Modeling method, device and equipment of short-range repulsive force model for thoroughly solving substance point embedding problem in key-based near-field dynamics and storage medium

Abstract

The invention discloses a modeling method of a short-range repulsive force model, which thoroughly solves the problem of substance point embedding in bond-based near-field dynamics, and aims to solve the problems of trigger mechanism defect, theoretical constitutive linearization defect and sudden failure of a model in the prior art. Constructing a hyperbolic non-local short-distance repulsive force model, and ensuring that the deformation of the key is always smaller than the initial key length by presetting a compression limit residual rate parameter; a trigger control mechanism based on substance point state perception is established, after the activation condition of the short-distance repulsive force is strictly limited to the condition that the substance point enters a discontinuous state, a constitutive expression of the short-distance repulsive force is reconstructed through a hyperbola function, and the substance point embedding problem is thoroughly solved.

Description

Technical Field

[0001] This application relates to the field of numerical simulation technology of contact mechanics of quasi-brittle materials, specifically to a modeling method, apparatus, device, and storage medium for a short-range repulsive force model that completely solves the problem of material point embedding in the near-field dynamics of bond groups. Background Technology

[0002] Compression and impact contact problems in quasi-brittle materials such as rock, concrete, gray cast iron, and ceramics are key challenges in mechanics research and engineering applications. Peri-field dynamics methods, based on the spatial nonlocal integral form of displacement, allow the governing equations to hold even at discontinuities. This eliminates the need for additional crack propagation criteria to simulate the spontaneous initiation and propagation of material cracks, giving them a natural advantage in simulating contact failure behavior in such materials.

[0003] When simulating highly nonlinear behaviors such as compression and impact failure, it is crucial to prevent non-physical overlap or self-penetration between material points, i.e., the embedding problem. To address this, peridynamics theory typically introduces short-range repulsive force models to ensure the spatial exclusivity of material points. However, both existing traditional short-range repulsive force models—the short-range force peridynamics (SRFPD) model based on the assumption of local interaction (referred to as the local SRF model) and the SRF-PD model based on the assumption of linear nonlocal interaction (referred to as the linear nonlocal SRF model)—have inherent limitations in solving embedding problems under complex deformation conditions. Specifically, existing technologies suffer from the following three main problems:

[0004] Triggering mechanism defects: Short-range repulsive forces are only triggered after actual material failure. However, in local SRF models, short-range repulsive forces exist from the beginning of deformation until failure occurs, thus interfering with the normal mechanical response of material points. This premature and additional intervention not only violates the original constitutive behavior of the material but also interferes with the normal mechanical response of material points. The triggering criterion of linear nonlocal SRF models is based solely on the compressive deformation rate, failing to fully consider the crucial factor of whether discontinuities have been formed at the material points. This results in short-range repulsive forces being erroneously activated prematurely while the material is still in a state of continuous deformation, causing distortion in the calculation results.

[0005] Linearity defects in theoretical constitutive models: Both existing models are based on the assumption of constant stiffness, assuming a linear relationship between short-range repulsive force and bond deformation rate. When the deformation exceeds the critical allowable value, the constant stiffness cannot provide sufficient repulsive force to resist further deformation, resulting in finite-amplitude embedding behavior between local material points and inducing non-physical tangential displacement field discontinuities at the contact surface.

[0006] Sudden failure problem: Under continuous compressive deformation, the two existing short-range repulsive force models will experience sudden failure, resulting in large-area material point embedding (non-physical annihilation phenomenon) near the contact surface and decoupling of the normal displacement fields on both sides of the contact surface. The system incorrectly treats the contact surface as a free boundary, ultimately causing the model to completely lose its contact function. Summary of the Invention

[0007] The main objective of this application is to provide a modeling method for a short-range repulsive force model that completely solves the problem of material point embedding in the near-field dynamics of bonded bases, including the following steps:

[0008] Step S10: Based on the constitutive relation of rock joint elements, construct a hyperbolic nonlocal short-range repulsion force model;

[0009] Step S20: Ensure that the bond deformation is always less than the initial bond length by using a preset compression limit residual rate parameter;

[0010] Step S30: Establish a trigger control mechanism based on the state perception of matter points, and strictly limit the activation condition of short-range repulsive force to after the matter point enters a discontinuous state;

[0011] Step S40: Embed the short-range repulsion force model, which integrates the constitutive relation and trigger control mechanism, into the equation of motion of the bond base peridynamics and perform numerical solution.

[0012] In one embodiment, the step of constructing a hyperbolic nonlocal short-range repulsion force model based on the constitutive relation of rock joint elements includes:

[0013] Starting with a hyperbolic model of the constitutive relation of rock joint elements, its original form is:

[0014]

[0015] In the formula, For effective normal stress, For joint normal closure quantity, and All are constants;

[0016] In peridynamics, tensile stress and tensile deformation are usually taken as positive. The above equation is then fitted with a sign according to the principles of peridynamics, resulting in the following functional form:

[0017]

[0018] When the effective normal stress approaches infinity, i.e. Sometimes, ,but It is a normal closure quantity;

[0019] After introducing the near-field dynamics of bond groups, Replace with , Replace with Then the expression for the hyperbolic nonlocal short-range repulsive force model is:

[0020]

[0021] In one embodiment, the step of ensuring that the bond deformation is always less than the initial bond length by using a preset compression limit residual rate parameter includes:

[0022] Define the compressibility limit residual rate parameter, denoted as . This represents the ratio of the minimum bond length that can be achieved during the compression process to the initial bond length. This value must be a positive number less than 1, expressed as:

[0023]

[0024] The compressibility residual rate ranges from 0 < < 1 is used to limit the maximum degree of compression deformation of the bond, ensuring that the deformation of the bond is less than the initial bond length throughout the entire process.

