Method for optimizing low-speed impact resistance of fiber metal laminate based on ABAQUS

Abstract

The invention provides an ABAQUS-based method for optimizing the low-speed impact resistance of a fiber metal laminate, and relates to the technical field of structural performance optimization evaluation, and the method comprises the steps: constructing a finite element model of a composite structure containing a honeycomb core, simulating impact, and collecting time sequence dynamics response data; two transformation points of elasticity-plasticity and plasticity-damage are identified based on a time-force curve, and the impact process is divided into three stages of elasticity evolution, plasticity evolution and damage evolution; the equivalent stiffness of the laminate is calculated in the elastic stage, the maximum impact force of the whole process is extracted, the critical stripping energy density is inversed based on internal energy change in the damage evolution stage, and the energy absorption proportion of the stage is calculated based on a time-displacement curve; and fusing the critical stripping energy density, the equivalent stiffness, the maximum impact force and the damage stage energy absorption ratio, constructing an impact resistance evaluation model to output a comprehensive impact resistance index, and performing grading evaluation and guiding structure iterative optimization according to the comprehensive impact resistance index.

Description

Technical Field

[0001] This invention relates to the field of structural performance optimization and evaluation technology, specifically to a method for optimizing the low-velocity impact resistance of fiber-reinforced metal laminates based on ABAQUS. Background Technology

[0002] Fiber-coated metal laminates, as an advanced composite material structure, are widely used in aerospace, transportation and other fields due to their excellent specific strength, specific stiffness and fatigue resistance. However, these structures are susceptible to low-velocity impact loads during service, such as tool drops and hail impacts, which can lead to imperceptible delamination and matrix cracking, seriously affecting their load-bearing safety and service life. Therefore, conducting research on the dynamic response of fiber-coated metal laminates under low-velocity impact and establishing quantitative evaluation and optimization methods for their impact resistance are of great significance for improving the impact resistance and reliability of structures.

[0003] In the prior art, the method for analyzing the energy absorption and containment characteristics of a foam and chopped fiber reinforced honeycomb sandwich containment casing under high-speed impact (publication number CN116933438A) provides a numerical simulation and performance evaluation method for composite material structures under high-speed impact scenarios. However, its focus is on the containment and areal density energy absorption characteristics under high-speed projectile impact, emphasizing strain rate effects, dynamic failure criteria, and VUMAT subroutine development. It does not involve the division of the elastic-plastic-damage three stages during low-speed impact, the inversion of critical peeling energy density, or the construction of a comprehensive impact resistance performance evaluation model based on multi-index fusion. In addition, this prior art lacks analysis of the energy absorption characteristics of the structure throughout the low-speed impact process and fails to provide a graded evaluation and iterative optimization strategy based on performance index. Therefore, it has significant limitations in optimizing the low-speed impact performance of fiber-metal laminates.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide an optimization method for the low-velocity impact resistance of fiber-reinforced metal laminates based on ABAQUS, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: An optimization method for the low-velocity impact resistance of fiber-reinforced metal laminates based on ABAQUS, comprising the following steps: Step 1: Construct a composite structure with a honeycomb core as the middle layer and symmetrical composite fiber metal layers on the upper and lower sides. Construct a finite element model of the composite structure based on ABAQUS, apply impact boundary conditions to the model to perform numerical simulation, and collect the time-series dynamic response data of the model during the impact process. Step 2: Extract the time-displacement curve, time-force curve, and internal energy change curve of the film layer from the time-series dynamic response data. After preprocessing, based on the time-force curve, use the adaptive threshold method to identify and calibrate the elastic-plastic transition point and the plastic-damage transition point in the curve, thereby dividing the impact process into three characteristic stages: elastic deformation, plastic deformation, and damage evolution. Step 3: Based on the time-displacement curve and time-force curve, calculate the equivalent stiffness of the laminate during the elastic deformation stage and extract the maximum impact force during the entire impact process; based on the internal energy change curve during the damage evolution stage, invert the critical peeling energy density of the laminate interface through the principle of energy conservation, and calculate the energy absorption ratio during the damage evolution stage according to the time-displacement curve. Step 4: Construct an impact resistance performance evaluation model based on critical peeling energy density, equivalent stiffness of the laminate, maximum impact force, and energy absorption ratio in the damage evolution stage. Use the model to determine the comprehensive impact resistance index of the fiber-metal laminate, and output the graded evaluation results by matching with the preset grading threshold. Iteratively adjust and optimize the composite structure based on the grading evaluation results.

[0007] Furthermore, the specific execution process of step 1 is as follows: Using ABAQUS's component and assembly modules, three-dimensional models of the upper fixture, lower fixture, punch, fiber-metal laminate, and aluminum honeycomb core were established. The fiber-metal laminate is composed of alternating layers of metal, prepreg, and adhesive film, and the aluminum honeycomb core is located between the upper and lower fiber-metal laminates. The punch, upper fixture, upper fiber-metal laminate, aluminum honeycomb core, lower fiber-metal laminate, and lower fixture were assembled in a top-to-bottom spatial order to form a complete composite structure finite element model. Material and section properties are set for the assembled model. The metal layer is set as a homogeneous solid section and given elastic-plastic parameters. The prepreg layer is set as a continuous shell composite layer and the layup direction and angle are defined. The adhesive film layer is set as a viscous section and a traction separation criterion is adopted. The aluminum honeycomb core is set as a homogeneous shell section. Impact boundary conditions are set to completely fix the upper and lower clamps in all degrees of freedom. The punch retains only the translational degree of freedom along the impact direction and is given an initial impact velocity. An initial impact velocity was set for the punch in the constructed finite element model, and all its degrees of freedom except for the impact direction were constrained. Fully fixed constraints were applied to the clamps on the upper and lower surfaces of the composite structure to limit its displacement and rotation. The dynamic display analysis method was adopted, and the impact duration and time increment step were set. During the simulation, time-displacement data and time-force data of the contact point between the punch and the layer plate, as well as the time series data of the internal energy changes of the metal layer, prepreg layer, adhesive film layer and honeycomb core were collected in real time to form complete time series dynamic response data.

