Near-field dynamic damage modeling method, system, electronic device, and storage medium

Abstract

This invention provides a method, system, electronic device, and storage medium for near-field dynamic damage modeling. The method includes: spatially discretizing the structure of the material to be analyzed to establish a near-field dynamic computational model containing multiple nodes; establishing near-field dynamic governing equations; transforming the near-field dynamic integral operator into a convolutional form and constructing a fast convolution computational framework using Fast Fourier Transform to calculate nonlocal interaction forces; calculating the nonlocal expansion of nodes, introducing a node integrity factor, and calculating the node strain energy density to establish a tensile-compression sensing damage criterion; updating the node integrity factor and degrading the nonlocal interaction forces to generate a near-field dynamic damage model. This invention improves physical consistency, reduces computational costs, avoids numerical instability risks such as zero-energy modes, and is applicable to various near-field dynamic theoretical frameworks.

Description

Technical Field

[0001] This invention relates to the fields of computational mechanics and numerical simulation technology, specifically to a near-field dynamic damage modeling method, system, electronic device, and storage medium. Background Technology

[0002] Material fracture and failure have long been important research topics in mechanical engineering, civil engineering, and aerospace engineering. Crack initiation and propagation directly affect the integrity and service safety of structural components; therefore, accurate prediction of crack behavior is crucial for structural safety assessment. Perifield dynamics is a theoretical framework based on nonlocal interactions. It describes the interactions between material points through integral forms, allowing discontinuities such as cracks to arise and evolve naturally during the calculation process without explicit crack tracking. Depending on the theoretical form, perifield dynamics models typically include bond-basis perifield dynamics, normal-state-basis perifield dynamics, and unconventional-state-basis perifield dynamics.

[0003] However, peridynamics involves nonlocal interaction calculations, resulting in high computational costs. Fast convolution methods utilize the convolution structure of peridynamic integral operators and accelerate the solution process through fast Fourier transform, significantly reducing computational complexity. To maintain the convolution structure, damage evolution in fast convolution methods typically needs to be expressed at the node level. Existing node-level damage models mainly fall into two categories: The first is damage models based on node strain energy density. This method is computationally efficient, but because strain energy density is a non-negative scalar, it is difficult to distinguish between tensile and compressive states, potentially generating non-physical damage in the compression-dominated region, thus affecting the accuracy of crack propagation prediction. The second category is damage models based on strain decomposition. This method decomposes the strain tensor, considering only the strain energy of the tensile portion in damage evolution, thus avoiding spurious damage in the compressive state. However, this method usually relies on unconventional state-based peridynamic frameworks, requiring the construction of nonlocal deformation gradients and matrix inversion and eigenvalue decomposition, resulting in high computational costs. It may also introduce numerical instability issues such as zero-energy modes, limiting its application in bond-based and conventional state-based peridynamic frameworks.

[0004] The first type of damage model based on nodal strain energy density has the following problems: it is difficult to distinguish between tensile and compressive states, and it may produce non-physical damage. The second type of damage model based on strain decomposition has the following problems: it has high computational complexity, making it difficult to balance computational efficiency; solving for nonlocal deformation gradients may introduce numerical instability, limiting the model's universality in different peri-field dynamic theory frameworks. Summary of the Invention

[0005] In view of this, it is necessary to provide a near-field dynamics damage modeling method, system, electronic device and storage medium to solve the technical problems of poor physical consistency, low computational efficiency, insufficient numerical stability and limited applicability between different near-field dynamics frameworks in existing damage models.

[0006] To address the aforementioned technical problems, in a first aspect, the present invention provides a near-field dynamics damage modeling method, comprising: The structure of the material to be analyzed is spatially discretized, and a near-field dynamics calculation model containing multiple nodes is established. Based on the near-field dynamics calculation model, near-field dynamics control equations are established. These near-field dynamics control equations describe the internal mechanical behavior of the material through the non-local interaction forces between nodes and other nodes in the near-field domain. The near-field dynamic integral operator in the near-field dynamic control equation is transformed into a convolution form, and a fast convolution calculation framework is constructed using the fast Fourier transform. Nonlocal interaction forces are calculated based on the fast convolution calculation framework. The nonlocal expansion of the node is calculated based on the relative displacement between the node and other nodes in the near field. A node integrity factor is introduced and the node strain energy density is calculated. A tensile-compression sensing damage criterion is established based on the nonlocal expansion and the node strain energy density. The node integrity factor is updated based on the tensile-compression sensing damage criterion, and the nonlocal interaction forces are degraded to generate a near-field dynamic damage model.

[0007] In one possible implementation, the near-field dynamics governing equations are expressed as follows:

[0008] in, For material density, Represents a node exist Displacement field at time t, Indicates body density. This is the near-field dynamics integral operator.

[0009] In one possible implementation, the near-field dynamics integral operator is expressed as follows:

[0010] in, For nodes The near field; For force density; For nodes Falling on the node Volume in the near field region.