[0025] In one embodiment, the step of establishing a trigger control mechanism based on matter point state perception, which strictly limits the activation condition of short-range repulsive force to after the matter point enters a discontinuous state, includes:

[0026] Establish a quantifiable state identifier for a matter point to distinguish between continuous and discontinuous states;

[0027] The discontinuous state of a material point is determined by the damage value ϕ of the corresponding material point. When the damage value ϕ of a material point is greater than zero, it is determined that the material point has entered a discontinuous state.

[0028] In one embodiment, the step of embedding the short-range repulsion force model integrating the constitutive relation and triggering control mechanism into the equations of motion of the bond base peridynamics and performing numerical solutions includes:

[0029] Based on joint stiffness The definitions are as follows:

[0030]

[0031] For the hyperbolic nonlocal short-range repulsive force model, when When the key stiffness is ,Right now

[0032]

[0033] By embedding the constitutive relation and the short-range repulsion force model of the triggering control mechanism, the constitutive expression of the linear nonlocal short-range repulsion force model is reconstructed, and its constitutive relation can be expressed as:

[0034]

[0035] In the formula, The magnitude of the short-range repulsive force, For the compression ratio of the bond, This represents the compressibility limit residual rate.

[0036] In one embodiment, the initial stiffness Set as a function proportional to the bond stiffness c of the bond base peri-field dynamics, the initial joint stiffness... for:

[0037]

[0038] In one embodiment, during the simulation, for the material points where short-range repulsion is activated, the short-range repulsion between them is calculated according to the hyperbolic constitutive relation, and the activation of the short-range repulsion follows the trigger control mechanism.

[0039] A modeling apparatus for a short-range repulsive force model that completely solves the problem of matter point embedding in the near-field dynamics of bonded groups, comprising:

[0040] The modeling module is used to construct hyperbolic nonlocal short-range repulsion force models based on the constitutive relations of rock joint elements;

[0041] The setting module is used to ensure that the bond deformation is always less than the initial bond length by using a preset compression limit residual rate parameter;

[0042] The triggering module is used to establish a trigger control mechanism based on the state perception of matter points, strictly limiting the activation condition of short-range repulsive force to after a matter point enters a discontinuous state; and limiting the effective area of ​​short-range repulsive force to a certain neighborhood of the discontinuous region.

[0043] The solution module is used to embed the short-range repulsion force model, which integrates the constitutive relation and trigger control mechanism, into the equations of motion of the bond base near-field dynamics for numerical solution.

[0044] Therefore, this application has the following beneficial effects:

[0045] This application provides a modeling method for a short-range repulsion force model that completely solves the problem of material point embedding in bond-based peridynamics, comprising the following steps: constructing a hyperbolic nonlocal short-range repulsion force model based on the constitutive relation of rock joint units; ensuring that the bond deformation is always less than the initial bond length by using a preset compressibility limit residual rate parameter; establishing a trigger control mechanism based on material point state perception, strictly limiting the activation condition of the short-range repulsion force to after the material point enters a discontinuous state; embedding the short-range repulsion force model integrating the constitutive relation and trigger control mechanism into the equations of motion of bond-based peridynamics for numerical solution.

[0046] This application discloses a modeling method for a short-range repulsion force model that completely solves the problem of material point embedding in the near-field dynamics of bonded bases. It aims to address the problems of triggering mechanism defects, linearization defects in theoretical constitutive models, and sudden failures in existing technologies. Based on the constitutive relation of rock joint units, a hyperbolic nonlocal short-range repulsion force model is constructed. By presetting the compressibility limit residual rate parameter, it ensures that the bond deformation is always less than the initial bond length. A triggering control mechanism based on material point state perception is established, strictly limiting the activation condition of the short-range repulsion force to after the material point enters a discontinuous state. The effective region of the short-range repulsion force is limited to a certain neighborhood of the discontinuous region. The constitutive expression of the short-range repulsion force is reconstructed using a hyperbolic function, thus achieving a complete solution to the material point embedding problem. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a system flowchart of a modeling method for a short-range repulsive force model that completely solves the problem of matter point embedding in the near-field dynamics of bond groups;

[0049] Figure 2 This is an example of a hyperbolic nonlocal short-range repulsion model, which is a modeling method for a short-range repulsion model that completely solves the problem of material point embedding in the near-field dynamics of bonded groups.

[0050] Figure 3 This is a comparison diagram of the hyperbolic nonlocal SRF model, which is a modeling method for a short-range repulsive force model that completely solves the problem of matter point embedding in the near-field dynamics of bonded groups, and two existing SRF models.

[0051] Figure 4It is a modeling method for short-range repulsive force models that completely solves the problem of material point embedding in bond group near-field dynamics. The embedded-non-embedded diagrams of the three models after the preset compressibility limit residual rate are used.

[0052] Figure 5 This is an example diagram of the compression and sliding of two flat plates at a perpendicular contact surface;

[0053] Figure 6 This is an example diagram of the short-range repulsive force region between two flat plates at their perpendicular contact surface.

[0054] Figure 7 These are x-direction displacement diagrams for three SRF models with vertically direct contact discontinuous plates.

[0055] Figure 8 These are the y-direction displacement diagrams of three SRF models with vertically direct contact discontinuous plates;

[0056] Figure 9 This is an example diagram of the compression and sliding of two flat plates on a horizontal contact surface;

[0057] Figure 10 This is an example diagram of the short-range repulsive force region between two flat plates at their horizontal contact surface.

[0058] Figure 11 The x-direction displacement diagrams of the linear nonlocal SRF model and the hyperbolic nonlocal SRF model of this application are shown when the load step is 530.

[0059] Figure 12 The x-direction displacement diagrams of the local SRF model and the hyperbolic nonlocal SRF model of this application at load step 2250 are shown.

[0060] Figure 13 This is a y-direction displacement diagram of the hyperbolic nonlocal SRF model of this application and two existing SRF models at a load step of 4100.

