A composite material hybrid connection performance modular rapid prediction method

Abstract

The application discloses a kind of composite material mixed connection performance modularization quick prediction method, comprising the following steps: S1. the circuit model of composite material connecting structure is constructed, and the circuit model is established based on the mechanical equivalent principle of spring stiffness method;S2. the displacement response signal and load information of connecting structure under the action of load are acquired by simulating composite material connecting structure using the circuit model;S3. based on the displacement response signal, whether the structure is damaged and damage type is judged in combination with corresponding damage criterion;S4. the circuit model is adjusted according to the judgment result;S5. based on the circuit model after adjustment, the complete load-displacement curve of the composite material connecting structure is output in combination with the load information predicted.The application can efficiently predict the nonlinear mechanical response of bolt connection, glue joint connection and glue screw mixed connection structure before damage occurs, and accurately simulate the whole process behavior of stiffness degradation and load redistribution after damage occurs.

Description

Technical Field

[0001] This invention relates to the prediction of the mechanical properties of composite material structures, specifically to a modular and rapid prediction method for the hybrid connection performance of composite materials, applicable to bolted connections, adhesive connections, and hybrid glue-bolt connections. Background Technology

[0002] Composite materials, especially advanced composite materials represented by carbon fiber reinforced polymer (CFRP), have become the preferred materials for weight reduction design of high-end equipment structures in aerospace, rail transportation, and other fields due to their excellent specific strength, specific stiffness, and corrosion resistance. In these structures, reliable connections between components are crucial, and bolted connections are widely used due to their high load-bearing capacity and detachability.

[0003] However, composite bolted connections are subject to complex stresses, with significant stress concentration around the bolt holes. Furthermore, the contact interface exhibits multiple nonlinear behaviors, including friction, slippage, and gaps, leading to a highly complex damage initiation and evolution process. This connection is often a weak point in the overall structure, and its performance directly affects the safety and lifespan of the entire structure. In addition, connection design involves numerous parameters such as geometric dimensions, layup sequence, and tightening torque; improper design can severely impact structural efficiency.

[0004] Currently, research on the performance of such structures mainly relies on experimental testing and finite element simulation. While experimental methods provide direct and reliable results, they are costly and time-consuming, making them unsuitable for screening a large number of design parameters. Although the finite element method can simulate complex mechanical behaviors, it is extremely time-consuming and computationally inefficient when modeling complex structures and calculating nonlinear contacts and damage evolution, thus also unsuitable for rapid preliminary design of structures.

[0005] To improve the efficiency of evaluation in the early stages of design, analytical methods based on simplified mechanical models have gained attention. Early studies mainly used spring or beam elements to simulate bolted connection behavior, developing a series of analytical models to predict the stiffness and load distribution of the connection. In recent years, some studies have proposed using circuit principles to simulate these mechanical models, equating stiffness and contact state in mechanical properties through electrical components such as resistors and switches. This method has shown certain advantages in terms of computational speed and modeling intuitiveness.

[0006] However, existing circuit-based analysis methods have fundamental limitations: First, they can only simulate the linear or partially nonlinear mechanical response of connected structures in an intact state, failing to effectively simulate and predict damage to composite materials after reaching their strength limits, and even less capable of analyzing stiffness degradation and load redistribution during damage evolution. Second, existing methods only model single-mode bolted connections, not extending to adhesive joints and hybrid adhesive-bolt connections, thus failing to meet the prediction needs of various connection methods in engineering practice. These limitations prevent existing circuit-based methods from comprehensively evaluating the damage tolerance and residual strength of structures under different connection modes, severely restricting their application in integrity design and safety assessment. Therefore, developing a novel predictive model that integrates efficient circuit simulation and multi-mode connection damage analysis capabilities is of great significance for achieving rapid and accurate design and performance evaluation of such structures. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a modular and rapid prediction method for the hybrid connection performance of composite materials. This method can efficiently predict the nonlinear mechanical response of bolted, glued, and glue-bolt hybrid connection structures before damage occurs, and accurately simulate the entire process of stiffness degradation and load redistribution after damage occurs.

[0008] To achieve the objective of this invention, the following solution is adopted: A modular and rapid prediction method for the hybrid bonding performance of composite materials includes the following steps: S1. Construct a circuit model for the composite material connection structure. The circuit model is established based on the mechanical equivalence principle of the spring stiffness method. The circuit model is applicable to bolted connection structures, adhesive connection structures, and hybrid adhesive-screw connection structures. For bolted connection structures, the circuit model can simulate the static friction stage, sliding friction stage, gap filling stage, and rigid bearing stage of the bolt connection. For adhesive connection structures, the circuit model fits the equivalent stiffness of the adhesive layer based on finite element simulation data and constructs an adhesive joint submodule. For hybrid adhesive-screw connection structures, the circuit model includes an adhesive joint submodule and a bolt joint submodule, and the switching of the three-stage force transmission mechanism is realized through a dynamic selection switch. S2. The circuit model is used to simulate the composite material connection structure to obtain the displacement response signal and load information of the composite material connection structure under load. S3. Based on the displacement response signal and the corresponding damage criteria, determine whether the structure has been damaged and the type of damage. For bolted connection structures, damage is determined based on the average strain combined with the strain form of the Hashin criterion. For adhesive connection structures, damage is determined based on the damage initiation criterion of the cohesive force model. For adhesive-bolt hybrid connection structures, the adhesive joint submodule uses the damage initiation criterion of the cohesive force model to determine adhesive layer damage, and the bolt joint submodule uses the average strain combined with the strain form of the Hashin criterion to determine laminate damage. The two criteria are dynamically activated as the three-stage force transmission mechanism switches. S4. Adjust the circuit model according to the judgment result: if damage is judged to have occurred, the parameters of the corresponding components in the circuit model are dynamically updated according to the damage type to simulate the stiffness degradation caused by the damage; if damage is judged not to have occurred, the current parameters of the circuit model are maintained. S5. Based on the adjusted circuit model and combined with the load information, output the predicted complete load-displacement curve of the composite material connection structure.