[0011] In one possible implementation, the computation of nonlocal interaction forces based on the fast convolutional computation framework includes: Based on the relative position and relative displacement of the material points, the force density is expressed as a function. The convolution form of the near-field dynamics integral operator is derived based on the aforementioned functional form. The convolutional form of the near-field dynamics integral operator is solved by fast Fourier transform to calculate the nonlocal interaction forces.

[0012] In one possible implementation, calculating the nonlocal expansion of the node based on the relative displacement between the node and other nodes in the near-field region includes: The elongation of the key is determined based on the relative displacement between the node and its adjacent nodes in the near field. Using the product of the preset influence function and the initial length of each bond as the weight, the elongation of all bonds in the near field is weighted and integrated, and the integration result is divided by the normalization coefficient to obtain the nonlocal expansion amount. Wherein, when the nonlocal expansion amount is greater than zero, it indicates that the node is in a state of volume expansion, and when it is less than zero, it indicates that the node is in a state of volume compression.

[0013] In one possible implementation, the tensile / compression-sensing damage criterion includes: When the value of the non-local expansion is greater than zero and the nodal strain energy density is greater than the preset critical strain energy density, the node is determined to be damaged. When the value of the non-local expansion is less than or equal to zero, it is determined that the node has not been damaged.

[0014] In one possible implementation, updating the node integrity factor based on the tensile / compressive sensing damage criterion and degrading nonlocal interaction forces to generate a near-field dynamic damage model includes: Based on the determination result of the tensile and compressive sensing damage criterion, the integrity factor of the damaged node is updated to the damage value. The product of the integrity factors of the damaged node and its neighboring nodes in the neighborhood is used as the degradation factor. The degradation factor is then substituted into the near-field dynamics integral operator to obtain the near-field dynamics integral operator after the node damage state is updated. The near-field dynamics integral operator updates the displacement and velocity motion states of the nodes based on the updated node damage state, thereby generating a near-field dynamics damage model.

[0015] On the other hand, the present invention also provides a near-field dynamic damage modeling system, comprising: The near-field dynamics calculation model establishment module is used to spatially discretize the structure of the material to be analyzed and establish a near-field dynamics calculation model containing multiple nodes. The near-field dynamics governing equation establishment module is used to establish near-field dynamics governing equations based on the near-field dynamics calculation model. The near-field dynamics governing equations describe the internal mechanical behavior of the material through the non-local interaction forces between the nodes and other nodes in the near-field domain. A fast convolution computation framework construction module is used to transform the near-field dynamic integral operator in the near-field dynamic control equation into a convolution form, and to construct a fast convolution computation framework using fast Fourier transform, and to calculate nonlocal interaction forces based on the fast convolution computation framework. The damage criterion establishment module is used to calculate the nonlocal expansion of the node based on the relative displacement between the node and the node in the near field, introduce the node integrity factor and calculate the node strain energy density, and establish a tensile-compression sensing damage criterion based on the nonlocal expansion and the node strain energy density. The near-field dynamic damage model generation module is used to update the node integrity factor based on the tensile-compression sensing damage criterion and to perform degradation processing on non-local interaction forces to generate a near-field dynamic damage model.

[0016] In a second aspect, the present invention also provides an electronic device, including a memory and a processor, wherein, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the near-field dynamic damage modeling method described in any of the above implementations.

[0017] Thirdly, the present invention also provides a computer-readable storage medium for storing a computer-readable program or instruction, which, when executed by a processor, can implement the steps in the near-field dynamic damage modeling method described in any of the above implementations.

[0018] The beneficial effects of this invention are as follows: The near-field dynamic damage modeling method provided by this invention calculates the nonlocal expansion of nodes based on the relative displacement between nodes and other nodes in the near-field domain, which is used to characterize the volumetric deformation state of the material. This effectively distinguishes between tensile and compressive deformation, avoiding the problem of non-physical spurious damage generated in the compression-dominant region by traditional pure strain energy density damage models. Directly using intermediate variables to calculate the nonlocal expansion fundamentally avoids the calculation of nonlocal deformation gradients, effectively avoiding numerical instability risks such as zero-energy modes, and greatly reducing the computational cost of large-scale fracture simulation. Furthermore, by introducing a node integrity factor and calculating the node strain energy density, a tensile-compression sensing damage criterion is established based on the nonlocal expansion and node strain energy density. Damage evolution modeling is achieved without changing the spatial convolution structure of the fast convolution method. This method is applicable to various theoretical frameworks such as bond-based near-field dynamics, conventional state-based near-field dynamics, and unconventional state-based near-field dynamics, providing a unified modeling method that balances physical fidelity, efficiency, and stability for simulating the fracture behavior of complex engineering structures. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A schematic flowchart of an embodiment of the near-field dynamic damage modeling method provided by the present invention; Figure 2 This invention provides a schematic diagram of material points in near-field dynamics. Figure 3 A schematic diagram of the geometric model of the quasi-brittle sandstone sample provided by the present invention; Figure 4 Comparison of crack propagation between the method of this invention and the conventional model provided by this invention; Figure 5 A comparison diagram of the results of simulating the compression failure of rock samples using the method of the present invention and conventional methods; Figure 6 A comparison chart of the computational efficiency of the method of this invention and the conventional method provided by this invention; Figure 7 A schematic diagram of the geometric model of the Kalthoff-Winkler impact test provided by this invention; Figure 8 A comparison diagram of the results of the simulated impact damage of a metal plate provided by the present invention and a conventional model; Figure 9A schematic diagram of an embodiment of the near-field dynamics damage modeling system provided by the present invention; Figure 10 A schematic diagram of an embodiment of the electronic device provided by the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0022] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0023] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0024] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0025] Before demonstrating the embodiments, the following terms will be explained.