[0061] Figure 14 This is a comparison of the y-direction stress-strain curves of the hyperbolic nonlocal SRF model of this application and two existing SRF models;

[0062] Figure 15 This is a comparison of the force density-compression ratio curves of the hyperbolic nonlocal SRF model of this application and two existing SRF models. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0064] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0065] To address the shortcomings of existing technologies, this application provides a modeling method for a short-range repulsive force model that completely solves the problem of material point embedding in the near-field dynamics of bond-based materials. Based on the constitutive relations of rock joint elements, the repulsive force constitutive model is extended from linear to hyperbolic. This retains the ability of nonlocal theory to describe long-range interactions globally, while the hyperbolic properties enhance the ability to characterize short-range strong nonlinearities, especially exhibiting progressive hardening characteristics near the compressibility limit, which better reflects the true mechanical response of rock-like materials. The compressibility limit residual rate parameter serves as the safety threshold of the model. By dynamically adjusting the allowable deformation range of the bonds, it ensures that under extreme compressive conditions (such as the high-pressure environment of deep rocks), the bond deformation is always controlled within a certain proportion (e.g., 80%) of the initial bond length, preventing numerical embedding of material points due to excessive compression, while retaining a certain residual deformation capacity to reflect the plastic characteristics of the material.

[0066] State-aware trigger control accurately identifies discontinuous states (such as crack propagation and joint slip) by real-time monitoring of state variables such as displacement field, strain field, and energy release rate of material points. It activates short-range repulsive forces only in these states, avoiding redundant calculations in the continuous deformation stage while ensuring accurate simulation of discontinuous problems (such as fracture and breakage). Traditional models often suffer from misactivation (e.g., premature triggering in the continuous deformation stage) or missed activation (failure to respond promptly to discontinuous states) of repulsive forces due to fuzzy state perception of material points. This model, through a state-aware trigger control mechanism, strictly limits the activation of repulsive forces to after a material point enters a discontinuous state (such as crack initiation or joint slip), and confines the area of ​​action of short-range repulsive forces to a certain neighborhood of the discontinuous region, avoiding interference with constitutive behavior in the continuous deformation stage. Conventional linear constitutive models struggle to accurately describe stress-strain relationships in strongly nonlinear scenarios (such as large deformation and fracture). This model employs a hyperbolic nonlocal constitutive expression, capturing the true mechanical behavior of rock joint elements under compression / tension through the nonlinear characteristics of hyperbolic functions. Simultaneously, the nonlocal design (considering the interaction of neighboring material points) enhances the model's adaptability to nonuniform deformation. Traditional models are prone to numerical instability or physically unreasonable results (such as excessive embedding of material points) when bond deformation approaches critical values. This model, by pre-setting a compressibility limit residual rate parameter, forces the bond deformation to always be less than the initial bond length, avoiding embedding failure caused by excessive compression from the outset and ensuring the robustness of the computational process.

[0067] This application provides a modeling method for a short-range repulsive force model that completely solves the problem of material point embedding in bond-based near-field dynamics, including steps S10-S40, referring to... Figure 1 , Figure 1 This is a system flowchart of a modeling method for a short-range repulsive force model that completely solves the problem of material point embedding in the near-field dynamics of bonded groups.

[0068] Step S10: Based on the constitutive relation of rock joint elements, construct a hyperbolic nonlocal short-range repulsion force model;

[0069] Step S20: Ensure that the bond deformation is always less than the initial bond length by using a preset compression limit residual rate parameter;

[0070] Step S30: Establish a trigger control mechanism based on the state perception of matter points, strictly limit the activation condition of short-range repulsive force to after the matter point enters a discontinuous state, and limit the action area of ​​short-range repulsive force to a certain neighborhood of the discontinuous region.

[0071] Step S40: Embed the short-range repulsion force model, which integrates the constitutive relation and trigger control mechanism, into the equation of motion of the bond base peridynamics and perform numerical solution.

[0072] Specifically, in this embodiment, this application provides a short-range repulsive force modeling method that completely solves the problem of material point embedding in bond-based near-field dynamics, which includes the following four core steps:

[0073] Step S10: Based on the constitutive relations of rock joint elements, a hyperbolic nonlocal short-range repulsion force model is constructed. This step is based on the classical joint element constitutive theory in rock mechanics. In rock joint research, the closure behavior of joint surfaces under normal loads exhibits obvious nonlinear characteristics, that is, as the closure amount increases, the joint stiffness gradually increases. This stiffness strengthening effect can effectively prevent excessive closure of joint surfaces. This application innovatively introduces this physical mechanism into the near-field dynamics framework, converting the concept of effective normal stress of joint elements into short-range repulsion force between material points, and converting the joint normal closure amount into the compressive deformation of bonds. Through this theoretical mapping, a novel hyperbolic nonlocal short-range repulsion force model is constructed. The core feature of this model is that the short-range repulsion force and bond compressibility exhibit a hyperbolic relationship, rather than the linear relationship in traditional models. This nonlinear constitutive relation allows the short-range repulsion force to increase sharply with the intensification of compressive deformation, thus providing a sufficiently strong repulsive force at the critical moment when material points are about to be embedded, fundamentally solving the problem that traditional linear models cannot provide sufficient repulsion force.

[0074] Step S20: By using a preset compressibility limit residual rate parameter, ensure that the bond deformation is always less than the initial bond length. This step establishes a precise deformation constraint mechanism by introducing a key control parameter—the compressibility limit residual rate. The compressibility limit residual rate represents the maximum allowable compressibility of the bond, and its value is strictly set to ensure that even under extreme compression conditions, the actual deformation of the bond is always less than the initial bond length. In practice, this parameter acts as an intrinsic constraint of the model, playing the role of a mechanical barrier in the numerical calculation process. When the bond compression approaches the preset limit value, the hyperbolic nonlocal short-range repulsive force model generates a repulsive force that tends towards infinity. This sharply enhanced repulsive effect effectively prevents the material points from approaching further. At the same time, to ensure the stability of the numerical calculation, a certain safety margin, namely the compressibility limit residual redundancy rate, is set near the limit value, so that the maximum compression ratio in the actual calculation is always slightly less than the theoretical limit value. This dual guarantee mechanism ensures that the distance between any two material points remains greater than zero throughout the entire deformation process, fundamentally preventing the occurrence of material point embedding or penetration.

