geometric characteristics, such as planar, conical, and hyperbolic parabolic shapes, this invention proposes an adaptive UV parameterized mapping and RBF interpolation rule. Combined with the quantized mapping of phase-field-damage variables and the elastic modulus degradation mechanism, it enables the computation of crack propagation in structures with different geometric types.
[0165] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these should also be considered within the scope of protection of the present invention. These will not affect the effectiveness of the implementation of the present invention or the practicality of the patent.
Claims
1. A hybrid calculation method for crack propagation, characterized in that, Includes the following steps: S1. Construct a Physical Information Convolutional Neural Network (PICNN). The training process of the PICNN includes: obtaining the historical maximum tensile strain energy density matrix of a local region on the surface of the structure in the training samples as input, constructing a loss function with the residual of the phase field control equation, and training the PICNN. S2. During the crack propagation calculation, the finite element method (FE) global solution and the PICNN local prediction are executed alternately, wherein: The global FE solution includes: performing finite element analysis on the target structure using a coarse mesh to obtain global mechanical field data; The PICNN local prediction includes: dividing a local region around the crack; extracting the boundary conditions of the local region through radial basis function interpolation based on the global mechanical field data; transforming the three-dimensional surface of the local region into a two-dimensional parametric plane through UV parametric mapping adapted to the geometry of the target structure, and generating the historical maximum tensile strain energy density matrix of the local region; and inputting the historical maximum tensile strain energy density matrix into the trained PICNN to obtain the predicted phase field of the local region. S3. Determine the damage variables based on the predicted phase field, and update the global model in the FE global solution based on the damage variables.
2. The hybrid calculation method for crack propagation according to claim 1, characterized in that, The training process of the PICNN also includes: transforming the historical maximum tensile strain energy density matrix according to the rule of corresponding Gaussian points for each pixel, and inputting it into the PICNN with a 4-layer symmetric convolution structure. The output of the PICNN is the phase field prediction matrix. The loss function is constructed based on the global average residual L2 norm of the strong form of the phase field control equation.
3. The hybrid calculation method for crack propagation according to claim 2, characterized in that, The method for generating the historical maximum tensile strain energy density matrix includes: calculating the tensile strain energy density of the current load step, traversing the historical load steps, and taking the maximum value of the tensile strain energy density as the historical maximum tensile strain energy density; wherein, the tensile strain energy density is calculated based on the strain field and material elastic parameters of the local region.
4. The hybrid calculation method for crack propagation according to claim 1, characterized in that, The step of extracting the boundary conditions of the local region by radial basis function interpolation includes: expanding outward from the boundary of the local region to form an interpolation domain, selecting global nodes as sample points within the interpolation domain, and using composite interpolation of radial basis functions and linear polynomials to calculate the stress and displacement on the boundary of the local region.
5. The hybrid calculation method for crack propagation according to claim 1, characterized in that, The UV parameterization mapping includes: for planar structures, a rectangular coordinate translation mapping; for conical structures, a polar coordinate to rectangular coordinate conversion mapping; and for hyperbolic paraboloid structures, a conformal correction mapping.
6. The hybrid calculation method for crack propagation according to claim 1, characterized in that, The step of generating the historical maximum tensile strain energy density matrix of the local region includes: discretizing the two-dimensional parameter plane obtained by the UV parameterization mapping into a pixel matrix, extracting the strain value corresponding to each pixel from the strain field of the local region by bilinear interpolation, and then calculating the historical maximum tensile strain energy density of each pixel.
7. The hybrid calculation method for crack propagation according to claim 1, characterized in that, The step of updating the global model in the global solution of the FE based on the damage variable includes: obtaining the damage variable according to the predicted phase field mapping, updating the elastic modulus of the local element according to the rule that the elastic modulus decreases monotonically with the damage variable, and integrating the updated local element stiffness matrix into the global stiffness matrix.
8. A hybrid computing device for crack propagation, characterized in that, include: The model building module is used to build a Physical Information Convolutional Neural Network (PICNN). The training process of the PICNN includes: obtaining the historical maximum tensile strain energy density matrix of a local region on the surface of the structure in the training samples as input, constructing a loss function with the residual of the phase field control equation, and training the PICNN. The staggered solution module is used to alternately execute the global solution of finite element method (FE) and the local prediction of PICNN during the crack propagation calculation process; The interleaved solution module includes: The FE solver element is used to perform finite element analysis on the target structure using a coarse mesh to obtain global mechanical field data. The PICNN prediction unit is used to divide a local region around the crack. Based on the global mechanical field data, it extracts the boundary conditions of the local region through radial basis function interpolation. By using UV parameterized mapping adapted to the geometry of the target structure, it transforms the three-dimensional surface of the local region into a two-dimensional parametric plane and generates the historical maximum tensile strain energy density matrix of the local region. The historical maximum tensile strain energy density matrix is input into the trained PICNN to obtain the predicted phase field of the local region. The update unit is used to determine the damage variable based on the predicted phase field and update the global model in the FE global solution based on the damage variable.
9. An electronic device, characterized in that, include: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the hybrid calculation method for crack propagation as described in any one of claims 1-7.
10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed by the processor, they implement the hybrid calculation method for crack propagation as described in any one of claims 1-7.