[0008] Furthermore, the time-series dynamic response data is preprocessed, specifically by employing a wavelet transform-based filtering algorithm to denoise the data. High-frequency noise components in the time-displacement curve, time-force curve, and internal energy change curves of each layer are filtered out, while retaining effective low-frequency signals characterizing the material's mechanical response. The data alignment process is achieved through a timestamp synchronization mechanism, unifying the time-displacement data, time-force data, and internal energy change time-series data of the contact point between the punch and the plate onto the same time reference, ensuring consistent correspondence between different data sources at the same impact moment. Time-displacement curves, time-force curves, and internal energy change curves for each layer are extracted from the preprocessed data. Based on the time-force curves, an adaptive threshold method is used to identify and calibrate the characteristic gradient change points in the curves. Specifically: The gradient first decreases to a preset first threshold. The point is designated as the elastic-plastic transition point, and the gradient is lowered twice to a preset second threshold. The point is designated as the plastic-damage transition point, where ; Based on the elastic-plastic transition point and the plastic-damage transition point, the impact process is divided into a first characteristic stage dominated by elastic deformation, a second characteristic stage dominated by plastic deformation, and a third characteristic stage dominated by damage evolution.

[0009] Furthermore, based on the elastic deformation stage calibrated in step 2, the starting force value and ending force value of the time-force curve, and the starting displacement value and ending displacement value of the time-displacement curve within this stage are extracted, and the equivalent stiffness of the plate is calculated according to the following formula: In the formula, The equivalent stiffness of the laminate is given. This represents the contact force between the punch and the plate at the beginning of the elastic deformation stage. The contact force corresponding to the elastic-plastic transition point. and The corresponding data points are taken from the preprocessed time-force curve; This represents the displacement of the punch at the beginning of the elastic deformation stage. This represents the displacement of the punch at the elastic-plastic transition point. and The corresponding data points are taken from the preprocessed time-displacement curve; Traverse the preprocessed time-force curves encompassing the entire impact process, select the peak data from the curves and label it as the maximum impact force, denoted as . ; Based on the damage evolution stages identified in step 2, the starting and ending internal energy values ​​of the internal energy change curve of the film layer within this stage are extracted. Combined with the contact area of ​​the lamination interface, the critical peeling energy density is derived and determined using the principle of energy conservation. The formula based on this is as follows: In the formula, The critical stripping energy density, This represents the internal energy value of the film layer at the initial stage of the damage evolution phase. This represents the internal energy value of the film layer at the end of the damage evolution stage. and The corresponding data points were taken from the internal energy change curve of the film layer at this stage. The contact area between the fiber-metal laminate and the honeycomb core layer is directly obtained from the geometric dimensions of the finite element model constructed in step 1. The energy absorption percentage during the damage evolution stage is calculated based on the time-displacement curve, specifically as follows: Based on the time-force curve and time-displacement curve, numerical integration is performed on each characteristic stage to calculate the energy absorbed in that stage. The formula used is as follows: In the formula, Indicates the first Energy absorbed in each characteristic stage This is an index for the characteristic stage. These represent the three characteristic stages: elastic deformation, plastic deformation, and damage evolution. It is a time-force curve function. The derivative of the time-displacement curve; and They represent the first The start and end times of each characteristic stage; The energy absorption percentage during the damage evolution stage can be calculated using the following formula: In the formula, This represents the percentage of energy absorbed during the damage evolution stage. , and These represent the energy absorbed during the three characteristic stages of elastic deformation, plastic deformation, and damage evolution.

[0010] Furthermore, the specific execution process of step 4 is as follows: The critical peel energy density, equivalent stiffness of the laminate, and maximum impact force were normalized using the following formulas: In the formula, , and These are the normalized critical peeling energy density, equivalent stiffness of the laminate, and maximum impact force, respectively. , and The benchmark values ​​for critical peel energy density, equivalent stiffness of the laminate, and maximum impact force were determined by statistical analysis of data obtained from finite element simulations of multiple standard fiber-metal laminate samples. An impact resistance performance evaluation model is constructed based on the normalized critical peel energy density, equivalent stiffness of the laminate, and maximum impact force. The comprehensive impact resistance index of the fiber-metal laminate is determined using the model. The expression for the impact resistance performance evaluation model is as follows: In the formula, To assess the overall impact resistance index, This represents the percentage of energy absorbed during the damage evolution stage. , , and These are the preset weights for the corresponding indicators. And satisfy , It is a natural constant.

[0011] Furthermore, the comprehensive impact resistance index is matched with a preset grading threshold to output a grading evaluation result. The specific logic behind this is as follows: Preset first level threshold Second-level threshold and the third-level threshold And satisfy ; The calculated comprehensive impact resistance index Match each threshold interval one by one: like If so, then the "Excellent" rating result will be output; like Output a "Good" rating result; like Output the "Pass" rating result; like Output the "Unqualified" evaluation result.