[0075] Step S30: Establish a trigger control mechanism based on material point state perception. The activation condition of short-range repulsive force is strictly limited to after the material point enters a discontinuous state, and the effective area of ​​short-range repulsive force is limited to a certain neighborhood of the discontinuous region. This step solves the fundamental defects of premature and global activation in traditional short-range repulsive force models. Traditional models either unconditionally and globally activate short-range repulsive force from the start of deformation, or trigger it based solely on a simple deformation rate threshold. Both methods interfere with the normal mechanical response of the material in a continuous state. This invention innovatively establishes an intelligent trigger mechanism based on the damage state of material points. Short-range repulsive force is only activated when the material point truly enters a discontinuous state (i.e., damage occurs), and the effective area of ​​short-range repulsive force is limited to a certain neighborhood of the discontinuous region. In specific implementation, the system monitors the damage degree of each material point in real time. When the damage variable reaches a preset critical threshold, it is determined that the material point has entered a discontinuous state. Simultaneously, the system automatically identifies the contact interface location and precisely defines the effective range of short-range repulsive force, including the area near the cross-object contact interface and the near-field region of the damaged material point. In non-target regions, the short-range repulsive force remains in an inactive state, thus ensuring that the material can respond normally according to its inherent constitutive relationship during the continuous deformation stage, avoiding interference from human intervention on the simulation results.

[0076] Step S40: Embed the short-range repulsion force model, which integrates the constitutive relation and trigger control mechanism, into the equations of motion of bond-based peridynamics for numerical solution. This step integrates the complete short-range repulsion force model constructed in the previous three steps into the numerical calculation framework of bond-based peridynamics. First, the hyperbolic nonlocal short-range repulsion force expression is combined with the trigger control function based on the state awareness of matter points to form a complete short-range repulsion force calculation module. Then, this module is embedded into the basic equations of motion of bond-based peridynamics, so that the acceleration calculation of matter points simultaneously considers the original point-to-point forces and the newly added short-range repulsion forces. In the numerical implementation, an adaptive dynamic relaxation algorithm is used for iterative solution. This algorithm can effectively handle nonlinear problems and ensure computational stability. During calculation, in each time step, it is first determined whether each pair of matter points satisfies the short-range repulsion force activation condition. For the pair of matter points that satisfy the condition, the corresponding short-range repulsion force is calculated and then added to the total force. Finally, the displacement, velocity, and acceleration of the matter points are solved and updated. The entire calculation process strictly follows the preset convergence criteria to ensure that high-precision numerical solutions are obtained, thereby accurately simulating the complex mechanical behavior of quasi-brittle materials during compression and impact contact.

[0077] Furthermore, in this embodiment, the step of constructing a hyperbolic nonlocal short-range repulsion force model based on the constitutive relation of rock joint elements includes:

[0078] Starting with a hyperbolic model of the constitutive relation of rock joint elements, its original form is:

[0079]

[0080] In the formula, For effective normal stress, For joint normal closure quantity, and All are constants;

[0081] In peridynamics, tensile stress and tensile deformation are usually taken as positive. The above equation is then fitted with a sign according to the principles of peridynamics, resulting in the following functional form:

[0082]

[0083] When the effective normal stress approaches infinity, i.e. Sometimes, ,but It is a normal closure quantity;

[0084] After introducing the near-field dynamics of bond groups, Replace with , Replace with Then the expression for the hyperbolic nonlocal short-range repulsive force model is:

[0085]

[0086] Specifically, in this embodiment, the core lies in the innovative introduction of classical theories from rock mechanics into the peri-field dynamics framework, presenting a complete derivation process from the normal constitutive relation of rock joint units to the short-range repulsion force model of bond-base peri-field dynamics.

[0087] First, a hyperbolic model of the constitutive relation of rock joint elements is introduced as a starting point, and its original form is:

[0088]

[0089] In this formula, For effective normal stress, For joint normal closure quantity, and All are constants; this model accurately describes the nonlinear closing behavior of rock joints under normal loads and is a classic theory in the field of rock mechanics.

[0090] Next, considering that tensile stress and tensile deformation are usually positive in near-field dynamics, the above formula was fitted with a sign. The fitted function form becomes:

[0091]

[0092] This adjustment ensures the physical consistency of the model across different coordinate systems, laying the foundation for subsequent theoretical mapping. Furthermore, when the effective normal stress approaches infinity, i.e. Sometimes, ,but The closure value is the normal closure value, which indicates that under limiting conditions, the closure value of the joint surface tends to a theoretical maximum value, reflecting the physical limiting properties of the material.

[0093] Finally, by introducing the near-field dynamics of the bond groups, the effective normal stress is... Replace with short-range repulsive force , joint normal closure quantity Replace with the compressive deformation of the key Thus, the expression for the hyperbolic nonlocal short-range repulsive force model is obtained:

[0094]

[0095] This final expression successfully transforms the constitutive relation of rock joint units into a short-range repulsive force model applicable to peri-field dynamics, realizing the cross-disciplinary application of the theory. The entire derivation process demonstrates how, through theoretical mapping and parameter substitution, the classical rock mechanics model can be innovatively applied to modern numerical simulation techniques, providing a solid theoretical foundation for solving the problem of material point embedding in bond-based peri-field dynamics.

[0096] Furthermore, in this embodiment, the step of ensuring that the bond deformation is always less than the initial bond length by using a preset compression limit residual rate parameter includes:

[0097] Define the compressibility limit residual rate parameter, denoted as . This represents the ratio of the minimum bond length that can be achieved during the compression process to the initial bond length. This value must be a positive number less than 1, expressed as:

[0098]

[0099] The compressibility residual rate ranges from 0 < < 1 is used to limit the maximum degree of compression deformation of the bond, ensuring that the deformation of the bond is less than the initial bond length throughout the entire process.