[0026] Nonlocal interaction force: In perifield dynamics, after the material is discretized, the resultant force of the interaction between a node and all other nodes in its perifield domain.

[0027] Fast convolution computation framework: This is a numerical solution framework that uses the convolution theorem and Fast Fourier Transform (FFT) to accelerate integral calculations, which can significantly reduce the computational cost of nonlocal internal forces and improve the solution speed of large-scale models.

[0028] Node nonlocal expansion: An average measure of the volume expansion or contraction of a material node in its near-field region, calculated based on the relative displacement between the node and other nodes in its near-field region.

[0029] Integrity factor: A variable used to characterize the intact or damaged state of material nodes.

[0030] This invention provides a near-field dynamic damage modeling method, system, electronic device, and storage medium, which are described below.

[0031] Example 1: Figure 1 This is a flowchart illustrating an embodiment of the near-field dynamic damage modeling method provided by the present invention. The execution subject of the method can be an electronic device with data processing capabilities, such as a computer, server, or dedicated simulation computing equipment. It can be applied to other engineering scenarios such as mechanical engineering, civil engineering, and aerospace engineering for high-precision and high-efficiency simulation of the tensile-compressive asymmetric fracture behavior of materials. Figure 1 As shown, near-field dynamic damage modeling methods include: S101. Spatial discretize the structure of the material to be analyzed and establish a near-field dynamics calculation model containing multiple nodes.

[0032] It should be noted that: in the embodiments of the present invention, the material structure to be analyzed is divided into multiple material nodes in the computational domain according to a preset spatial discrete scale, and each node is assigned material parameters and initial state. The near-field dynamics calculation model is based on near-field dynamics theory, which discretizes the continuous material into a series of interacting material nodes and assigns material parameters, near-field domain range, initial and boundary conditions to form a numerical calculation model, which is used to describe the deformation, damage and fracture process of the material under stress.

[0033] S102. Based on the near-field dynamics calculation model, establish near-field dynamics control equations. The near-field dynamics control equations describe the internal mechanical behavior of the material through the non-local interaction forces between nodes and other nodes in the near-field domain.

[0034] S103. Transform the peri-field dynamic integral operator in the peri-field dynamic control equation into a convolution form, and construct a fast convolution calculation framework using the fast Fourier transform. Calculate the nonlocal interaction force based on the fast convolution calculation framework. S104. Calculate the nonlocal expansion of the node based on the relative displacement between the node and other nodes in the near field, introduce the node integrity factor and calculate the node strain energy density, and establish a tensile-compression sensing damage criterion based on the nonlocal expansion and node strain energy density.

[0035] S105. The node integrity factor is updated based on the tensile-compression sensing damage criterion, and the nonlocal interaction forces are degraded to generate a near-field dynamic damage model.

[0036] In summary, the near-field dynamics damage modeling method provided by this invention calculates the nonlocal expansion of nodes based on the relative displacement between nodes and other nodes in the near-field domain. This nonlocal expansion is used to characterize the volumetric deformation state of the material, effectively distinguishing between tensile and compressive deformation. This avoids the problem of non-physical spurious damage generated in the compression-dominant region by traditional pure strain energy density damage models. Directly using intermediate variables to calculate the nonlocal expansion fundamentally avoids the calculation of nonlocal deformation gradients, effectively avoiding numerical instability risks such as zero-energy modes, and significantly reducing the computational cost of large-scale fracture simulation. Furthermore, by introducing a node integrity factor and calculating the node strain energy density, a tensile-compression sensing damage criterion is established based on the nonlocal expansion and node strain energy density. Damage evolution modeling is achieved without altering the spatial convolution structure of the fast convolution method. This method is applicable to various theoretical frameworks such as bond-based near-field dynamics, conventional-based near-field dynamics, and unconventional-based near-field dynamics, providing a unified modeling method that balances physical fidelity, efficiency, and stability for simulating the fracture behavior of complex engineering structures.

[0037] In some embodiments of the present invention, the near-field dynamics control equations are expressed as follows:

[0038] in, For material density, Represents a node exist Displacement field at time t, Indicates body density. This is the near-field dynamics integral operator.

[0039] In some embodiments of the present invention, the near-field dynamics integral operator The formula is as follows:

[0040] in, For nodes The near field; For force density, used to describe nodes Its near-field nodes The forms and constitutive relations of their interactions; For nodes Falling on the node Volume in the near field region.

[0041] This invention describes the motion of material nodes through peridynamic governing equations, expressing the acceleration response of nodes under the combined action of nonlocal interaction forces and external forces in integral form, thus providing a mechanical theoretical foundation for the entire fracture simulation. The peridynamic integral operator, as the core term of the peridynamic governing equations, obtains the total nonlocal interaction force on the node by integrating and accumulating the force density between the central node and all other nodes in its perifield domain, achieving a unified expression of nonlocal mechanical effects.