[0012] Furthermore, the composite structure is iteratively adjusted and optimized based on the hierarchical evaluation results. The specific logic behind this is as follows: If the evaluation result is "excellent", then keep the current parameters of the composite structure unchanged; If it is "good", based on the weight ratio of each normalized index in the comprehensive impact resistance index, the structural parameters corresponding to the indexes whose weight ratio is less than the preset weight ratio threshold are adjusted, such as increasing the thickness of the film layer to increase the critical peel energy density, or changing the prepreg layup angle to adjust the equivalent stiffness. If it is "qualified", prioritize adjusting the structural parameters corresponding to the critical peel energy density and maximum impact force, including changing the film material, increasing the number of prepreg layers, changing the size of the honeycomb core cell, and adjusting the parameters related to the equivalent stiffness of the layer. If it is "unqualified", the key parameters of the composite structure will be fully adjusted, including redesigning the lamination sequence and number of fiber metal layers, replacing the metal layers and prepreg materials, and adjusting the height and cell size of the honeycomb core. After adjustment, return to step 1 to rebuild the finite element model, and repeat steps 1-4 until a "good" or "excellent" evaluation result is output, and the number of iterations is controlled within the preset range. This completes the optimization of the low-velocity impact resistance of the fiber metal laminate based on ABAQUS.

[0013] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a finite element model of a fiber-metal laminate containing a honeycomb core and combines it with time-series dynamic response data during the impact process to achieve precise quantification and systematic optimization of the structure's resistance to low-velocity impacts. Specifically, this invention identifies the transition points between the elastic, plastic, and damage stages based on the time-force curve, achieving a multi-stage fine division of the impact process. By extracting the equivalent stiffness of the laminate, maximum impact force, critical peel energy density, and the proportion of energy absorption during the damage stage, a comprehensive impact resistance index evaluation model integrating multiple indicators is constructed, comprehensively reflecting the mechanical response and damage evolution characteristics of the structure at different stages. Furthermore, based on the graded evaluation results, a targeted structural iterative optimization strategy is proposed, achieving directional improvement from parameter adjustment to overall configuration.

[0014] Compared with traditional methods, this invention not only improves the systematicness and accuracy of impact resistance performance evaluation, but also forms a closed-loop process of optimization-evaluation-re-optimization, providing reliable technical support for the performance improvement and structural design of fiber metal laminates under low-speed impact conditions. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 for , , , and Parallel coordinate image; Figure 3 for , , and Multi-Y axis schematic diagram; Figure 4 for and The fitted image; Figure 5 This is a schematic diagram of a low-speed impact resistant model for a honeycomb sandwich fiber metal laminate, where 1 is a punch; 2 is an upper clamp; 3 is a honeycomb sandwich fiber metal laminate; and 4 is a lower mold. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0017] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0018] Example: Please see Figures 1-5 The present invention provides a technical solution: An optimization method for the low-velocity impact resistance of fiber-reinforced metal laminates based on ABAQUS, comprising the following steps: Step 1: Construct a composite structure with a honeycomb core as the middle layer and symmetrical composite fiber metal layers on the upper and lower sides. Construct a finite element model of the composite structure based on ABAQUS, apply impact boundary conditions to the model to perform numerical simulation, and collect the time-series dynamic response data of the model during the impact process. In this embodiment, the specific execution process of step 1 is as follows: Using ABAQUS's component and assembly modules, three-dimensional models of the upper fixture, lower fixture, punch, fiber-metal laminate, and aluminum honeycomb core were established. The fiber-metal laminate is composed of alternating layers of metal, prepreg, and adhesive film, and the aluminum honeycomb core is located between the upper and lower fiber-metal laminates. The punch, upper fixture, upper fiber-metal laminate, aluminum honeycomb core, lower fiber-metal laminate, and lower fixture were assembled in a top-to-bottom spatial order to form a complete composite structure finite element model. Material and section properties are set for the assembled model. The metal layer is set as a homogeneous solid section and given elastic-plastic parameters. The prepreg layer is set as a continuous shell composite layer and the layup direction and angle are defined. The adhesive film layer is set as a viscous section and a traction separation criterion is adopted. The aluminum honeycomb core is set as a homogeneous shell section. Impact boundary conditions are set to completely fix the upper and lower clamps in all degrees of freedom. The punch retains only the translational degree of freedom along the impact direction and is given an initial impact velocity. An initial impact velocity was set for the punch in the constructed finite element model, and all its degrees of freedom except for the impact direction were constrained. Fully fixed constraints were applied to the clamps on the upper and lower surfaces of the composite structure to limit its displacement and rotation. The dynamic display analysis method was adopted, and the impact duration and time increment step were set. During the simulation, time-displacement data and time-force data of the contact point between the punch and the layer plate, as well as the time series data of the internal energy changes of the metal layer, prepreg layer, adhesive film layer and honeycomb core were collected in real time to form complete time series dynamic response data.

[0019] In this embodiment, the specific layup structure of the fiber-metal laminate is as follows: the metal layer is a titanium alloy plate, an aluminum alloy plate, or a magnesium alloy plate, and the thickness of a single layer is [missing information]. The prepreg layer includes at least one of carbon fiber reinforced polyetheretherketone prepreg and aramid fiber reinforced epoxy resin prepreg, with a single layer thickness of [missing information]. The adhesive film layer includes epoxy resin film and polyetheretherketone film, with a single layer thickness of [missing information]. The fiber-metal laminate has a total of 8-12 layers, including 2 metal layers, 6 prepreg layers, and adhesive film layers, the number of which depends on the number of contact interfaces between the metal layers and the prepreg layers. The aluminum honeycomb core has a hexagonal cell shape and a cell wall thickness of [missing information]. The height of the honeycomb core is During modeling, a honeycomb core structure was formed by arraying and replicating regular hexagonal unit cells, and this structure was set as a three-dimensional deformable shell element. During assembly, no gaps are maintained between the layers; they are designed for tight contact. The layers and the upper and lower fixtures maintain surface-to-surface contact, with a friction coefficient set to [value missing]. A penalty function algorithm is employed; the layers within the laminate are connected by an adhesive film layer, and binding constraints are applied to simulate interface behavior without relative sliding. When setting material properties, the metal layer adopts an elastoplastic constitutive model, and the prepreg layer adopts a continuous shell composite layer model with the layup direction defined as follows. Orthogonal paving or The layup and film layers adopt a viscous cross section and their damage evolution behavior is defined according to the traction separation criterion; the aluminum honeycomb core adopts a homogeneous shell cross section and is endowed with elasto-plastic material parameters. In the impact boundary condition settings, the punch is set to a hemispherical shape with a mass of [missing information]. The initial impact velocity was The impact direction is along the normal direction of the laminate; the upper and lower clamps are set to be completely fixed, restricting all translational and rotational degrees of freedom; a dynamic explicit analysis method is used, and the impact duration is set to... The time increment step is During the simulation, time-displacement data and time-force data of the contact point between the punch and the plate, as well as time-series data of the internal energy changes of the metal layer, prepreg layer, adhesive film layer and honeycomb core, are collected in real time to form complete time-series dynamic response data.