[0100] Specifically, in this embodiment, the core safety parameter "compression limit residual rate" is strictly defined mathematically. The goal is to abandon vague qualitative descriptions and ensure, through precise mathematical language, that there is an absolute and insurmountable lower limit when the bond length between material points is compressed in numerical simulation. This theoretically eliminates the occurrence of embedding phenomena and achieves precise limitation on the degree of bond deformation.

[0101] Define the compressibility limit residual rate parameter, denoted as . This represents the ratio of the minimum bond length allowed to be reached during compression to the initial bond length. This parameter is a positive number less than 1, and its mathematical expression is: Where α and β are constants in the model, Represents the initial bond length.

[0102] Secondly, it was clarified that the range of values ​​for the compressibility limit residual rate is 0 < <1. This range is crucial because it defines the maximum degree of compressive deformation of the key. By... Setting it to a value less than 1 ensures that the actual length of the bond is strictly greater than zero under any circumstances, thus fundamentally eliminating the possibility of material point embedding or penetration.

[0103] Specifically, in this embodiment, the size of dn can be precisely controlled by appropriately selecting the values ​​of α and β. For example, when α is relatively small and β is large, It will be closer to 1, which means the bond allows for less compression; conversely, when α is large and β is small, The compression of the bond is further away from 1, and the degree of compression is more strictly limited. This flexible parameter adjustment capability allows the method to adapt to the needs of different materials and working conditions. Furthermore, the compressibility limit residual rate parameter is not only a mathematical constraint but also a parameter reflecting the physical properties of the material. It embodies the material's ability to maintain structural integrity under extreme compression conditions and serves as a crucial bridge connecting macroscopic mechanical behavior and microscopic structural characteristics.

[0104] Furthermore, in this embodiment, the step of establishing a trigger control mechanism based on the state perception of matter points, which strictly limits the activation condition of short-range repulsive force to after the matter point enters a discontinuous state, includes:

[0105] Establish a quantifiable state identifier for a matter point to distinguish between continuous and discontinuous states;

[0106] The discontinuous state of a material point is determined by the damage value ϕ of the corresponding material point. When the damage value ϕ of a material point is greater than zero, it is determined that the material point has entered a discontinuous state.

[0107] Specifically, in this embodiment, a damage variable ϕ is first defined for each material point. This variable is a continuous function between 0 and 1, used to accurately quantify the degree of damage and mechanical state of the material point. When ϕ = 0, it indicates that the material point is in a completely continuous state, the internal structure of the material is intact, and no damage has occurred. When 0 < ϕ < 1, it indicates that the material point is in a partially damaged state, microcracks or microdefects have appeared inside the material, but it has not yet completely fractured. When ϕ = 1, it indicates that the material point is completely damaged, the internal structure of the material is completely destroyed, and it enters a completely discontinuous state.

[0108] In actual calculations, the failure criterion used is based on the bond compressibility criterion. When the compressibility reaches the limiting compressibility, it indicates that the bond has been broken. The damage to a material point is quantified by the interaction between the point itself and other material points in its neighborhood within the overall global interaction.

[0109] The material point enters a discontinuous state based on the damage value of the corresponding material point. The damage value of the material point is used for determination. When the value is greater than zero, the material point is considered to have entered a discontinuous state. In near-field dynamics, the proportion of the interaction between a material point and other material points in its neighborhood to the total interaction is typically calculated. This is used to quantify each point of matter. The damage is the proportion of the total original interactions that have disappeared within the system. This is achieved by using a scalar function closely related to historical states. To accurately record the integrity or breakage state of the key, the expression is:

[0110] , This indicates the maximum compression ratio.

[0111] The core logic of the trigger control mechanism is that short-range repulsion is activated between two interacting material points only when at least one of them has a damage value ϕ > 0. This criterion ensures that short-range repulsion is activated only in discontinuous regions where it is truly necessary to prevent the embedding of material points, while remaining completely inactive in regions where the material is still in a continuous state.

[0112] In practice, the system calculates and updates the damage value ϕ of all material points in real time within each computational step, and then performs a state judgment on each pair of material points. For any two interacting material points i and j, if ϕ_i > 0 or ϕ_j > 0 (or both simultaneously), a short-range repulsive force is calculated and applied between them; if ϕ_i = ϕ_j = 0, the short-range repulsive force remains zero, producing no additional mechanical action. This damage variable-based trigger control mechanism has multiple advantages: First, it completely avoids the problems of premature and global activation of short-range repulsive forces in traditional models, ensuring that the material can respond normally according to its inherent constitutive relation during continuous deformation; second, it achieves precise localization of the short-range repulsive force, activating it only near the damage region and contact interface, greatly improving computational efficiency; finally, it is consistent with the actual damage evolution process of the material, ensuring the physical reality of the numerical simulation.

[0113] Furthermore, in this embodiment, the step of embedding the short-range repulsion force model integrating the constitutive relation and trigger control mechanism into the equations of motion of the bond base near-field dynamics and performing numerical solutions includes:

[0114] Based on joint stiffness The definition has

[0115]

[0116] For hyperbolic nonlocal SRF models, when When the key stiffness is ,Right now

[0117]

[0118] By embedding the constitutive relation and the short-range repulsion force model of the triggering control mechanism, the constitutive expression of the linear nonlocal SRF model is reconstructed, and its constitutive relation can be expressed as:

[0119]

[0120] In the formula, The magnitude of the short-range repulsive force, For the compression ratio of the bond, This represents the compressibility limit residual rate.