[0042] In some embodiments of the present invention, the calculation of nonlocal interaction forces based on the fast convolutional computation framework includes: S201. Based on the relative position and relative displacement of the material points, express the force density as a function. S202. Based on the function form, the convolution form of the near-field dynamics integral operator is derived. S203. Solve the convolution form of the near-field dynamics integral operator using the Fast Fourier Transform to calculate the nonlocal interaction forces.

[0043] It should be noted that, for a general near-field dynamic microelastic material model, the nonlocal interaction force depends on the relative position and relative displacement of the material points, and the force density is expressed as a function as follows:

[0044] In the formula, , , For scalar or vector functions, It is a positive number.

[0045] Based on the functional expression of force density, the near-field dynamics integral operator can be derived. The convolutional form of the expression is derived as follows:

[0046] In the formula, This represents the convolution operator. For nodes The near field region, For nodes Falling on the node Volume in the near field For near-field dynamics integral operators The convolutional form.

[0047] Among them, the convolution form of the near-field dynamics integral operator through Fast Fourier Transform Solving for the nonlocal interaction forces acting on the nodes yields the following formula:

[0048] In the formula, , These represent the Fast Fourier Transform and its inverse transform operators, respectively. , , For scalar or vector functions, It is a positive number.

[0049] The embodiments of the present invention significantly reduce the computational complexity of nonlocal integration by transforming the near-field dynamic integral operator into a convolutional form and combining it with the fast Fourier transform to construct a computational framework, thereby significantly improving the solution efficiency of large-scale model damage simulation, while ensuring the stability and accuracy of numerical calculation.

[0050] In some embodiments of the present invention, the step of calculating the nonlocal expansion of a node based on the relative displacement between the node and other nodes in the near-field region includes: S301. Determine the elongation of the key based on the relative displacement between the node and each adjacent node in the near field. S302. Using the product of the preset influence function and the initial length of each bond as weights, perform a weighted integral on the elongation of all bonds in the near field, and divide the integral result by the normalization coefficient to obtain the nonlocal expansion amount. Wherein, when the nonlocal expansion amount is greater than zero, it indicates that the node is in a state of volume expansion, and when it is less than zero, it indicates that the node is in a state of volume compression.

[0051] It should be noted that, for the general form of state-ground perifield dynamics, the aforementioned force density The general form is: ;

[0052] In the formula, Represents the key vector, i.e., the node. Relative to node The relative position vector; and They are nodes and exist The force state at any given moment.

[0053] Next, define and Let represent the deformation vectors of the material points under the reference configuration and the current configuration, respectively, as follows: ; ;

[0054] in, Nodes under reference configuration along The reference deformation vector in the direction is equal to the bond vector. itself; For the nodes in the current configuration exist Time along The current deformation vector in the direction; It is a relative displacement vector. , Representing nodes respectively and nodes exist The displacement vector at time t.

[0055] Correspondingly, and The scalar form is: ; ;Right now ;

[0056] in, , They are respectively and scalar form, express scalar form, express Scalar form.

[0057] Furthermore, the elongation of the bonds between material points ( )for:

[0058] In the formula, For reference configuration, the scalar length of the bond. This represents the scalar length of the bond under the current configuration.

[0059] Based on the above parameter definitions, an average measure of the volume expansion of a material point in its near-field domain can be constructed, namely, the non-local expansion amount. Its expression is as follows:

[0060] In the formula, This represents the elongation of the bond. The influence function can be selected in different forms depending on the research question and material properties; The normalized weight coefficients are in scalar form and are used to normalize the weighted results. They are defined as follows:

[0061] In the formula, Represents the bond vector. For nodes The near field region, For nodes Falling on the node Volume in the near field region.

[0062] The parameters related to model dimensions have the following possible values:

[0063] in, Let be the Poisson's ratio of the material.

[0064] It should be noted that strain energy density The calculation formula is expressed as follows:

[0065] In the formula, and These are parameters to be determined, and can be determined using the material's bulk modulus and shear modulus. This is a non-local expansion amount. These are normalized weighting coefficients in scalar form. For the influence function, For nodes The near field region, For nodes Falling on the node Volume in the near field region.

[0066] Compared to traditional pure strain energy density damage models that rely solely on non-negative strain energy density for damage assessment and cannot distinguish between tension and compression, leading to non-physical spurious damage in the compression region, this invention directly identifies tension and compression states using the scalar quantity of nonlocal expansion. This eliminates the need to construct a nonlocal deformation gradient tensor and perform matrix inversion and eigenvalue decomposition, resulting in high computational costs and the potential introduction of zero-energy modes.

[0067] In some embodiments of the present invention, the tensile / compression sensing damage criterion includes: When the value of the non-local expansion is greater than zero and the nodal strain energy density is greater than the preset critical strain energy density, the node is determined to be damaged. When the value of the non-local expansion is less than or equal to zero, it is determined that the node has not been damaged.