[0009] Furthermore, in step S1, for bolted connection structures, the circuit model achieves dynamic switching and stiffness simulation of the four mechanical stages by selecting a combination of a switch module and a sliding rheostat module.

[0010] Furthermore, step S2 specifically includes: S21. The displacement response signal of the composite material connection structure is obtained by integrating the voltage signal output by the circuit model; S22. By accumulating the current signals output by the circuit model, the total load constituting the load information is obtained.

[0011] Further, in step S3, for bolted connection structures, the calculated average strain is multiplied by a preset strain amplification factor k to obtain the local maximum strain at the bolt hole edge used for damage assessment; wherein, the strain amplification factor k is determined based on the anisotropy of the composite material and the ply structure. Material anisotropy and ply sequence affect strain distribution; for example, orthogonal plies have higher stiffness uniformity, and their k value is lower than that of unidirectional plies, which can be varied according to different materials and structures.

[0012] Furthermore, in step S3, the damage criterion for the strain form is the Hashin criterion for the strain form, which includes at least four damage modes: fiber tension, fiber compression, matrix tension, and matrix compression.

[0013] Furthermore, in step S1, for a connection structure containing multiple bolts, the circuit model is a parallel circuit network model, wherein the connection part corresponding to each bolt is constructed as an independent circuit sub-module, and multiple circuit sub-modules are connected in parallel.

[0014] Furthermore, during the simulation, the parallel circuit network model can automatically simulate the initial distribution of load among the bolts and the dynamic transfer process after damage occurs, based on the real-time resistance changes of each circuit sub-module.

[0015] Further, in step S1, for the adhesive joint structure, the construction method of the adhesive joint submodule includes: obtaining the load-displacement curve data of the adhesive joint through finite element simulation, extracting the load-displacement response of the joint area, calculating the equivalent stiffness of the adhesive joint through data fitting, and converting the stiffness into the resistance parameter in the circuit model; after the adhesive layer is damaged, the equivalent stiffness is reduced to simulate the damage evolution, and the stiffness is reduced to zero when the adhesive layer completely fails.

[0016] Furthermore, in step S1, for the glue-screw hybrid connection structure, the three-stage force transmission mechanism includes: the first stage is the glue-dominated stage, when the joint displacement is less than the gap between the bolt and the screw hole, only the glue joint sub-module is connected to the circuit, and the glue layer bears the load alone; the second stage is the collaborative bearing stage, when the joint displacement is greater than or equal to the gap and the glue layer is not completely failed, the glue joint sub-module and the bolt joint sub-module are connected to the circuit simultaneously, and the load is borne by the glue layer and the bolt together; the third stage is the bolt-dominated stage, when the glue layer is completely failed, only the bolt joint sub-module is connected to the circuit, and the bolt bears the load alone until the structure is finally destroyed.

[0017] Furthermore, during the collaborative load-bearing stage, the adhesive joint submodule and the bolt joint submodule are connected to the circuit in parallel, and the load is automatically distributed according to the reciprocal of the equivalent resistance of each submodule. When the adhesive layer completely fails, the load output value is corrected by an improved accumulation module to simulate the sudden drop in load caused by the sudden breakage of the adhesive layer.

[0018] Furthermore, the circuit model is constructed and implemented in the Simulink platform; the material and geometric parameters in the circuit model are uniformly managed and called through the global variable module, supporting the modular design of the model and rapid modification of parameters; the bolt joint submodule, the adhesive joint submodule, and the laminate module used to simulate the stiffness of the laminate are all independent standardized modules, which can be flexibly assembled into different connection configurations through series or parallel connection.

[0019] Compared with the prior art, the technical advantages of the present invention are as follows: 1. This invention realizes a unified circuit prediction framework for multi-mode connection structures. Through a modular circuit modeling strategy, three connection modes—bolted connection, adhesive connection, and hybrid adhesive-bolted connection—are incorporated into a unified circuit simulation framework. By utilizing standardized bolt joint sub-modules, adhesive joint sub-modules, and laminate modules, different connection configurations can be rapidly modeled through flexible combinations in series or parallel, greatly improving the model's versatility and engineering applicability.

[0020] 2. The simulation efficiency and accuracy of this invention are significantly improved. The constructed circuit model achieves extremely high computational efficiency; for example, the simulation time for a single bolt connection structure can be reduced to approximately 1.5 seconds, far lower than the 2-3 hours typically required by traditional finite element methods. Simultaneously, this invention maintains excellent prediction accuracy. For single bolt structures, the predicted initial stiffness is consistent with experimental results, the prediction error of the damage initiation load is controlled within 10%, and the prediction error of the ultimate load does not exceed 13%.

[0021] 3. This invention achieves dynamic simulation of progressive damage processes. For bolted connections, a feedback mechanism based on strain monitoring and the Hashin criterion is introduced to dynamically simulate the initiation and evolution of damage in composite material structures; for adhesive connections, stiffness reduction guided by the cohesive force model is used to achieve circuit-based characterization of adhesive layer damage; for hybrid connections, a three-stage dynamic switching mechanism is used to achieve complete simulation of multi-path force transmission and failure processes.

[0022] 4. This invention simulates the load distribution between the adhesive layer and bolts in a hybrid connection structure. During the collaborative load-bearing stage, the automatic current distribution principle of the parallel circuit accurately reflects the load proportion borne by the adhesive layer and bolts respectively. After the adhesive layer fails, the load is automatically transferred to the bolts, and the improved accumulation module accurately captures the phenomenon of sudden load drop, thus reproducing the real mechanical behavior of multi-stage failure in the hybrid connection structure.