[0121] Specifically, in this embodiment, the hyperbolic constitutive relation and triggering mechanism based on rock joint theory, as defined earlier, are integrated and incorporated into the core equations of motion of bond-base peri-field dynamics through rigorous mathematical derivation, thereby forming a complete enhanced numerical model that can be solved by a computer. Based on joint stiffness... The definition of is given, and its mathematical expression is provided:

[0122]

[0123] The formula describes the nonlinear characteristics of joint stiffness as a function of normal closure, reflecting the physical phenomenon that the material stiffness gradually increases during compression. Next, for the hyperbolic nonlocal SRF model, when the bond compressibility s = 0, the bond stiffness c, i.e. c is the intrinsic bond stiffness of the near-field dynamics of the bond base, a direct function of material parameters (such as Young's modulus). This indicates that in the initial state without compressive deformation, the short-range repulsive force has a definite initial stiffness value, providing a benchmark for the subsequent mechanical response. By embedding the constitutive relation and the short-range repulsive force model of the trigger control mechanism, the constitutive expression of the linear nonlocal SRF model is reconstructed, and its constitutive relation can be expressed as:

[0124]

[0125] In the denominator As the compression ratio s increases, the value of this term also increases. This is the limiting compressibility, making this term extremely sensitive to changes in s. When s is small, this factor is approximately 1, in which case fs≈cs, which is no different from a linear model. However, when s increases significantly, the denominator... The reciprocal effect of the rapid increase in the factor value, which causes a sharp decrease in the overall factor value, actually affects the preceding cs, ultimately leading to fs growing at a rate far exceeding the linear relationship with s, exhibiting a strong nonlinear strengthening characteristic. This is precisely the mathematical manifestation of the hyperbolic property.

[0126] The change of short-range repulsive force with compressibility is as follows: Figure 2 As shown, when bond deformation causes the distance between material points to approach a critical threshold, the two existing SRF models, both based on the constant stiffness assumption, cannot accurately describe the nonlinear mechanical response under extreme compression conditions, leading to non-physical penetration of material points. The improved hyperbolic nonlocal SRF model introduces variable stiffness characteristics, reconstructing the short-range repulsive stiffness as a dynamic strengthening function that evolves with the degree of bond deformation. Under the influence of this function, the stiffness parameter is no longer constant but dynamically and nonlinearly increases as the distance between material points gradually decreases, thus maintaining the topological constraints between material points more accurately at the microscale. The hyperbolic nonlocal SRF model employs a variable stiffness approach.

[0127] Furthermore, in this embodiment, the initial stiffness Set as a function proportional to the bond stiffness c of the bond base peri-field dynamics, the initial joint stiffness... for:

[0128]

[0129] Specifically, this embodiment clarifies how a core parameter in the model—the initial joint stiffness—is determined through its relationship with another model parameter, α. This definition is a crucial step in the internal parameterization of the model. It uses a simple mathematical relationship to connect the abstract model parameter α with the mechanically meaningful initial joint stiffness. In connection with this, during model calibration or parameter setting, researchers can first determine a desired initial joint stiffness based on physical intuition or numerical stability requirements. The value of α (for example, set it to a multiple of the key stiffness c), and then the formula is used to reverse-engineer the value of the parameter α. Figure 3 It can be seen that in the two existing SRF models, short-range repulsive force bond compressibility It exhibits a linear constitutive relation, that is Among them, compression ratio .when At that time, the distance between matter points The system is in a non-contact state; when When the distance between matter points approaches zero, it indicates that the matter points at both ends of the bond completely overlap, and the matter points annihilate. This occurs just before the matter points are about to actually embed or penetrate ( The short-range repulsive force is always a finite value. At this point, while the SRF model can alleviate some of the bond compression deformation, it cannot generate a sufficiently large repulsive force through linear constitutive relations to prevent the intercalation behavior between material points. Once Embedding or penetration will inevitably occur. This will cause finite-amplitude embedding between local material points and induce non-physical tangential displacement field shifts (discontinuities) at the contact surface.

[0130] In the hyperbolic nonlocal SRF model, it is a deformation rate-dependent variable stiffness constitutive framework that reconstructs the short-range repulsive stiffness as a dynamic hardening function that evolves with the degree of bond deformation, thus enabling the short-range repulsive force... bond compressibility It exhibits a nonlinear constitutive relationship, as the compressibility approaches the limiting compressibility ( When ), short-range repulsive force The sufficiently large short-range repulsive force inhibits the embedding behavior and also eliminates the non-physical tangential displacement field slippage (discontinuity) phenomenon at the contact surface.

[0131] When simulating the two existing SRF models, in the later stages of deformation, as the bonds continue to deform, large-area material points are embedded near the contact surface, causing the SRF model to suddenly fail. Figure 4This is a modeling method for a short-range repulsive force model that completely solves the problem of material point embedding in the near-field dynamics of bond groups. The embedding-non-embedding diagrams of the three models after the preset compressibility limit residual rate are used. When the hyperbolic nonlocal SRF model is used for simulation, the bond deformation rate infinitely approaches the limit compressibility threshold. The material points at both ends will not be embedded. The key to this mechanism lies in the pre-setting of the critical parameter of the compressibility limit residual rate, which enables the construction of a precise mechanical constraint mechanism. Specifically, even if the short-range repulsive force field inside the model is activated to a near-infinite theoretical strength, the degree of bond deformation will still be strictly limited, only infinitely approaching the preset limit compressibility threshold. Under this unique mechanism, although the bond deformation process continues, the material point pairs maintain a relatively close motion. Thanks to the nonlinear growth characteristics of the short-range repulsive force, it dynamically adjusts and generates a sufficiently strong repulsive force, thus forming an effective mechanical barrier before the material points come into contact. This mechanism cleverly avoids direct physical contact between material points and the potential annihilation effect, thus obtaining correct simulation results. The short-range repulsive force is only activated after the material points are damaged to prevent physical contact and embedding. This solves the design flaw in the triggering mechanism of the short-range repulsive force model. A triggering control mechanism based on material point state perception is established, strictly limiting the activation condition of the short-range repulsive force to after the material point enters a discontinuous (damaged) state, and limiting the effective area of ​​the short-range repulsive force to a certain neighborhood of the discontinuous region. This effectively blocks the non-physical pre-activation and global activation of the short-range repulsive force in the continuous medium region, completely eliminating its interference with the normal compressive deformation constitutive path.