[0020] Step 1 involves constructing a finite element model of a fiber-metal laminate composite structure with a honeycomb core based on the ABAQUS platform, and setting boundary conditions and load parameters that conform to actual low-speed impact conditions, thereby achieving high-fidelity numerical simulation of the impact process. This step not only accurately reproduces the dynamic response behavior of the laminate under impact load, but also systematically collects time-series dynamic response data, including time-displacement, time-force, and changes in internal energy of each layer, providing a complete and reliable data source for subsequent stage division, feature parameter extraction, and performance evaluation.

[0021] Step 2: Extract the time-displacement curve, time-force curve, and internal energy change curve of the film layer from the time-series dynamic response data. After preprocessing, based on the time-force curve, use the adaptive threshold method to identify and calibrate the elastic-plastic transition point and the plastic-damage transition point in the curve, thereby dividing the impact process into three characteristic stages: elastic deformation, plastic deformation, and damage evolution. In this embodiment, the time-series dynamic response data is preprocessed, specifically by using a wavelet transform-based filtering algorithm to denoise the data. High-frequency noise components in the time-displacement curve, time-force curve, and internal energy change curves of each layer are filtered out, while retaining the effective low-frequency signals characterizing the material's mechanical response. The data alignment process is achieved through a timestamp synchronization mechanism, unifying the time-displacement data, time-force data, and internal energy change time-series data of the contact point between the punch and the plate onto the same time reference, ensuring that the correspondence between different data sources is consistent at the same impact moment. Time-displacement curves, time-force curves, and internal energy change curves for each layer are extracted from the preprocessed data. Based on the time-force curves, their gradient change curves are calculated using numerical differentiation. Subsequently, an adaptive thresholding method is used to identify and calibrate the characteristic gradient change points in the curves. Specifically: The gradient first decreases to a preset first threshold. The point is designated as the elastic-plastic transition point, and the gradient is lowered twice to a preset second threshold. The point is designated as the plastic-damage transition point, where ; Based on the elastic-plastic transition point and the plastic-damage transition point, the impact process is divided into a first characteristic stage dominated by elastic deformation, a second characteristic stage dominated by plastic deformation, and a third characteristic stage dominated by damage evolution.

[0022] Step 2 ensured the accuracy and synchronization of the data through wavelet denoising and timestamp alignment. Based on gradient change and dual threshold adaptive recognition method, it achieved objective and accurate calibration of the elastic-plastic-damage transition point during the impact process, thus scientifically dividing the impact response process into three characteristic stages, laying a reliable foundation for the extraction and evaluation of performance parameters in subsequent stages.

[0023] Step 3: Based on the time-displacement curve and time-force curve, calculate the equivalent stiffness of the laminate during the elastic deformation stage and extract the maximum impact force during the entire impact process; based on the internal energy change curve during the damage evolution stage, invert the critical peeling energy density of the laminate interface through the principle of energy conservation, and calculate the energy absorption ratio during the damage evolution stage according to the time-displacement curve. In this embodiment, based on the elastic deformation stage calibrated in step 2, the starting force value and ending force value of the time-force curve, and the starting displacement value and ending displacement value of the time-displacement curve within this stage are extracted, and the equivalent stiffness of the plate is calculated according to the following formula: In the formula, The equivalent stiffness of the laminate is given. This represents the contact force between the punch and the plate at the beginning of the elastic deformation stage. The contact force corresponding to the elastic-plastic transition point. and The corresponding data points are taken from the preprocessed time-force curve; This represents the displacement of the punch at the beginning of the elastic deformation stage. This represents the displacement of the punch at the elastic-plastic transition point. and The corresponding data points are taken from the preprocessed time-displacement curve.

[0024] For this formula, the dependent variable Used to characterize the ability of fiber-reinforced metal laminates to resist impact deformation during the elastic deformation stage. The larger the value, the greater the force the material needs to withstand per unit displacement, meaning the laminate exhibits higher rigidity in the initial stage of impact and is less prone to deformation; conversely, a smaller value indicates a lower value. A smaller value indicates that the material has lower rigidity and is more prone to deformation under the same impact force.

[0025] Independent variable This represents the increase in impact force within the elastic phase, while This represents the change in the corresponding displacement, and the stiffness. Force increment within the elastic phase With displacement increment The larger the ratio, the greater the force the material can withstand per unit displacement, i.e., the higher its stiffness. This is consistent with the basic physical concept that material stiffness is defined as the ratio of stress to strain. In actual impact processes, if a material can withstand a large increase in force under a small displacement, it indicates that its internal structure (such as fiber layup or honeycomb core support) can effectively transfer and disperse the load, thus exhibiting high stiffness characteristics.