[0023] 5. This invention realistically reproduces the load distribution and damage transfer mechanism of multi-bolt connections. By adopting a strategy of parallel connection of standardized single-bolt sub-modules, an equivalent circuit network for multi-bolt connections is constructed, which automatically realizes the realistic mechanical response of "initial load distribution according to stiffness" and "dynamic transfer of load to healthy bolts after damage occurs".

[0024] 6. This invention possesses excellent versatility, scalability, and engineering applicability. The modular circuit modeling strategy allows the model to flexibly adapt to various connection configurations, including single-bolt, multi-bolt, adhesive, and hybrid connections, demonstrating strong versatility. The graphical implementation based on the Simulink platform makes the modeling process intuitive and modification convenient.

[0025] In summary, this invention provides a high-efficiency and high-precision method for predicting the performance of composite material connection structures by equating the nonlinear loading process of composite material connection structures to a modular circuit system. This invention not only significantly improves simulation efficiency but also successfully introduces damage analysis and load distribution simulation, effectively solving the shortcomings of traditional methods in the initial design stage, such as low efficiency and difficulty in handling nonlinear damage problems. It provides an engineering solution for the rapid design and evaluation of composite material connection structures. Attached Figure Description

[0026] Figure 1 This is a flowchart of a modular rapid prediction method for the hybrid bonding performance of composite materials in an embodiment of the present invention; Figure 2 This is a schematic diagram showing the geometric dimensions of a single-bolt connection structure in an embodiment of the present invention; Figure 3 This is a schematic diagram of the circuit switching module for the four-stage connection joint in an embodiment of the present invention; Figure 4 This is a schematic diagram of the real-time control circuit for introducing a selection switch (SPDT Switch module) in an embodiment of the present invention; Figure 5 This is a schematic diagram of the accumulation module in an embodiment of the present invention; Figure 6 This is a schematic diagram of the circuit model with a damage module added in this embodiment of the invention. Figure 7 This is a schematic diagram of the load-displacement curves obtained using circuit models with different strain amplification factors in an embodiment of the present invention; Figure 8 This is a schematic diagram of the three-bolt connection structure in an embodiment of the present invention; Figure 9 This is a schematic diagram illustrating the construction of a circuit model for a three-bolt connection structure in an embodiment of the present invention. Figure 10 This is a schematic diagram of the bilinear constitutive model of the cohesive unit in an embodiment of the present invention; Figure 11 This is a schematic diagram of the geometric parameters of the adhesive bonding structure in an embodiment of the present invention; Figure 12 This is a finite element model and a partial enlarged view of the adhesive bonding connection in an embodiment of the present invention; Figure 13 This is a schematic diagram of the load-displacement curve of the finite element simulation of the adhesive structure in an embodiment of the present invention; Figure 14 This is a schematic diagram of the adhesive connection circuit model in an embodiment of the present invention; Figure 15 This is a schematic diagram of a rubber-screw hybrid connection circuit model in an embodiment of the present invention; Figure 16 This is a schematic diagram of the improved accumulation module for the hybrid connection of rubber and screw in an embodiment of the present invention; Figure 17 This is a schematic diagram of the geometric parameters of the hybrid connection structure in an embodiment of the present invention. Detailed Implementation

[0027] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0028] like Figure 1 As shown in the figure, this invention provides a modular and rapid prediction method for the hybrid bonding performance of composite materials, including the following steps: S1. Construct a circuit model for the composite material connection structure. The circuit model is established based on the mechanical equivalence principle of the spring stiffness method. The circuit model is applicable to bolted connection structures, adhesive connection structures, and hybrid adhesive-screw connection structures. For bolted connection structures, the circuit model can simulate the static friction stage, sliding friction stage, gap filling stage, and rigid bearing stage of the bolt connection. For adhesive connection structures, the circuit model is constructed by fitting the equivalent stiffness of the adhesive layer based on finite element simulation data and constructing an adhesive joint submodule. For hybrid adhesive-screw connection structures, the circuit model includes an adhesive joint submodule and a bolt joint submodule, and the switching of the three-stage force transmission mechanism is realized through a dynamic selection switch.

[0029] S2. The circuit model is used to simulate the composite material connection structure to obtain the displacement response signal and load information of the composite material connection structure under load.

[0030] S3. Based on the displacement response signal and the corresponding damage criteria, determine whether the structure has been damaged and the type of damage. For bolted connection structures, damage is determined based on the average strain combined with the strain form of the Hashin criterion. For adhesive connection structures, damage is determined based on the damage initiation criterion of the cohesive force model. For adhesive-bolt hybrid connection structures, the adhesive joint submodule uses the damage initiation criterion of the cohesive force model to determine adhesive layer damage, and the bolt joint submodule uses the average strain combined with the strain form of the Hashin criterion to determine laminate damage. The two criteria are dynamically activated as the three-stage force transmission mechanism switches.

[0031] S4. Adjust the circuit model according to the judgment result: If damage is judged to have occurred, the parameters of the corresponding components in the circuit model are dynamically updated according to the damage type to simulate the stiffness degradation caused by the damage; if damage is judged not to have occurred, the current parameters of the circuit model are maintained.

[0032] S5. Based on the adjusted circuit model and combined with the load information, output the predicted complete load-displacement curve of the composite material connection structure.

[0033] The modular rapid prediction method for composite material hybrid bonding performance according to embodiments of the present invention will be further described in detail below: This invention, based on the mechanical equivalence principle of spring stiffness, establishes an equivalent multi-stage load-displacement prediction model through circuit simulation, enabling response prediction throughout the entire process of friction-gap-rigidity-damage evolution. Specifically, it includes the following: In this embodiment, the circuit model of the bolt connection structure is as follows: 1. Construct a four-stage bolted joint circuit model: Divide the nonlinear loading behavior of the joint in the composite bolted joint structure into four stages (static friction stage, sliding friction stage, gap filling stage, and rigid bearing stage). Use different resistance values ​​and selection switches to realize stiffness switching and nonlinear modeling in the circuit.