[0132] It is particularly important to note that in this embodiment, displacement analysis is performed on a discontinuous plate with a vertical direct contact surface, and the force diagram is shown below. Figure 5 As shown, the area of ​​short-range repulsive force is as follows Figure 6 As shown, the specific operation steps are as follows:

[0133] Three two-dimensional plane stress conditions were used to construct SRF-BPD numerical models for quasi-brittle materials. Two identical specimens were placed side by side with a vertical contact surface between them. The model length and width were 0.032 m and 0.06 m, respectively, and the thickness was 0.01 m. The material parameters were Young's modulus of 60 GPa and mass density of 2400 kg / m³. 3 Poisson's ratio is 1 / 3.

[0134] Two rectangular thin plates are discretized into uniformly distributed PD (partially distributed particle) material points. Four virtual boundary layers are set on each of the left and right sides, and four virtual boundary layers are set on the upper layer of the left plate and the lower layer of the right plate. The particle point spacing is selected to be 4 times the BPD neighborhood radius, with a particle point spacing of 0.001m. The thickness is 0.004 mm. The specimen is divided into 3840 material points, and a neighborhood matrix of all material points is constructed.

[0135] Using displacement boundary conditions, the lower ends of the left and right plates of the numerical model are fixed, and a uniform displacement load is applied along the positive y-axis at the upper end of the left plate. A uniform displacement load is applied to the right end of the right plate along the negative x-axis. An adaptive dynamic relaxation algorithm is used for static solution. The virtual mass density matrix and virtual damping coefficient are input, and the acceleration, velocity and displacement of the material point at each time step are solved iteratively.

[0136] The displacement increment of all material points at any time step is less than 10. -10m To meet the convergence criteria, the optimized hyperbolic model of this application is used to calculate the displacement of all material points during the elastic deformation stage of the object. Simultaneously, the unoptimized local SRF model and the linear nonlocal SRF model are also used to calculate the displacement of all material points. The results of the three short-range repulsive force models along the x and y directions are as follows: Figures 7-8 As shown. Based on the calculated cloud diagrams of the three models above, it can be seen that for a discontinuous plate with a vertical direct contact surface, a uniform displacement load is applied along the positive y-axis at the upper end of the left side plate. A uniform displacement load is applied to the right plate along the negative x-axis. Under the influence of the local and linear nonlocal SRF models, the displacement contour maps in the x and y directions are discontinuous at the contact surface, while the displacement contour maps in the x and y directions of the hyperbolic nonlocal SRF model are continuous at the contact surface and have good performance.

[0137] In this embodiment, displacement analysis is performed on a two-plate system with a horizontal contact surface under uniform compressive load, wherein the force diagram is as follows. Figure 9 As shown, the area of ​​short-range repulsive force is as follows Figure 10 As shown, the specific operation steps are as follows:

[0138] Three two-dimensional plane stress-based SRF-BPD numerical models of quasi-brittle materials were constructed. Two identical specimens were placed one above the other with a horizontal contact surface between them. The model length and width were 0.1 m and 0.05 m, respectively, and the thickness was 0.01 m. The material parameters were Young's modulus of 200 GPa and mass density of 7850 kg / m³. 3 Poisson's ratio is 1 / 3.

[0139] Two rectangular thin plates are discretized into uniformly distributed PD material points. Four virtual boundary layers are set on the outer upper end of the upper specimen and the outer lower end of the lower specimen. The material point spacing is selected to be 4 times the BPD neighborhood radius. The material point spacing is 0.005m, that is, δ is 0.02mm. The two specimens are divided into 10,000 material points in total, and a neighborhood matrix of all material points is constructed.

[0140] Displacement boundary conditions are applied at the upper boundary of rectangular plate A and the lower boundary of rectangular plate B. Uniform normal load and Horizontal load.

[0141] All three SRF-BPD models employ an adaptive dynamic relaxation algorithm for static solution. The virtual mass density matrix and virtual damping coefficient are input, and the acceleration, velocity, and displacement of the material point at each time step are iteratively solved.

[0142] The displacement increment of all material points at any time step is less than 10. -10m To meet the convergence criteria, the optimized hyperbolic SRF-BPD model of this invention was used to calculate the displacement of all material points during the elastic deformation stage of the object. Simultaneously, traditional local and linear nonlocal SRF models were also used to calculate the displacement of all material points. The calculation results of the three short-range repulsive force models along the x and y directions are as follows: Figures 11-13 As shown.

[0143] Based on the calculation contour maps of the three models above, it can be seen that when a linear nonlocal SRF model is used to simulate a two-plate system with a horizontal contact surface under uniform compressive load, as shown in the figure... Figure 11 As shown, the x-direction displacement contour plot at a load step of 530 steps exhibits discontinuities at the contact surface, accompanied by slight embedding behavior. This phenomenon indicates that at this point, the model can no longer accurately reflect the actual situation, and its effective phase is nearing its end; when simulating using a localized SRF model, as... Figure 12 As shown in the figure, the x-direction displacement contour plot at a load step of 2250 steps reveals discontinuities at the contact surface, accompanied by slight embedding behavior. This further illustrates that the local SRF model has reached its simulation limit at this point, and its validity period has ended. In contrast, the hyperbolic nonlocal SRF model performs exceptionally well throughout the deformation process. Its x-direction displacement at the contact surface remains continuous, demonstrating excellent simulation results and showcasing the model's strong adaptability and stability; its validity period can be considered infinite. Figure 13 As shown in the figure, the y-direction displacement contour plots of the local and linear nonlocal SRF models at a load step of 4100 show that the material points exhibit large-scale embedding at the contact surface, indicating that the short-range repulsion force model has completely failed, while the hyperbolic nonlocal SRF model does not show embedding.