[0026] This formula is based on the slope of the linear segment of the force-displacement curve. It is simple in form and has a clear physical meaning. By selecting the start and end points of the elastic stage for calculation, it effectively avoids the influence of nonlinear response in the plastic and damage stages, ensuring the accuracy and representativeness of stiffness parameter extraction. It conforms to the basic principle of evaluating the mechanical properties of composite materials within the elastic range.

[0027] Traverse the preprocessed time-force curves encompassing the entire impact process, select the peak data from the curves and label it as the maximum impact force, denoted as . ; Based on the damage evolution stages identified in step 2, the starting and ending internal energy values ​​of the internal energy change curve of the film layer within this stage are extracted. Combined with the contact area of ​​the lamination interface, the critical peeling energy density is derived and determined using the principle of energy conservation. The formula based on this is as follows: In the formula, The critical stripping energy density, This represents the internal energy value of the film layer at the initial stage of the damage evolution phase. This represents the internal energy value of the film layer at the end of the damage evolution stage. and The corresponding data points were taken from the internal energy change curve of the film layer at this stage. The contact area between the fiber-metal laminate and the honeycomb core layer is directly obtained from the geometric dimensions of the finite element model constructed in step 1. For this formula, the dependent variable Used to characterize the ability of the adhesive layer in a fiber-reinforced metal laminate to resist delamination propagation, i.e., the energy required per unit area to cause peeling failure at the interface. A higher value indicates better interfacial adhesion, stronger resistance to delamination, and less susceptibility to debonding failure under impact loads; conversely, a lower value indicates better interfacial adhesion, stronger resistance to delamination, and less susceptibility to debonding failure under impact loads. A smaller value indicates insufficient interface toughness, making it prone to rapid peeling during the damage evolution stage.

[0028] molecular The denominator represents the increase in internal energy absorbed by the film layer during the damage evolution stage. This energy is mainly used to overcome interfacial adhesion forces and generate new peel surfaces, among other damage processes. It is the contact area of ​​the laminated interface, which reflects the spatial distribution range of energy dissipation. According to the principle of energy conservation, the more internal energy the film layer absorbs to resist peeling on a given interface area, the higher its critical peeling energy density. This intuitively reflects that the interface toughness depends on the combined effect of its ability to dissipate impact energy and the bonding area.

[0029] This formula defines the critical peeling energy density by the ratio of internal energy increment to interface area. Its form directly reflects the core concept of energy per unit area in energy release rate or fracture toughness. It is a specific application of classical fracture mechanics theory in the analysis of interlaminar damage in composite materials. The formula has a simple structure and clear physical meaning. It can effectively quantify and correlate the internal energy data obtained from finite element simulation with the peeling resistance of the interface, and has good theoretical basis and practicality.

[0030] The energy absorption percentage during the damage evolution stage is calculated based on the time-displacement curve, specifically as follows: Based on the time-force curve and time-displacement curve, numerical integration is performed on each characteristic stage to calculate the energy absorbed in that stage. The formula used is as follows: In the formula, Indicates the first Energy absorbed in each characteristic stage This is an index for the characteristic stage. These represent the three characteristic stages: elastic deformation, plastic deformation, and damage evolution. It is a time-force curve function. The derivative of the time-displacement curve; and They represent the first The start and end times of each characteristic stage.

[0031] For this formula, the dependent variable Used to characterize fiber-reinforced metal laminates in the first The total energy absorbed by each characteristic stage through structural deformation and internal damage. The larger the value, the more impact energy the material dissipates in this stage, and the greater its contribution to the overall impact resistance; conversely, the smaller the value, the weaker the energy absorption capacity in this stage.

[0032] Independent variable and These represent the instantaneous impact force and the differential of instantaneous displacement, respectively. The integral of their product is essentially the area under the force-displacement curve, i.e., mechanical work. In physics, the impact force acts on the material to cause displacement. During this process, energy is absorbed and dissipated through the elastic deformation, plastic yielding, and internal damage (such as fiber breakage, matrix cracking, and interface peeling) of the material. Therefore, the greater the force and the more significant the displacement change, the more energy is absorbed in this stage.

[0033] This formula uses an integral form to calculate energy, which conforms to the definition in physics that work is the integral of force along the displacement path. It is the most classic and fundamental method for calculating mechanical energy absorption. By integrating different characteristic stages separately, it can accurately separate and quantify the role of each stage in energy absorption. It has a rigorous form, clear physical meaning, and good theoretical rationality and engineering applicability.

[0034] The energy absorption percentage during the damage evolution stage can be calculated using the following formula: In the formula, This represents the percentage of energy absorbed during the damage evolution stage. , and These represent the energy absorbed during the three characteristic stages of elastic deformation, plastic deformation, and damage evolution.

[0035] Dependent variable in the formula Used to characterize the proportion of energy absorbed during the damage evolution stage in the total impact energy absorption. A higher value indicates that the structure dissipates more energy through damage mechanisms during impact, and its failure mode is more inclined to absorb a large amount of energy at the expense of local integrity; conversely, a lower value indicates a higher energy dissipation. A smaller value means that energy is mainly absorbed through recoverable elastic deformation and controllable plastic deformation, resulting in a lower damage tolerance for the structure or a greater likelihood of overall instability under impact.