[0034] 2. Introducing a damage module with strain amplification factor and Hashin criterion: The displacement of the connecting structure is simulated by voltage measurement. The average strain of the laminate is converted into the local maximum strain at the bolt hole edge by the strain amplification factor (k=2.75). The Hashin criterion of strain form is used to determine whether there are various typical damage modes such as fiber tension, fiber compression, matrix tension and matrix compression. The stiffness of the corresponding module is dynamically reduced (e.g., after fiber damage, the longitudinal modulus is reduced to 60% of the original value and the transverse modulus is reduced to 30% of the original value), so as to realize the staged degradation simulation of the stiffness of the connecting structure.

[0035] 3. Constructing a parallel resistance network model for multi-bolt connections: Multiple joint modules are combined in parallel in Simulink to simulate the load distribution of multiple bolts in the connection structure. This network supports setting different initial gaps and friction coefficients for different bolt holes and can track the stress state and damage evolution of each bolt module in real time, accurately simulating the real mechanical response process of "strong bolts damage first, weak bolts bear load later".

[0036] In this embodiment, the circuit model of the adhesive bonding structure is as follows: The adhesive joint submodule based on finite element data fitting obtains load-displacement curve data of the adhesive joint using finite element simulation. In the finite element model, reference points are set at both ends of the joint region, and the difference in displacement between the two reference points is taken as the joint displacement. This difference is then combined with the overall load data to obtain the joint's load-displacement response. Data from the linear phase before damage is fitted to calculate the equivalent stiffness of the joint, which corresponds to the reciprocal of the resistance in the circuit model. After adhesive layer damage, a reduction factor is applied to the stiffness to simulate the nonlinear degradation process; when the adhesive layer completely fails, the stiffness drops to zero, indicating that the adhesive joint has lost its load-bearing capacity.

[0037] By leveraging the modularity of circuit models, the bolt connection joints in the aforementioned bolt connection structure circuit model can be replaced with adhesive joint modules to obtain a complete circuit model of the adhesive structure.

[0038] In this embodiment, the circuit model of the glue-screw hybrid connection structure is as follows: 1. Three-stage force transmission mechanism and dynamic switching logic: The loading process of the glue-screw hybrid connection structure has multi-path force transmission characteristics, which can be divided into three stages: Phase 1 (Adhesive Layer Dominant Phase): When the joint displacement is less than the gap between the bolt and the threaded hole, the load is entirely borne by the adhesive layer. In the circuit model, selector switches 1 and 2 are both off, and only the adhesive joint module is connected to the circuit.

[0039] Phase Two (Collaborative Load-Bearing Phase): When the joint displacement exceeds the gap between the bolt and the bolt hole and the adhesive layer has not completely failed, the adhesive layer and the bolt jointly bear the load. When selector switch 2 is closed, the adhesive joint module and the bolt joint module are simultaneously connected to the circuit, forming a parallel circuit.

[0040] The third stage (bolt-dominated stage): When the adhesive layer completely fails, selector switch 1 is closed, and only the bolt joint module is connected to the circuit. The load of the connection structure is entirely borne by the bolt until the final failure.

[0041] 2. Handling the Sudden Drop in Load Due to Adhesive Layer Failure: When the adhesive layer completely fails, the load-displacement curve of the connection structure shows a sudden drop, caused by the sudden fracture of the adhesive layer. Since the load and displacement data in the circuit model are obtained by accumulating the increments at each step using an accumulation module, the conventional accumulation method only increases the data and cannot accurately simulate the load decrease. Therefore, the accumulation module is improved: upon receiving a signal indicating complete adhesive layer damage, the output value of the accumulation module is reduced by a fitted value through the Add module, thereby achieving accurate simulation of the sudden load drop in the load-displacement curve.

[0042] 3. All modules adopt a reusable and callable subsystem structure. Through Simulink global variable settings, material properties and geometric parameters can be updated quickly, adapting to the needs of rapid modeling and extended analysis for different connection configurations. The bolt joint submodule, adhesive joint submodule, and laminate module are all standardized independent modules that can be flexibly assembled in series or parallel.

[0043] The following describes the specific operation procedure for the circuit model of the single-bolt connection structure containing the damage module.

[0044] Taking a composite material single-lap joint single-bolt connection structure as the object, an equivalent circuit prediction model is established. For example... Figure 2 As shown, the composite laminate with a single-bolt connection structure has a width of 40 mm, a length of 150 mm, an overlap length of 70 mm, and a total thickness of 5.2 mm. It is composed of 40 layers with a thickness of 0.13 mm. The bolt hole diameter is 8 mm, with a corresponding gap of 0.1 mm. The bolt material is titanium alloy, and the tightening torque applied to the bolt in the model is 6 N·m.

[0045] Specifically, the establishment, simulation, and damage analysis of the circuit model of the single-bolt connection structure containing the damage module mainly include the following steps: Define the system input, set the voltage source constant value to 0.005 V, corresponding to a displacement increment of 0.005 mm; the load (current) is measured by an ammeter; material parameters and geometric parameters are input through the Data Store Memory module, including: plate elastic modulus Ep, bolt modulus Eb; layer thickness, bolt diameter, bolt head diameter and other geometric parameters.

[0046] Step 1: Construct a three-segment structural model: Upper plate: equivalent to a constant resistance R1, representing the elastic stiffness of the plate; Connecting joints: constructing composite modules with a four-stage switching structure, such as... Figure 3 As shown, the stiffness changes sequentially according to the friction-sliding-gap-contact stages; the lower plate is equivalent to a constant resistance R2.