[0144] like Figure 14The comparison results show that when using local and linear nonlocal SRF models for simulation, the y-direction stress exhibits a sharp decrease during deformation, eventually reaching zero. This phenomenon indicates that the short-range repulsion model causes material points at the contact surface to embed prematurely before reaching the strain condition required to induce embedding, leading to sudden model failure. In stark contrast, the hyperbolic nonlocal SRF model does not show this sharp decrease in y-direction stress, and no embedding occurs at the contact surface. Furthermore, selecting one material point on each side of the contact surface to form a bond pair, the force density-compressibility relationship of this bond pair is as follows... Figure 15 As shown, when the compressibility reaches a critical value (0.29303 for the local SRF model and 0.72347 for the linear nonlocal SRF model), the short-range repulsive force density significantly decreases and eventually approaches zero. At this point, the short-range repulsive model fails, unable to provide sufficient repulsive force to resist further bond deformation, leading to penetration between material points. In contrast, the force density-compressibility curve of the hyperbolic nonlocal SRF model exhibits typical hyperbolic characteristics, with its force density increasing exponentially with increasing compressibility. As deformation approaches the limiting compressibility, this model can generate a reaction force approaching infinity. Furthermore, because the model pre-determines the compressibility limit residual (redundancy) rate, the mutual penetration between material points at both ends of the bond is fundamentally avoided. This fully demonstrates that the hyperbolic nonlocal SRF model has the ability to effectively address and completely solve the material point embedding problem in near-field dynamics simulations.

[0145] Other embodiments or specific implementations of the modeling apparatus for the short-range repulsive force model that completely solves the problem of material point embedding in the near-field dynamics of bonded bases can be found in the above-described method embodiments, and will not be repeated here.

[0146] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0147] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0148] It should be particularly noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, or of course, by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0149] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A modeling method of a short-range repulsive force model that completely solves the problem of particle embedding in key-based near-field dynamics, characterized by, The method comprises the following steps: Step S10: constructing a hyperbolic non-local short-range repulsive force model based on the constitutive relation of rock joint element; Step S20: ensuring that the deformation of the bond is always less than the initial bond length by a preset compression limit residual rate parameter; Step S30: establishing a trigger control mechanism based on the state awareness of the material point, and strictly limiting the activation condition of the short-range repulsive force to after the material point enters a discontinuous state; Step S40: embedding the short-range repulsive force model integrated with the constitutive relation and the trigger control mechanism into the motion equation of the bond-based near-field dynamics for numerical solution.

2. The method of claim 1, wherein, The step of constructing a hyperbolic non-local short-range repulsive force model based on the constitutive relation of rock joint element comprises: A hyperbolic model of the normal constitutive relation of the rock joint element is introduced as a starting point, and the original form is: ; wherein is the effective normal stress, is the joint normal closure, and are constants; In near-field dynamics, the tensile stress and tensile deformation are usually positive, and the function form after symbol adaptation according to the principle of near-field dynamics is: ; When the effective normal stress approaches infinity, i.e. then and is the normal closure. After introducing the key-based near-field dynamics, replaced by , replaced by The expression of the hyperbolic non-local short-range repulsive force model is 。 3. The method of claim 1, wherein, The step of ensuring that the deformation of the bond is always less than the initial bond length by a preset compression limit residual rate parameter comprises: The compression limit residual rate parameter is defined as , which represents the ratio of the minimum length that the bond length can reach during compression to the initial length. This value must be a positive number less than 1 but infinitely close to 1, and is represented as: ; The compression limit residual rate is valued in the range 0 < r < 0.2 < 1, for limiting the maximum compression deformation of the key, ensuring that the deformation of the key throughout is less than the initial key length.

4. The method of claim 1, wherein, The step of establishing a trigger control mechanism based on the state awareness of the material point, and strictly limiting the activation condition of the short-range repulsive force to after the material point enters a discontinuous state comprises: A quantifiable state identifier is established for the material point to distinguish between continuous and discontinuous states; The material point enters a discontinuous state by judging the damage value of the corresponding material point, and when the damage value of the material point is greater than zero, it is determined that the material point has entered a discontinuous state.

5. The method of claim 1, wherein, The step of embedding the short-range repulsive force model integrated with the constitutive relation and the trigger control mechanism into the motion equation of the bond-based near-field dynamics for numerical solution comprises: Based on the definition of joint stiffness there is: ; For the hyperbolic non-local short-range repulsive force model, when the bond stiffness is i.e. ; The short-range repulsive force model integrated with the constitutive relation and the trigger control mechanism is embedded to reconstruct the constitutive expression of the linear non-local short-range repulsive force model, and the constitutive relation can be expressed as: ; In the formula, is the magnitude of the short-range repulsive force, is the compressibility of the bond, is the compressive ultimate residual rate.

6. The method of claim 5, wherein, The initial stiffness The initial joint stiffness is set as a function proportional to the key stiffness c of the key-based near field dynamics is: 。 7. The method of claim 1, wherein, In the simulation process, for the material points with activated short-range repulsive force, the short-range repulsive force therebetween is calculated according to the hyperbolic constitutive relation in claim 1, and the activation of the short-range repulsive force follows the trigger control mechanism in claim 1 or 4.

8. A modeling device of a short-range repulsive force model that completely solves the problem of particle embedding in key-based near-field dynamics, characterized by, It comprises: A modeling module for constructing a hyperbolic non-local short-range repulsive force model based on the constitutive relation of rock joint element; A setting module for ensuring that the deformation of the bond is always less than the initial bond length by a preset compression limit residual rate parameter; A trigger module for establishing a trigger control mechanism based on the state awareness of the material point, and strictly limiting the activation condition of the short-range repulsive force to after the material point enters a discontinuous state; A solution module for embedding the short-range repulsive force model integrated with the constitutive relation and the trigger control mechanism into the motion equation of the bond-based near-field dynamics for numerical solution.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the modeling method of the short-range repulsive force model for completely solving the material point embedding problem in the bond-based near-field dynamics according to any one of claims 1-7 when executing the program.

10. A computer-readable storage medium, characterized in that, The computer program is stored in the memory and is executed by the processor to implement the modeling method according to any one of claims 1-7.

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