[0036] Step 4: Construct an impact resistance performance evaluation model based on critical peeling energy density, equivalent stiffness of the laminate, maximum impact force, and energy absorption ratio in the damage evolution stage. Use the model to determine the comprehensive impact resistance index of the fiber-metal laminate, and output the graded evaluation results by matching with the preset grading threshold. Iteratively adjust and optimize the composite structure based on the grading evaluation results. In this embodiment, the specific execution process of step 4 is as follows: The critical peel energy density, equivalent stiffness of the laminate, and maximum impact force were normalized using the following formulas: In the formula, , and These are the normalized critical peeling energy density, equivalent stiffness of the laminate, and maximum impact force, respectively. , and The benchmark values ​​for critical peel energy density, equivalent stiffness of the laminate, and maximum impact force were determined by statistical analysis of data obtained from finite element simulations of multiple standard fiber-metal laminate samples. An impact resistance performance evaluation model is constructed based on the normalized critical peel energy density, equivalent stiffness of the laminate, and maximum impact force. The comprehensive impact resistance index of the fiber-metal laminate is determined using the model. The expression for the impact resistance performance evaluation model is as follows: In the formula, To assess the overall impact resistance index, This represents the percentage of energy absorbed during the damage evolution stage. , , and These are the preset weights for the corresponding indicators. And satisfy , It is a natural constant.

[0037] The weight is set as This is because the critical delamination energy density directly determines the delamination resistance of the laminate interface and is the primary factor in preventing catastrophic delamination failure of the structure; therefore, it is given the highest weight. The maximum impact force reflects the peak load-bearing capacity of a structure under impact and is crucial for preventing instantaneous penetration or overall failure; therefore, it is important for weighting. Secondly, the equivalent stiffness of the laminate mainly affects the initial impact response, but its contribution is relatively indirect, hence the weighting is low. The weighting is relatively low; while the proportion of energy absorption during the damage phase can reflect resilience and energy dissipation mechanisms, its effectiveness depends on the absence of fatal structural damage. Therefore, it is given the lowest weight as a supplementary indicator. .

[0038] For this formula, the dependent variable Used to characterize the overall low-velocity impact resistance of fiber-reinforced metal laminates. The higher the value, the better the overall performance of the material during impact, that is, the stronger its ability to resist deformation, withstand load, suppress damage and effectively absorb energy; conversely, it indicates that the material has poor impact resistance.

[0039] Independent variables affect each other through functions of different forms Critical stripping energy density Acting exponentially, it reflects the crucial fundamental contribution of interfacial toughness to impact resistance; even a small increase can significantly improve overall performance; equivalent stiffness of the laminate. The logarithmic effect demonstrates that the gain effect of stiffness gradually weakens after reaching a certain level; maximum impact force The square term highlights the decisive role of structural strength in resisting high-speed impacts and preventing instantaneous damage; the energy absorption ratio η during the damage stage acts in a linear form, characterizing the material's ability to continuously and stably absorb energy during damage evolution; different function forms reflect the nonlinear contribution characteristics of different mechanical mechanisms during the impact process.

[0040] This model normalizes indices with different dimensions and physical meanings, and then integrates them using a function combining exponential, logarithmic, square, and linear terms. This approach considers the nonlinear coupling effects and differences in contribution among the various performance indices, while also ensuring dimensional uniformity and computational feasibility through normalization. This composite function structure can more precisely capture and characterize the comprehensive response of composite materials under complex impact loads, and has better physical consistency and evaluation accuracy than a simple linear weighted model.

[0041] Table 1: Comprehensive Impact Resistance Index Statistics Table

[0042] Based on the 15 sets of data provided in Table 1, the comprehensive impact resistance index... There is a clear nonlinear growth relationship between the input parameters and the critical stripping energy density. Equivalent stiffness of the slab Maximum impact force and the proportion of energy absorbed during the damage phase The gradual improvement The value shows an accelerating upward trend, especially in and When it is higher, its exponential term and square term are paired. Its contribution has increased significantly, becoming a key factor driving the improvement of overall performance.

[0043] Data analysis further reveals that, in the composition of impact resistance, the critical stripping energy density The interfacial toughness and maximum impact force represented The structural strength reflected by the weight has the most prominent impact; while the equivalent stiffness of the laminate... The impact is relatively mild, with energy absorption accounting for a small percentage during the damage phase. The steady increase also has This resulted in a sustained gain effect. This indicates that in the structural optimization of fiber-reinforced metal laminates, priority should be given to improving the critical peel energy density at the interface and the maximum impact load capacity of the structure, thereby most effectively enhancing its overall resistance to low-velocity impacts.

[0044] The comprehensive impact resistance index is matched with a preset grading threshold to output the grading evaluation result. The specific logic behind this is as follows: Preset first level threshold Second-level threshold and the third-level threshold And satisfy ; The calculated comprehensive impact resistance index Match each threshold interval one by one: like If the result is "Excellent", the output will be "Excellent", indicating that the low-velocity impact resistance of the laminate does not need to be optimized at this time. like The output is a "good" rating, indicating that the impact resistance of the shelf meets the standard, and selective optimization can be performed according to actual needs. like The output of the "qualified" evaluation result indicates that the impact resistance performance of the shelf basically meets the standard, but targeted optimization is required. like The output of the "Unqualified" evaluation result indicates that the impact resistance of the shelf does not meet the standard and needs to be fully optimized. Among them, the tiered threshold , and The logic is as follows: By conducting extensive finite element simulations of typical fiber-reinforced metal laminate structures and statistically calculating the numerical distribution range of the comprehensive impact resistance index, combined with the performance requirements in actual engineering, the comprehensive impact resistance index values ​​are divided into four intervals from high to low, corresponding to four evaluation levels: "Excellent," "Good," "Acceptable," and "Unacceptable," respectively. This is used to obtain the grading thresholds. , and .