[0068] It should be noted that the integrity factor is introduced. The tensile-compression sensing damage criterion, used to describe the damage state of material nodes, is expressed by the following formula:

[0069] In the formula, Indicates the node exist The damage status at any given time, where 0 represents damage and 1 represents intactness; This represents the critical strain energy density for nodal damage in the material, and its value can be calibrated using the material's fracture energy parameters. Only when the non-local expansion... This means that the node is in a state of volume expansion and the strain energy density exceeds the critical threshold. When the node is damaged, its integrity factor is updated. ;like That is, if a node is in a state of volume compression, then the damage evolution of that node is suppressed.

[0070] This invention introduces a tension-compression sensing damage criterion at the node level, achieving damage evolution modeling without altering the spatial convolution structure of the fast convolution method. This avoids the high computational cost and zero-energy mode risk of traditional strain decomposition methods, balancing physical accuracy and numerical stability. Furthermore, by jointly constructing the tension-compression sensing damage criterion using strain energy density and nonlocal expansion, it can accurately identify tensile damage and strictly suppress non-physical fracture in the compression region, making crack propagation more consistent with the actual material failure behavior, significantly improving the physical rationality and numerical reliability of damage simulation.

[0071] It should be noted that step S105 includes: S401. Based on the determination result of the tensile and compressive sensing damage criterion, update the integrity factor of the damaged node to the damage value. S402. The product of the integrity factors of the damaged node and its neighboring nodes in the neighborhood is used as the degradation factor. The degradation factor is substituted into the near-field dynamics integral operator to obtain the near-field dynamics integral operator after the node damage state is updated. S403. Based on the updated near-field dynamics integral operator of the node damage state, update the displacement and velocity motion state of the node to generate a near-field dynamics damage model.

[0072] It should be noted that, in this embodiment of the invention, even functions are defined. For nodes and its neighboring nodes The product of the integrity factors is expressed as follows:

[0073] in, Represents a node Integrity factor Represents a node The integrity factor.

[0074] Furthermore, Substituting the above near-field dynamics integral operator, we can obtain the near-field dynamics integral operator after updating the node damage state, expressed as follows:

[0075] In the formula, For the near-field dynamics integral operator after updating the node damage state; Represents a node Integrity factor Represents a node Integrity factor For nodes The near field region, For nodes Falling on the node Volume in the near field region.

[0076] The above structure retains the convolutional form of the internal force density, and can still be solved efficiently using the Fast Fourier Transform.

[0077] It should be noted that the near-field dynamics integral operator after updating the node damage state... Substitute the displacement and velocity motion states of the nodes into the integral algorithm, repeat steps S102-S105 until the set calculation time is reached, realize the numerical simulation of the internal damage accumulation, complex crack initiation and propagation process of the material, and generate a near-field dynamic damage model.

[0078] This invention employs the product of the integrity factors of two interacting nodes as a degradation factor to perform symmetric degradation treatment on nonlocal interaction forces. This ensures physically correct damage evolution and force degradation while maintaining the convolutional structure of the integral operator after the damage effect is incorporated through the design of the node-to-integrity factor product. This ensures that the entire modeling process does not require switching the solution framework, achieving a balance between physical consistency and efficient computation. The entire damage modeling method does not depend on a specific force state form and is applicable to various theoretical frameworks such as bond-basis peridynamics, conventional-basis peridynamics, and unconventional-basis peridynamics. It provides a unified modeling method for simulating the fracture behavior of complex engineering structures that balances physical fidelity, efficiency, and stability.

[0079] Example 2: This invention uses tensile and compression experiments on quasi-brittle rock specimens to verify the effectiveness and physical consistency of the near-field dynamic damage modeling method in distinguishing between tensile and compressive states of materials and avoiding non-physical damage in the compression zone.

[0080] like Figure 3 As shown, the simulation object in this embodiment is a two-dimensional rectangular sandstone sample subjected to uniaxial tension and compression, with the following geometric dimensions: width ,high The specimen center contains a pre-fabricated inclined crack, 20 mm long, 2.5 mm wide, and with an inclination angle of 45°. Specimen material parameters include: Young's modulus. Poisson's ratio Critical energy release rate The computational domain is discretized using uniform nodes, with a node spacing of [missing information]. The near-field radius is To simulate the quasi-static loading process, the upper and lower boundary layers of the sample (thickness: Apply a constant velocity boundary condition, with a loading speed of... An adaptive dynamic relaxation algorithm is used to solve the steady-state equilibrium, with a time step size of 1. .

[0081] In this embodiment of the invention, crack propagation behavior is compared between the traditional pure strain energy nodal damage model and the tension-compression sensing damage model based on nonlocal expansion identification proposed in this invention under two loading conditions: uniaxial tension and uniaxial compression.