[0047] Step 2: Implement the stiffness switching logic: The circuit path is controlled using three selector switch modules; a sliding rheostat module is used to simulate the reciprocal (1 / K) of stiffness (K) at different stages; the displacement is calculated and compared with thresholds a, b, and c to control the switching, such as... Figure 4 As shown: a: Slip start displacement b: Slip termination, gap initiation displacement c: Gap filling complete, contact begins to shift; the value of c is b plus the bolt hole gap. The coefficient of friction of the contact surfaces is represented by , and T represents the tightening torque applied to the bolt. This constant represents the relationship between bolt torque and tightening force, and is set to 0.2.

[0048] The joint stiffness of the four stages are as follows: In the above formulas, the parameter with subscript p represents the material parameter of the plate, and the parameter with subscript b represents the material parameter of the bolt. A, G, E, and I represent the cross-sectional area, shear modulus, elastic modulus, and moment of inertia of the section, respectively, and d represents the diameter of the bolt head and nut. This represents the proportion of bolt bending moment borne by the support stress in the laminate, with the remaining portion... The bolt head and nut will then bear the load. Therefore, The value range varies depending on the bolt type: for pure shear pins, For countersunk fasteners, This study uses convex head bolts. The value is 0.15.

[0049] Step 3: Add load-displacement output module: The load increment (physical signal) acquired by the ammeter is converted into a Simulink-processable numerical signal by the PS-Simulink Converter module; this signal is then input to the accumulation module, such as... Figure 5 As shown, the real-time total load is obtained by superimposing the historical load values ​​stored in the Memory module; the displacement increment signal output by the voltage source is integrated to obtain the total displacement, and finally a complete load-displacement response curve is generated through the curve output module.

[0050] Step 4: Integration and Implementation of the Progressive Damage Module: like Figure 6 As shown, a damage module is connected in series in the fourth stage circuit of the connecting joint. Through closed-loop logic of strain monitoring, damage judgment and stiffness reduction, the progressive damage process of composite materials is simulated.

[0051] Step 5: Strain Monitoring and Conversion By connecting a voltmeter, the displacement data of the connection nodes and the overall structure can be acquired in real time. Based on this, the displacement response of the upper and lower laminates can be further determined. By collecting voltage data, the average strain value of the composite laminate under tension can be calculated. The introduction of the strain amplification factor k aims to solve the difference between the average strain and the maximum local strain of the bolt hole. Its core function is to convert the overall average strain of the laminate output by the circuit model into the true strain of the critical region at the hole edge, thereby accurately triggering the damage criterion. Figure 7 A comparison of predicted and experimental curves for different values ​​of k is presented, based on which k=2.75 is determined to be the optimal value. The average strain is then calculated. Multiply by the magnification factor k=2.75 to obtain the strain at the edge of the bolt hole. .

[0052] Step Six: Change the ply angle: The following matrix transformation is used to convert the strain in the load direction into strain components in the local coordinate system of each ply: in It's the angle of the ply. , , These are fiber-direction strain, fiber-normal strain, and local shear strain, respectively. , , For tensile strain, tensile normal strain, and local shear strain.

[0053] Step 7: Determining the Damage Criteria Substitute the strain into the strain form of the Hashin criterion to determine whether the tensile and compressive damage of the fiber / matrix is ​​satisfied. Fiber stretching: Fiber compression: Matrix stretching: Matrix compression: in E represents strain, E represents the elastic modulus in one direction, and G represents the shear modulus. , , , , Material strength expressed in terms of strain.

[0054] Step 8: Stiffness Reduction and Resistance Update If damage occurs, the elastic modulus is reduced (e.g., fiber-direction modulus). Reduced to 60% of the original value, matrix transverse modulus (Reduced to 30% of the original value); the stiffness of the connecting joint is recalculated based on the reduced modulus, and the resistance value is updated by controlling the sliding rheostat through Simulink variables to achieve stiffness degradation; the current in the circuit is automatically distributed to the undamaged branch to simulate the load redistribution behavior induced by damage.

[0055] The following describes the specific operation procedure for the circuit model of the multi-bolt connection structure.

[0056] Using a three-bolt connection structure as the modeling object, each bolt joint is an independent sub-module. Overall simulation is achieved through modular design and parallel combination. The three-bolt connection structure uses the same HTA / 6376 composite laminate as the single-bolt connection structure described above, with expanded geometric dimensions of 272 mm in length and 48 mm in width. The three bolts are arranged at equal intervals of 36 mm, with an 8 mm hole diameter. The gap between the bolts and the bolt holes is ignored. The three-bolt connection structure, as shown... Figure 8 As shown. The bolt material is the same as that of the single-bolt connection structure described above, which is titanium alloy. The key parameters such as the elastic modulus and Poisson's ratio of the laminate, the elastic modulus and shear modulus of the bolt, the coefficient of friction of the contact surface, and the bolt tightening torque are all set using the settings in the circuit model of the single-bolt connection structure of the damage module described above. These parameters are globally called through the Data Store Memory module to ensure the consistency of parameters across multiple sub-modules.

[0057] Specifically, the construction, simulation, and damage analysis of the multi-bolt connection structure circuit model mainly include the following steps: Step 1: Submodule Construction: Each bolt's corresponding connection joint is independently constructed as a standardized circuit sub-module. This sub-module fully inherits the core functions of the single-bolt connection structure circuit model mentioned above, including: four-stage stiffness switching, elastic modulus reduction after damage, and dynamic resistance update function.

[0058] Step 2: Constructing the parallel resistor network: A parallel circuit topology is used to integrate three standardized single-bolt submodules to construct an equivalent circuit model of a three-bolt connection structure: the input terminals of the three single-bolt submodules are connected in parallel to the same voltage source (output constant voltage 0.005 V), and the output terminals are combined and connected in series with a total ammeter; each submodule is independently configured with a branch ammeter to collect the load increment corresponding to a single bolt in real time, share the same voltage input, and output the total current. In the system response, each bolt automatically bears different loads according to its stiffness (resistance).