[0045] The composite structure is iteratively adjusted and optimized based on the results of the hierarchical evaluation. The specific logic behind this is as follows: If the evaluation result is "excellent", then keep the current parameters of the composite structure unchanged; If it is "good", based on the weight ratio of each normalized index in the comprehensive impact resistance index, the structural parameters corresponding to the indexes whose weight ratio is less than the preset weight ratio threshold are adjusted, such as increasing the thickness of the film layer to increase the critical peel energy density, or changing the prepreg layup angle to adjust the equivalent stiffness. If it is "qualified", prioritize adjusting the structural parameters corresponding to the critical peel energy density and maximum impact force, including changing the film material, increasing the number of prepreg layers, changing the size of the honeycomb core cell, and adjusting the parameters related to the equivalent stiffness of the layer. If it is "unqualified", the key parameters of the composite structure will be fully adjusted, including redesigning the lamination sequence and number of fiber metal layers, replacing the metal layers and prepreg materials, and adjusting the height and cell size of the honeycomb core. After adjustment, return to step 1 to rebuild the finite element model, and repeat steps 1-4 until a "good" or "excellent" evaluation result is output, and the number of iterations is controlled within the range of 5-15 times. This completes the optimization of the low-velocity impact resistance of fiber metal laminate based on ABAQUS.

[0046] Step 4 involves constructing a multi-index fusion impact resistance performance evaluation model, normalizing and weighting key performance parameters, outputting a comprehensive impact resistance index, achieving quantitative evaluation and classification of structural performance, and proposing targeted optimization strategies based on the classification results. This forms a closed loop of simulation-evaluation-re-optimization after structural optimization, significantly improving the systematic nature and engineering applicability of optimizing the low-velocity impact resistance performance of fiber metal laminates.

[0047] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0048] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0049] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for optimizing the low-velocity impact resistance of a fiber metal laminate based on ABAQUS, characterized in that, The specific steps include: Step 1: Construct a composite structure with a honeycomb core as the middle layer and symmetrical composite fiber metal layers on the upper and lower sides. Construct a finite element model of the composite structure based on ABAQUS, apply impact boundary conditions to the model to perform numerical simulation, and collect the time-series dynamic response data of the model during the impact process. Step 2: Extract the time-displacement curve, time-force curve, and internal energy change curve of the film layer from the time-series dynamic response data. After preprocessing, based on the time-force curve, use the adaptive threshold method to identify and calibrate the elastic-plastic transition point and the plastic-damage transition point in the curve, thereby dividing the impact process into three characteristic stages: elastic deformation, plastic deformation, and damage evolution. Step 3: Based on the time-displacement curve and time-force curve, calculate the equivalent stiffness of the laminate during the elastic deformation stage and extract the maximum impact force during the entire impact process; based on the internal energy change curve during the damage evolution stage, invert the critical peeling energy density of the laminate interface through the principle of energy conservation, and calculate the energy absorption ratio during the damage evolution stage according to the time-displacement curve. Step 4: Construct an impact resistance performance evaluation model based on critical peeling energy density, equivalent stiffness of the laminate, maximum impact force, and energy absorption ratio in the damage evolution stage. Use the model to determine the comprehensive impact resistance index of the fiber-metal laminate, and output the graded evaluation results by matching with the preset grading threshold. Iteratively adjust and optimize the composite structure based on the grading evaluation results.

2. The method for optimizing the low-velocity impact resistance of a fiber metal laminate based on ABAQUS according to claim 1, characterized in that: The specific execution process of step 1 is as follows: Using ABAQUS's component and assembly modules, three-dimensional models of the upper fixture, lower fixture, punch, fiber-metal laminate, and aluminum honeycomb core were established. The fiber-metal laminate is composed of alternating layers of metal, prepreg, and adhesive film, and the aluminum honeycomb core is located between the upper and lower fiber-metal laminates. The punch, upper fixture, upper fiber-metal laminate, aluminum honeycomb core, lower fiber-metal laminate, and lower fixture were assembled in a top-to-bottom spatial order to form a complete composite structure finite element model. Material and section properties are set for the assembled model. The metal layer is set as a homogeneous solid section and given elastic-plastic parameters. The prepreg layer is set as a continuous shell composite layer and the layup direction and angle are defined. The adhesive film layer is set as a viscous section and a traction separation criterion is adopted. The aluminum honeycomb core is set as a homogeneous shell section. Impact boundary conditions are set to completely fix the upper and lower clamps in all degrees of freedom. The punch retains only the translational degree of freedom along the impact direction and is given an initial impact velocity. An initial impact velocity was set for the punch in the constructed finite element model, and all its degrees of freedom except for the impact direction were constrained. Fully fixed constraints were applied to the clamps on the upper and lower surfaces of the composite structure to limit its displacement and rotation. The dynamic display analysis method was adopted, and the impact duration and time increment step were set. During the simulation, time-displacement data and time-force data of the contact point between the punch and the layer plate, as well as the time series data of the internal energy changes of the metal layer, prepreg layer, adhesive film layer and honeycomb core were collected in real time to form complete time series dynamic response data.

3. The method for optimizing the low-velocity impact resistance of a fiber metal laminate based on ABAQUS according to claim 2, characterized in that: The time-series dynamic response data is preprocessed as follows: a wavelet transform-based filtering algorithm is used to denoise the data, removing high-frequency noise components from the time-displacement curve, time-force curve, and internal energy change curves of each layer, while retaining effective low-frequency signals characterizing the material's mechanical response. The data alignment process is achieved through a timestamp synchronization mechanism, unifying the time-displacement data, time-force data, and internal energy change time-series data of the contact point between the punch and the plate onto the same time reference, ensuring consistent correspondence between different data sources at the same impact moment. Time-displacement curves, time-force curves, and internal energy change curves for each layer are extracted from the preprocessed data. Based on the time-force curves, an adaptive threshold method is used to identify and calibrate the characteristic gradient change points in the curves. Specifically: the first gradient descent to a preset first threshold the second gradient descent to a preset second threshold the point is marked as a plastic-damage transition point, wherein ; Based on the elastic-plastic transition point and the plastic-damage transition point, the impact process is divided into a first characteristic stage dominated by elastic deformation, a second characteristic stage dominated by plastic deformation, and a third characteristic stage dominated by damage evolution.