[0082] like Figure 4As shown, under uniaxial tensile conditions, the calculation results of the traditional pure strain energy damage model and the damage model based on nonlocal expansion identification proposed in this invention are consistent: cracks all initiate from the pre-existing crack tip and propagate horizontally in a direction perpendicular to the tensile load, which conforms to the physical expectations of fracture mechanics. This indicates that under pure tensile conditions, both the traditional model and the model of this invention can give correct results. However, under uniaxial compression conditions, the two models show significant differences. The traditional pure strain energy model, unable to distinguish between tensile and compressive strain energies, generates non-physical bond fracture in the compression-dominated region, incorrectly predicting a horizontal crack trajectory almost identical to that under tensile conditions. In contrast, the method of this invention, by introducing nonlocal expansion to identify the tensile / compression state of material nodes, can accurately identify the volume expansion region at the crack tip caused by local transverse deformation (i.e., satisfying the requirements of the proposed model) even when the specimen is under global macroscopic compression. (under certain conditions), to accurately capture tensile airfoil cracks that originate from the tip of a pre-existing crack, and for the cracks to extend along a curved path and gradually turn toward a direction parallel to the compressive load.

[0083] like Figure 5 As shown, the calculation results of the method of the present invention are in high agreement with the observations of classical rock mechanics experiments. Compared with the traditional model, the angle between the crack propagation direction and the overall compression direction is smaller, and the crack morphology is closer to the real physical experiment. This fully demonstrates the significant advantages of the method in capturing complex mixed cracks and ensuring physical consistency.

[0084] To further verify the computational efficiency and stability of the method of the present invention, this embodiment compares the method of the present invention with a pure strain energy nodal damage model, a damage model based on strain decomposition, and a traditional unconventional state basis peri-field dynamics model. The statistical results of their computation time and memory consumption are as follows: Figure 6 As shown in the figure. The results show that the method of the present invention can significantly improve physical consistency with only a small increase in computational overhead while maintaining the fast convolutional near-field dynamics computational framework. Compared with strain decomposition models that require the construction of nonlocal deformation gradients and traditional unconventional state basis near-field dynamics models, the computational efficiency is significantly improved, while avoiding the numerical instability problem caused by zero-energy modes.

[0085] In summary, the embodiments of the present invention effectively verify that the near-field dynamic damage modeling method of the present invention can accurately simulate the crack initiation and propagation process of quasi-brittle rocks under compressive loading conditions while maintaining high computational efficiency and high numerical stability, and has good physical consistency and engineering applicability.

[0086] Example 3: The embodiments of the present invention use the classic Kalthoff-Winkler impact test as a verification example to verify the universality of the method of the present invention under different near-field dynamic theory frameworks and its accuracy in simulating fracture behavior under high-speed dynamic impact conditions.

[0087] Reference Figure 7 In this embodiment, the simulated object is a rectangular metal plate with double-sided notches, and its geometric parameters are as follows: mm, mm, mm. And the length of the notch. mm and notch spacing mm. Material parameters are taken as: density Elastic modulus GPa, Poisson's ratio Critical energy release rate In the numerical calculation, uniform node discretization is used, and the node spacing is... mm, near-field radius taken Apply velocity boundary conditions at the top boundary between the two precast notches. The transient impact velocity from the cylindrical impactor is simulated using m / s. The calculation employs an explicit time integration algorithm, with a time step set to... .

[0088] To verify the universality of the method of the present invention, this embodiment introduces the tensile-compression sensing damage criterion based on nonlocal expansion identification proposed in this invention under three different theoretical frameworks: bond-based peri-field dynamics model, conventional state-based peri-field dynamics model, and unconventional state-based peri-field dynamics model, and compares their crack propagation simulation results.

[0089] Reference Figure 8 The calculation results of each model show that the cracks all initiate from the tip of the notch and propagate outwards to both sides of the plate at an angle of approximately 70°. This crack propagation angle is highly consistent with the observation results of the Kalthoff-Winkler benchmark impact test. Under different near-field dynamic theory frameworks, the method of this invention can obtain stable and consistent crack propagation paths, indicating that the method of this invention does not depend on a specific force state and has good versatility.

[0090] Meanwhile, comparing the method of the present invention with the pure strain energy damage model reveals that the pure strain energy damage model is prone to generating non-physical damage in the compression region and incorrectly predicting additional crack branches; while the method of the present invention effectively distinguishes between tensile and compressive states through non-local expansion, so that damage only occurs in a reasonable tensile region, the crack morphology is clearer and more uniform, and the physical reliability of impact fracture simulation is significantly improved.

[0091] Therefore, the embodiments of the present invention effectively verify that the near-field dynamic damage modeling method proposed in this invention can work stably under various theoretical frameworks such as bond-based, conventional-based, and unconventional-based near-field dynamics, and can accurately simulate dynamic fracture behavior under high-speed impact conditions, and has good versatility, stability and engineering application value.

[0092] Example 4: To better implement the near-field dynamics damage modeling method in the embodiments of the present invention, based on the near-field dynamics damage modeling method, correspondingly, as follows: Figure 9 As shown, this embodiment of the invention also provides a near-field dynamics damage modeling system, the near-field dynamics damage modeling system 700 comprising: The near-field dynamics calculation model establishment module 701 is used to spatially discretize the structure of the material to be analyzed and establish a near-field dynamics calculation model containing multiple nodes.