[0059] Step 3: Load Distribution and Dynamic Transfer In the initial stage (undamaged state), the stiffness of each bolt sub-module is determined by its geometric parameters and material properties. The load is distributed proportionally according to the stiffness of each sub-module. When a bolt sub-module is damaged (such as tensile damage to the fibers around the edge bolt hole), the elastic modulus of that sub-module is reduced according to the rules in the circuit model of the single bolt connection structure containing the damaged module, resulting in an increase in the corresponding circuit resistance. According to the current distribution law of parallel circuits, the current in the branch with increased resistance automatically decreases, while the current in the branch of the undamaged or less damaged bolt sub-module increases accordingly, realizing the dynamic transfer of load from the damaged bolt to the healthy bolt. Figure 9 The diagram shows the layout structure of each subsystem in the circuit simulation.

[0060] The following describes the specific operational procedures for the circuit model of the adhesive bonding structure.

[0061] Step 1: Establishing the finite element model of the adhesive joint structure: A finite element simulation model was constructed using CFRP single-lap adhesive joints as the research object. For example... Figure 11 As shown, the model's geometric parameters are: CFRP laminate dimensions of 120 mm × 25 mm × 3.6 mm, adhesive layer thickness of 0.12 mm, and overlap length of 20 mm for analysis.

[0062] The CFRP laminate uses T300 / 7901 carbon fiber reinforced epoxy resin matrix composite material, and the layup sequence is as follows: The formula is denoted by 's', where 's' represents a symmetrical layup, with a single layer thickness of 0.3 mm and a total of 12 layers. LJM-170 type medium-temperature curing epoxy resin is used as the adhesive. The longitudinal modulus of elasticity (E11) of the CFRP laminate is 125 GPa, the transverse modulus of elasticity (E22 and E33) is 11.3 GPa, the in-plane shear modulus G12 is 5.43 GPa, and the out-of-plane shear moduli G13 and G23 are 5.43 GPa and 3.98 GPa, respectively. The adhesive has an elastic modulus of 3.4 GPa, a shear modulus of 1.3 GPa, a normal strength of 31.5 MPa, and a shear strength of 36.5 MPa.

[0063] like Figure 12 As shown, Abaqus finite element simulation software was used for modeling. The CFRP laminate used S4R continuous shell elements, and the adhesive layer used COH3D8 cohesive elements. The mesh element size for the overlapping area was 2 mm × 2 mm × 3.6 mm, the mesh element size for the non-overlapping area was 5 mm × 2 mm × 3.6 mm, and the adhesive layer element size was 2 mm × 2 mm × 0.12 mm.

[0064] The left clamping region of the model is completely fixed, while the right clamping region is subjected to axial displacement load. A reference point is established at the right end of the model to facilitate the extraction of load and displacement data during the tensile process.

[0065] Step 2: Extract load-displacement data for the connecting joints: In the finite element model, two reference points are set at both ends of the joint region. The displacement difference between the two reference points after the analysis is completed represents the displacement of the joint during loading. Since the load on each part of the connected structure is the same throughout the loading process, the load on the joint can be obtained by reading the overall load data. Combining this data with the displacement difference at the reference points yields the load-displacement curve of the joint.

[0066] like Figure 13 As shown, the load-displacement curves of the adhesive structure obtained by the finite element method indicate that before damage occurs in the joint structure, the load-displacement curves show a linear increasing trend, and the stiffness of the joint is constant. After damage occurs in the adhesive layer, the overall stiffness decreases, cracks appear in the adhesive part and gradually expand until the load reaches its maximum value, the adhesive structure is completely destroyed, and the curve drops sharply.

[0067] Step 3: Construction and Damage Analysis of the Adhesive-Bonded Circuit Model: like Figure 14 As shown, a circuit model of the adhesive-bonded structure is constructed based on finite element simulation data. Taking advantage of the modularity of the circuit model, only the connecting joints need to be modeled; the bolted joints can be replaced with adhesive-bonded joint modules.

[0068] In the circuit model, a constant voltage source of 0.005 V corresponds to a displacement increment of 0.005 mm. Therefore, the load-displacement data obtained from the finite element method requires further processing before use. The specific method is as follows: extract the joint load-displacement data during the linear phase before damage, and calculate the slope of the load-displacement curve through data fitting, which represents the stiffness of the joint and corresponds to the reciprocal of the resistance in the circuit model. Damage to the adhesive joint occurs at the joint. After damage, the stiffness of the joint is reduced (reduction factor is 0.5). When the load is sufficiently large, the adhesive structure is completely damaged, the adhesive layer completely breaks, and the stiffness of the joint structure drops to zero.

[0069] This invention employs a bilinear cohesive force model to analyze the damage of bonded structures. For example... Figure 10 As shown, the cohesive force model characterizes the nonlinear mechanical behavior of materials or interfaces throughout the entire process of damage initiation, propagation, and failure by defining the relationship between the traction force and separation displacement of the adhesive layer.

[0070] The constitutive relation of the bilinear model is divided into two stages: the linear elastic stage and the separated displacement stage. Less than the critical value At that time, traction force As the displacement increases linearly, it satisfies the following relationship. ,in This is the interface stiffness matrix, which includes the normal stiffness. and shear stiffness , During the damage evolution stage, when the separation displacement exceeds... When the interface enters a damaged state, the traction force decreases with increasing displacement until it reaches the complete failure displacement, at which point the interface's load-bearing capacity drops to zero. The damage evolution process is mediated by the damage variable D ( Quantization, D=0 indicates no damage, D=1 indicates complete failure.

[0071] Damage initiation in the cohesive model is determined using the second nominal stress criterion: In the formula Represents the normal strength of the adhesive layer. , This represents the shear strength of the adhesive layer in two directions. The determination formula only considers tensile stress.