4. The method for optimizing the low-velocity impact resistance of a fiber metal laminate based on ABAQUS according to claim 3, characterized in that: Based on the elastic deformation stage calibrated in step 2, the starting force value and ending force value of the time-force curve, and the starting displacement value and ending displacement value of the time-displacement curve within this stage are extracted. The equivalent stiffness of the plate is calculated according to the following formula: wherein, is the equivalent stiffness of the laminate, is the contact force between the punch and the laminate at the beginning of the elastic deformation phase, is the contact force corresponding to the elastic-plastic transition point, and are the corresponding data points taken from the time-force curve after pre-processing; is the displacement of the punch at the beginning of the elastic deformation phase, is the displacement of the punch corresponding to the elastic-plastic transition point, and are the corresponding data points taken from the time-displacement curve after pre-processing; The time-force curve containing the whole impact process after pretreatment is traversed, the peak value data in the curve is selected and marked as the maximum impact force, recorded as ; Based on the damage evolution stages identified in step 2, the starting and ending internal energy values ​​of the internal energy change curve of the film layer within this stage are extracted. Combined with the contact area of ​​the lamination interface, the critical peeling energy density is derived and determined using the principle of energy conservation. The formula based on this is as follows: wherein, is the critical debonding energy density, is the internal energy value of the adhesive film layer at the beginning of the damage evolution stage, is the internal energy value of the adhesive film layer at the end of the damage evolution stage, and corresponding data points taken from the internal energy variation curve of the adhesive film layer at the end of the damage evolution stage; is the contact area between the fiber metal laminate and the honeycomb core layer, which is directly obtained from the geometry of the finite element model constructed in step 1. The energy absorption percentage during the damage evolution stage is calculated based on the time-displacement curve, specifically as follows: Based on the time-force curve and time-displacement curve, numerical integration is performed on each characteristic stage to calculate the energy absorbed in that stage. The formula used is as follows: In the formula, Indicates the first Energy absorbed in each characteristic stage This is an index for the characteristic stage. These represent the three characteristic stages: elastic deformation, plastic deformation, and damage evolution. It is a time-force curve function. The derivative of the time-displacement curve; and They represent the first The start and end times of each characteristic stage; The energy absorption percentage during the damage evolution stage can be calculated using the following formula: In the formula, This represents the percentage of energy absorbed during the damage evolution stage. , and These represent the energy absorbed during the three characteristic stages of elastic deformation, plastic deformation, and damage evolution.

5. The method for optimizing the low-velocity impact resistance of fiber-reinforced metal laminates based on ABAQUS according to claim 1, characterized in that: The specific execution process of step 4 is as follows: The critical peel energy density, equivalent stiffness of the laminate, and maximum impact force were normalized using the following formulas: In the formula, , and These are the normalized critical peeling energy density, equivalent stiffness of the laminate, and maximum impact force, respectively. , and The benchmark values ​​for critical peel energy density, equivalent stiffness of the laminate, and maximum impact force were determined by statistical analysis of data obtained from finite element simulations of multiple standard fiber-metal laminate samples. An impact resistance performance evaluation model is constructed based on the normalized critical peel energy density, equivalent stiffness of the laminate, and maximum impact force. The comprehensive impact resistance index of the fiber-metal laminate is determined using the model. The expression for the impact resistance performance evaluation model is as follows: In the formula, To assess the overall impact resistance index, This represents the percentage of energy absorbed during the damage evolution stage. , , and These are the preset weights for the corresponding indicators. And satisfy , It is a natural constant.

6. The method for optimizing the low-velocity impact resistance of fiber-reinforced metal laminates based on ABAQUS according to claim 5, characterized in that: The comprehensive impact resistance index is matched with a preset grading threshold to output the grading evaluation result. The specific logic behind this is as follows: Preset first level threshold Second-level threshold and the third-level threshold And satisfy ; The calculated comprehensive impact resistance index Match each threshold interval one by one: like If so, then the "Excellent" rating result will be output; like Output a "Good" rating result; like Output the "Pass" rating result; like Output the "Unqualified" evaluation result.

7. The method for optimizing the low-velocity impact resistance of fiber-reinforced metal laminates based on ABAQUS according to claim 6, characterized in that: The composite structure is iteratively adjusted and optimized based on the results of the hierarchical evaluation. The specific logic behind this is as follows: If the evaluation result is "excellent", then keep the current parameters of the composite structure unchanged; If it is "good", based on the weight ratio of each normalized index in the comprehensive impact resistance index, the structural parameters corresponding to the indexes whose weight ratio is less than the preset weight ratio threshold are adjusted, such as increasing the thickness of the film layer to increase the critical peel energy density, or changing the prepreg layup angle to adjust the equivalent stiffness. If it is "qualified", prioritize adjusting the structural parameters corresponding to the critical peel energy density and maximum impact force, including changing the film material, increasing the number of prepreg layers, changing the size of the honeycomb core cell, and adjusting the parameters related to the equivalent stiffness of the layer. If it is "unqualified", the key parameters of the composite structure will be fully adjusted, including redesigning the lamination sequence and number of fiber metal layers, replacing the metal layers and prepreg materials, and adjusting the height and cell size of the honeycomb core. After adjustment, return to step 1 to rebuild the finite element model, and repeat steps 1-4 until a "good" or "excellent" evaluation result is output, and the number of iterations is controlled within the preset range. This completes the optimization of the low-velocity impact resistance of the fiber metal laminate based on ABAQUS.

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