[0093] It should be noted that the near-field dynamics calculation model establishment module 701 receives the geometric model data, material parameter data and simulation control parameters of the structure to be analyzed obtained through the input device or data interface, and transmits the discretized nodal model data to the near-field dynamics control equation establishment module 702.

[0094] The near-field dynamics governing equation establishment module 702 is connected to the near-field dynamics calculation model establishment module 701 and is used to establish near-field dynamics governing equations based on the near-field dynamics calculation model. The near-field dynamics governing equations describe the internal mechanical behavior of the material through the non-local interaction forces between the nodes and other nodes in the near-field domain.

[0095] The fast convolution calculation framework construction module 703 is connected to the near-field dynamics control equation establishment module 702. It is used to transform the near-field dynamics integral operator in the near-field dynamics control equation into a convolution form, and to construct a fast convolution calculation framework using fast Fourier transform. Based on the fast convolution calculation framework, nonlocal interaction forces are calculated.

[0096] The damage criterion establishment module 704 is connected to the fast convolution calculation framework construction module 703. It is used to calculate the nonlocal expansion of the node based on the relative displacement between the node and the node in the near field, introduce the node integrity factor and calculate the node strain energy density, and establish a tension-compression sensing damage criterion based on the nonlocal expansion and the node strain energy density.

[0097] The near-field dynamic damage model generation module 705 is connected to the damage criterion establishment module 704, the processor, and the memory. It is used to update the node integrity factor based on the tension-compression sensing damage criterion and to perform degradation processing on non-local interaction forces to generate a near-field dynamic damage model.

[0098] It should be noted that the damage model data generated by the near-field dynamic damage model generation module 705 includes the integrity factor, displacement field and velocity field information of each node; this data is output in the form of structured data and transmitted to a display device for visualization, or transmitted to a storage device for saving for subsequent engineering evaluation and analysis; the display device is a display screen or a remote monitoring terminal connected to the computer device that performs the modeling calculation.

[0099] The near-field dynamic damage modeling system 700 provided in the above embodiments can realize the technical solutions described in the above near-field dynamic damage modeling method embodiments. The specific implementation principles of each module or unit can be found in the corresponding content in the above near-field dynamic damage modeling method embodiments, and will not be repeated here.

[0100] Example 5: like Figure 10 As shown, the present invention also provides an electronic device 800. The electronic device 800 includes a processor 801, a memory 802, and a display 803. Figure 10 Only some components of the electronic device 800 are shown, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead.

[0101] In some embodiments, processor 801 may be a central processing unit (CPU), microprocessor, or other data processing chip, used to run program code stored in memory 802 or process data, such as the near-field dynamic damage modeling method of the present invention.

[0102] In some embodiments, processor 801 may be a single server or a group of servers. The server group may be centralized or distributed. In some embodiments, processor 801 may be local or remote. In some embodiments, processor 801 may be implemented on a cloud platform. In one embodiment, the cloud platform may include a private cloud, public cloud, hybrid cloud, community cloud, distributed cloud, intranet, multi-cloud, etc., or any combination thereof.

[0103] In some embodiments, memory 802 may be an internal storage unit of electronic device 800, such as a hard disk or memory of electronic device 800. In other embodiments, memory 802 may also be an external storage device of electronic device 800, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on electronic device 800.

[0104] Furthermore, the memory 802 may include both internal storage units of the electronic device 800 and external storage devices. The memory 802 is used to store application software and various types of data installed on the electronic device 800.

[0105] In some embodiments, display 803 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 803 is used to display information from electronic device 800 and to display a visual user interface. Components 801-803 of electronic device 800 communicate with each other via a system bus.

[0106] In one embodiment, when processor 801 executes the near-field dynamics damage modeling program in memory 802, the following steps can be implemented: The structure of the material to be analyzed is spatially discretized, and a near-field dynamics calculation model containing multiple nodes is established. Based on the near-field dynamics calculation model, near-field dynamics control equations are established. These near-field dynamics control equations describe the internal mechanical behavior of the material through the non-local interaction forces between nodes and other nodes in the near-field domain. The near-field dynamic integral operator in the near-field dynamic control equation is transformed into a convolution form, and a fast convolution calculation framework is constructed using the fast Fourier transform. Nonlocal interaction forces are calculated based on the fast convolution calculation framework. The nonlocal expansion of the node is calculated based on the relative displacement between the node and other nodes in the near field. A node integrity factor is introduced and the node strain energy density is calculated. A tensile-compression sensing damage criterion is established based on the nonlocal expansion and the node strain energy density. The node integrity factor is updated based on the tensile-compression sensing damage criterion, and the nonlocal interaction forces are degraded to generate a near-field dynamic damage model.

[0107] It should be understood that when the processor 801 executes the near-field dynamics damage modeling program in the memory 802, in addition to the functions mentioned above, it can also perform other functions, as detailed in the description of the corresponding method embodiments above.

[0108] Example 6: Accordingly, this application also provides a computer-readable storage medium for storing computer-readable programs or instructions. When the programs or instructions are executed by a processor, they can implement the steps or functions of the near-field dynamic damage modeling methods provided in the above-described method embodiments.