[0072] Damage evolution was described using the Benzeggaggh-Kenane (BK) criterion, which uses energy release rate to characterize fracture behavior under mixed modes. in , These are Type I and Type II fracture energies, respectively. , The energy release rates of Type I and Type II during actual loading are given. These are material parameters.

[0073] The following describes the specific operation process of the circuit model of the glue-screw hybrid connection structure.

[0074] Step 1: Building the hybrid connection circuit model: like Figure 15 As shown, the hybrid connection circuit model uses selector switches connected before the bolt joint module and the adhesive joint module to control whether each module is connected to the circuit. The adhesive layer state in the adhesive module and the displacement of the connecting joint are used as the criteria for judgment. The three-stage switching logic is as follows: When the displacement is less than the gap between the bolt and the bolt hole, selector switches 1 and 2 are simultaneously open, and only the adhesive module is connected to the circuit, indicating that only the adhesive structure bears the load. When the displacement is greater than the gap and the adhesive layer is not completely damaged, selector switch 2 is closed, and both the adhesive module and the bolt module are connected to the circuit, meaning that the load is shared by the adhesive layer and the bolt. When the adhesive layer is completely damaged, selector switch 1 is closed, and only the bolt module is connected to the circuit, indicating that the connection structure is a bolted connection structure.

[0075] Step 2: Handling a sudden drop in adhesive layer failure: Before the bolts bear the load alone after the adhesive layer has completely failed, the load-displacement curve of the connection structure drops sharply. For example... Figure 16 As shown, the accumulation module is improved: the MATLAB Function module is used to determine whether the adhesive layer is completely damaged. If the adhesive layer is completely damaged within the analysis step, a value obtained by fitting the load-displacement curve is output, representing the magnitude of the load drop; otherwise, the output is 0. This value is subtracted from the output value of the accumulation module by the Add module, thereby achieving accurate simulation of the sudden drop in the load-displacement curve.

[0076] Step 3: Verification example of hybrid connection structure: like Figure 17 As shown, a single-bolt adhesive-bolt hybrid connection structure was used as the verification object. The connection structure consists of two identical composite laminates with a length, width, and thickness of 480 mm, 160 mm, and 20 mm, respectively. The overlap length is 192 mm, the bolt hole diameter is 16 mm, and the adhesive layer thickness is approximately 1 mm.

[0077] First, the corresponding adhesive bonding module was built. A boltless, pure adhesive bonding structure was constructed using Abaqus finite element simulation software. Holes were made in the laminate overlaps to maintain geometric consistency and mitigate local stiffness reduction. The finite element model was run to obtain load-displacement curve data for the adhesive joints, which was then used to build the adhesive bonding module for the circuit model. After obtaining the adhesive bonding module, the parameters of the laminate and bolt joint modules were modified to complete the hybrid connection circuit model. Since the circuit model uses a global variable module, only the values ​​in the Data Store Memory module needed to be modified to complete the model construction.

[0078] The modular rapid prediction method for the hybrid bonding performance of composite materials according to embodiments of the present invention has the following technical effects: 1. This invention achieves high-efficiency and high-precision electro-mechanical equivalent simulation analysis. Based on the equivalent mapping of the spring stiffness method and Ohm's law, the stiffness, load, and displacement of the structure are respectively mapped to the reciprocal of the circuit resistance, current, and voltage. The mechanical force transmission path is accurately reproduced through series / parallel circuits. This framework fundamentally solves the problems of cumbersome modeling and low computational efficiency of traditional finite element methods, laying a core foundation for the rapid evaluation of the performance of connected structures.

[0079] 2. The embodiments of this invention accurately simulate the complex nonlinear mechanical behavior of bolted connections. Through a circuit design consisting of a selector switch and a sliding rheostat, the four-stage nonlinear process from "static friction" to "sliding friction," "gap filling," and finally "rigid bearing" is accurately reproduced in the model. Furthermore, the circuit switching rules based on displacement thresholds (a, b, c) are clearly defined, thereby achieving dynamic and accurate simulation of the complex stiffness changes at the connection interface.

[0080] 3. This invention provides a circuit-based characterization and closed-loop simulation of the progressive damage process in composite materials. It innovatively introduces a strain amplification factor to convert the average strain of the laminate output by the circuit model into the local maximum strain at the bolt hole edge. This is then combined with the Hashin criterion for strain form to determine tensile / compressive damage to the fiber and matrix. Through damage-triggered elastic modulus reduction and dynamic updating of the circuit resistance, a closed-loop simulation of the entire process from damage initiation and evolution to load redistribution is achieved.

[0081] 4. The embodiments of this invention realistically reproduce the load distribution and damage transfer mechanisms of multi-bolt connections. A standardized parallel strategy of single-bolt submodules is adopted to construct an equivalent circuit network for multi-bolt connections. This network, through shared voltage input, aggregated current output, and real-time monitoring using branch ammeters, automatically realizes the realistic mechanical responses of "initial load distribution according to stiffness" and "dynamic transfer of load to healthy bolts after damage occurs," significantly improving the engineering realism of multi-bolt connection analysis.

[0082] 5. This invention enables rapid circuit-based prediction of adhesive joint structures. Based on finite metadata fitting of the equivalent stiffness of the adhesive layer, stiffness reduction guided by the cohesive force model is used to achieve circuit-based characterization of adhesive layer damage, integrating the adhesive joint as a standardized module into the circuit simulation framework.

[0083] 6. This invention successfully constructed a three-stage force transmission model for a hybrid glue-bolt connection. An automatic switching mechanism is used to achieve the three stages of glue-dominated, cooperative bearing, and bolt-dominated loads. The current distribution principle of parallel circuits is used to achieve automatic load distribution between the glue layer and the bolt. An improved accumulation module accurately simulates the sudden load drop caused by glue layer failure.

[0084] 7. The embodiments of this invention form a flexible and scalable modular engineering application system. The Data StoreMemory module enables global storage and unified retrieval of material and geometric parameters, supporting rapid parameter modification and one-click model updates. This modular design allows the model to easily adapt to different connection configurations such as single-bolt and multi-bolt connections, greatly improving the model's reusability, expansion potential, and engineering practical value.

[0085] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A modular and rapid prediction method for the hybrid bonding performance of composite materials, characterized in that, Includes the following steps: S1. Construct a circuit model for the composite material connection structure. The circuit model is established based on the mechanical equivalence principle of the spring stiffness method. The circuit model is applicable to bolted connection structures, adhesive connection structures, and hybrid adhesive-screw connection structures. For bolted connection structures, the circuit model can simulate the static friction stage, sliding friction stage, gap filling stage, and rigid bearing stage of the bolted connection. For adhesive connection structures, the circuit model is based on fitting the equivalent stiffness of the adhesive layer using finite element simulation data to construct an adhesive joint submodule. For the glue-screw hybrid connection structure, the circuit model includes a glue joint submodule and a bolt joint submodule, and the switching of the three-stage force transmission mechanism is realized by a dynamic selection switch; S2. The circuit model is used to simulate the composite material connection structure to obtain the displacement response signal and load information of the composite material connection structure under load. S3. Based on the displacement response signal and the corresponding damage criteria, determine whether the structure has been damaged and the type of damage; for bolted connection structures, damage is determined based on the average strain combined with the strain form of the Hashin criterion; for adhesive connection structures, damage is determined based on the damage initiation criterion of the cohesion model. For the glue-bolt hybrid connection structure, the glue joint submodule uses the damage initiation criterion of the cohesive force model to judge the glue layer damage, and the bolt joint submodule uses the average strain combined with the strain form of the Hashin criterion to judge the laminate plate damage. The two criteria are dynamically activated as the three-stage force transmission mechanism switches. S4. Adjust the circuit model according to the judgment result: if damage is judged to have occurred, the parameters of the corresponding components in the circuit model are dynamically updated according to the damage type to simulate the stiffness degradation caused by the damage; if damage is judged not to have occurred, the current parameters of the circuit model are maintained. S5. Based on the adjusted circuit model and combined with the load information, output the predicted complete load-displacement curve of the composite material connection structure.

2. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 1, characterized in that, In step S1, for bolted connection structures, the circuit model achieves dynamic switching and stiffness simulation of the four mechanical stages by selecting a combination of switch module and sliding rheostat module.

3. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 1, characterized in that, Step S2 specifically includes: S21. The displacement response signal of the composite material connection structure is obtained by integrating the voltage signal output by the circuit model; S22. By accumulating the current signals output by the circuit model, the total load constituting the load information is obtained.

4. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 1, characterized in that, In step S3, the calculated average strain is multiplied by a preset strain amplification factor k to obtain the maximum local strain at the bolt hole edge for damage assessment; wherein, the strain amplification factor k is determined based on the anisotropy and ply structure of the composite material.

5. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 4, characterized in that, In step S3, the damage criterion for strain mode is the Hashin criterion for strain mode, which includes at least four damage modes: fiber tension, fiber compression, matrix tension, and matrix compression.

6. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 1, characterized in that, In step S1, for a connection structure containing multiple bolts, the circuit model is a parallel circuit network model, wherein the connection part corresponding to each bolt is constructed as an independent circuit sub-module, and multiple circuit sub-modules are connected in parallel.

7. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 6, characterized in that, During the simulation, the parallel circuit network model can automatically simulate the initial distribution of load among the bolts and the dynamic transfer process after damage occurs, based on the real-time resistance changes of each circuit sub-module.

8. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 1, characterized in that, In step S1, for the adhesive joint structure, the construction method of the adhesive joint submodule includes: obtaining the load-displacement curve data of the adhesive joint through finite element simulation, extracting the load-displacement response curve of the joint area, calculating the equivalent stiffness of the adhesive joint through data fitting, and converting the stiffness into the resistance parameter in the circuit model; after the adhesive layer is damaged, the equivalent stiffness is reduced to simulate the damage evolution, and the stiffness is reduced to zero when the adhesive layer completely fails.

9. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 1, characterized in that, In step S1, for the glue-screw hybrid connection structure, the three-stage force transmission mechanism includes: the first stage is the glue-dominated stage, when the joint displacement is less than the gap between the bolt and the screw hole, only the glue joint sub-module is connected to the circuit, and the glue layer bears the load alone; the second stage is the cooperative bearing stage, when the joint displacement is greater than or equal to the gap and the glue layer is not completely failed, the glue joint sub-module and the bolt joint sub-module are connected to the circuit simultaneously, and the load is borne by the glue layer and the bolt together; the third stage is the bolt-dominated stage, when the glue layer is completely failed, only the bolt joint sub-module is connected to the circuit, and the bolt bears the load alone until the structure is finally destroyed.

10. The modular rapid prediction method for the hybrid bonding performance of composite materials according to claim 9, characterized in that, During the collaborative load-bearing phase, the adhesive joint submodule and the bolt joint submodule are connected to the circuit in parallel, and the load is automatically distributed according to the reciprocal of the equivalent resistance of each submodule. When the adhesive layer completely fails, the load output value is corrected by an improved accumulation module to simulate the sudden load drop caused by the sudden breakage of the adhesive layer. And / or, the circuit model is built and implemented in the Simulink platform; The material and geometric parameters in the circuit model are managed and called uniformly through the global variable module, which supports the modular design of the model and the rapid modification of parameters. The bolt joint submodule, the adhesive joint submodule, and the laminate module used to simulate the stiffness of the laminate are all independent standardized modules, which can be flexibly assembled into different connection configurations through series or parallel connection.

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