[0109] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.), and the computer program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0110] The foregoing has provided a detailed description of the near-field dynamic damage modeling method, system, electronic device, and storage medium provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, those skilled in the art will recognize that there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A near-field dynamic damage modeling method, characterized in that, include: The structure of the material to be analyzed is spatially discretized, and a near-field dynamics calculation model containing multiple nodes is established. Based on the near-field dynamics calculation model, near-field dynamics control equations are established. The near-field dynamics control equations describe the internal mechanical behavior of the material through the non-local interaction forces between nodes and other nodes in the near-field domain. The near-field dynamic integral operator in the near-field dynamic control equation is transformed into a convolution form, and a fast convolution calculation framework is constructed using the fast Fourier transform. Nonlocal interaction forces are calculated based on the fast convolution calculation framework. The nonlocal expansion of the node is calculated based on the relative displacement between the node and other nodes in the near field. A node integrity factor is introduced and the node strain energy density is calculated. A tensile-compression sensing damage criterion is established based on the nonlocal expansion and the node strain energy density. The node integrity factor is updated based on the tensile-compression sensing damage criterion, and the nonlocal interaction forces are degraded to generate a near-field dynamic damage model.

2. The near-field dynamic damage modeling method according to claim 1, characterized in that, The near-field dynamics governing equations are expressed as follows: in, For material density, Represents a node exist Displacement field at time t, Indicates body density. This is the near-field dynamics integral operator.

3. The near-field dynamic damage modeling method according to claim 2, characterized in that, The near-field dynamics integral operator is expressed as follows: in, For nodes The near field; For force density; For nodes Falling on the node Volume in the near-field region.

4. The near-field dynamic damage modeling method according to claim 3, characterized in that, The calculation of nonlocal interaction forces based on the fast convolution computation framework includes: Based on the relative position and relative displacement of the material points, the force density is expressed as a function. The convolution form of the near-field dynamics integral operator is derived based on the aforementioned functional form. The convolutional form of the near-field dynamics integral operator is solved by fast Fourier transform to calculate the nonlocal interaction forces.

5. The near-field dynamic damage modeling method according to claim 1, characterized in that, The calculation of the nonlocal expansion of a node based on the relative displacement between the node and other nodes in the near-field region includes: The elongation of the key is determined based on the relative displacement between the node and its adjacent nodes in the near field. Using the product of the preset influence function and the initial length of each bond as the weight, the elongation of all bonds in the near field is weighted and integrated, and the integration result is divided by the normalization coefficient to obtain the nonlocal expansion amount. Wherein, when the nonlocal expansion amount is greater than zero, it indicates that the node is in a state of volume expansion, and when it is less than zero, it indicates that the node is in a state of volume compression.

6. The near-field dynamic damage modeling method according to claim 1, characterized in that, The tensile / compressive damage sensing criteria include: When the value of the non-local expansion is greater than zero and the nodal strain energy density is greater than the preset critical strain energy density, the node is determined to be damaged. When the value of the non-local expansion is less than or equal to zero, it is determined that the node has not been damaged.

7. The near-field dynamic damage modeling method according to claim 6, characterized in that, The process of updating the node integrity factor based on the tensile-compression sensing damage criterion and degrading nonlocal interaction forces to generate a near-field dynamic damage model includes: Based on the determination result of the tensile and compressive sensing damage criterion, the integrity factor of the damaged node is updated to the damage value. The product of the integrity factors of the damaged node and its neighboring nodes in the neighborhood is used as the degradation factor. The degradation factor is then substituted into the near-field dynamics integral operator to obtain the near-field dynamics integral operator after the node damage state is updated. The near-field dynamics integral operator updates the displacement and velocity motion states of the nodes based on the updated node damage state, thereby generating a near-field dynamics damage model.

8. A near-field dynamic damage modeling system, characterized in that, include: The near-field dynamics calculation model establishment module is used to spatially discretize the structure of the material to be analyzed and establish a near-field dynamics calculation model containing multiple nodes. The near-field dynamics governing equation establishment module is used to establish near-field dynamics governing equations based on the near-field dynamics calculation model. The near-field dynamics governing equations describe the internal mechanical behavior of the material through the non-local interaction forces between nodes and other nodes in the near-field domain. A fast convolution computation framework construction module is used to transform the near-field dynamic integral operator in the near-field dynamic control equation into a convolution form, and to construct a fast convolution computation framework using fast Fourier transform, and to calculate nonlocal interaction forces based on the fast convolution computation framework. The damage criterion establishment module is used to calculate the nonlocal expansion of the node based on the relative displacement between the node and the node in the near field, introduce the node integrity factor and calculate the node strain energy density, and establish a tensile-compression sensing damage criterion based on the nonlocal expansion and the node strain energy density. The near-field dynamic damage model generation module is used to update the node integrity factor based on the tensile-compression sensing damage criterion and to perform degradation processing on non-local interaction forces to generate a near-field dynamic damage model.

9. An electronic device, characterized in that, Including memory and processor, among which, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the near-field dynamic damage modeling method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store computer-readable programs or instructions, which, when executed by a processor, can implement the steps in the near-field dynamic damage modeling method according to any one of claims 1 to 7.

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