Prediction method for multiple times of hail impact damage accumulation of composite radome

Abstract

The invention discloses a method for predicting accumulation of multiple hail impact damages of a composite radome, and belongs to the technical field of composite mechanics and structural mechanics. The method comprises the following steps: firstly, establishing a hail model by adopting a smoothed particle hydrodynamics (SPH) method so as to accurately simulate the impact crushing behavior of the hail model; secondly, performing refined finite element modeling on the composite panel and the honeycomb sandwich structure of the radome, and introducing a progressive damage evolution model based on a Hashin criterion and fracture energy; the core of the method is that a stress field, a damage variable and a deformation field which are obtained by previous impact simulation are used as initial conditions to be imported into subsequent impact analysis, so that accurate transmission of a damage state under multiple impacts and real simulation of an accumulation process are realized. According to the method, the problems that the damage history cannot be reflected by traditional single-time impact analysis, the grid dependence is high and the like are effectively solved, the accuracy and efficiency of multi-time impact damage prediction can be remarkably improved, and a reliable tool is provided for achieving anti-impact design and life evaluation of the radome.

Description

Technical Field

[0001] This application relates to the fields of composite material mechanics and structural mechanics, and in particular to a method for predicting the cumulative damage of composite material radomes from repeated hail impacts. Background Technology

[0002] Composite honeycomb sandwich structures are widely used in aircraft radomes due to their high specific strength, high specific stiffness, and excellent electromagnetic wave transmission properties. However, during flight, radomes are highly susceptible to high-speed impacts from foreign objects such as hail.

[0003] Currently, research on impact damage to composite material structures has the following limitations and shortcomings: Limitations of single-impact analysis: Existing research methods and commercial simulation software mostly focus on the analysis of single-impact events. However, in actual service environments, radomes may be subjected to multiple hail impacts during the same voyage or different voyages. Single-impact analysis cannot reflect the cumulative effect of damage, and will seriously overestimate the remaining strength and life of the structure, posing significant safety hazards.

[0004] Damage simulation lacks physical realism: Hail modeling: Traditional methods typically employ the mesh-based finite element method to simulate hail. However, high-speed impacts can cause severe mesh distortion, leading to computational interruptions or loss of accuracy. While erosion criteria can alleviate this problem, they result in non-physical mass loss, violate energy conservation, and their parameters are difficult to determine.

[0005] Material damage evolution: Many models rely solely on stress / strain criteria to determine damage initiation, leading to calculation results that are heavily dependent on mesh size and lack objectivity. Furthermore, the failure to introduce fracture energy-based damage evolution models fails to guarantee the mesh independence of energy absorption during material failure.

[0006] Lack of efficient multi-impact analysis process: To simulate multiple impacts, traditional methods require researchers to manually set the initial conditions for each impact. This process is cumbersome, prone to errors, and makes it difficult to guarantee the accuracy and consistency of state variables (such as stress, damage, and deformation) transfer between different analysis steps. The analysis efficiency is extremely low, making it impossible to conduct large-scale parametric studies and engineering applications.

[0007] Therefore, there is an urgent need in this field for an analytical method that can accurately and efficiently predict the accumulation and expansion of damage to composite radomes under repeated hail impacts, so as to scientifically assess their damage tolerance and residual performance and provide key theoretical basis for the design, maintenance and replacement of radomes. Summary of the Invention

[0008] This invention addresses the technical problems existing in the background art by proposing a method for predicting the cumulative damage of composite material radomes from repeated hail impacts. For the first time, it systematically solves the problem of predicting the damage of composite material radomes from repeated hail impacts, and also achieves significant breakthroughs in simulation accuracy, numerical stability, and engineering application efficiency, which is of great value to improving the safety and reliability of aviation equipment.

[0009] To solve the technical problem, the technical solution of the present invention is as follows: A method for predicting cumulative damage from repeated hail impacts on a composite material radome, the method comprising: After establishing an explicit dynamic analysis model of the hail-radome coupling system, the hail parameters for the first impact and the material parameters of the radome honeycomb sandwich panel are set, and the explicit dynamic analysis model is solved to obtain the structural field variables of the radome at the end of the first impact. For the Nth hail impact, N≥2; execute the following loop steps: The structural field variables at the end of the (N-1)th impact are imported into the explicit dynamic analysis model of the Nth impact through field variable mapping. An explicit dynamic analysis model of the Nth impact containing historical damage states is constructed. The updated structural field variables at the end of the Nth impact are obtained by setting the hail parameters and the material parameters of the radome honeycomb sandwich panel of the Nth impact. Repeat the impact process multiple times until the preset M impact simulations are completed, M≥1; obtain the final cumulative damage state of the radome structure after M impacts.

[0010] Specifically, the structural field variables at the end of the (N-1)th impact are imported into the explicit dynamic analysis model of the Nth impact through field variable mapping. This means that all key state variables contained in the solver's output file (the .odb file in Abaqus) are used as initial conditions and completely imported into the simulation model for the next impact. These state variables constitute a complete field defining the initial state of the system, used to construct the explicit dynamic analysis model for the Nth impact, which includes historical damage states. Explicit dynamic solutions are performed by setting the hail parameters for the Nth impact to obtain the updated structural field variables at the end of the Nth impact. A script written in Python automatically calls the Abaqus solver to repeatedly execute multiple impact processes until the preset M impact simulations are completed (M≥1). The final cumulative damage state of the radome structure after M impacts is then obtained.

[0011] Furthermore, after obtaining the final cumulative damage state, a post-damage mechanical analysis model of the radome honeycomb sandwich panel is constructed based on the final cumulative damage state, or a quasi-static / low-speed load is directly applied to the explicit dynamic model corresponding to the final cumulative damage state to obtain the overall force-displacement response data of the radome structure; the equivalent stiffness degradation ratio and ultimate bearing capacity are calculated based on the overall force-displacement response data to obtain the quantitative evaluation results of the remaining stiffness and remaining strength of the structure.

[0012] Furthermore, the hail parameters include: initial velocity, diameter, incident direction and impact position of the hail, and the sandwich panel parameters include: panel thickness, number of layers, layup angle, honeycomb height and wall thickness.

[0013] Furthermore, the construction of the explicit dynamic analysis model of the hail-radome coupling system includes: A finite element model of the radome composite structure and a hail finite element model were constructed. The radome composite structure finite element model includes upper and lower composite material skins and a honeycomb core material. The upper and lower composite material skins were modeled using continuous shell elements to obtain the upper and lower composite material skin models. The honeycomb core material was modeled using continuous shell elements to obtain the honeycomb core material model. The hail finite element model was obtained by creating a spherical geometric model and discretizing the spherical geometric model into a series of interacting SPH particles using the smoothed particle hydrodynamics method. Anisotropic elastic parameters are defined for each ply of the upper and lower composite material skin models, and the Hashin damage initiation criterion and the progressive damage evolution model based on fracture energy are integrated to obtain upper and lower composite material skin models with material properties; the anisotropic constitutive model of Nomex material is applied to the honeycomb core material model, and the crushing characteristics are defined to obtain a honeycomb core material model with material properties; a strain rate-related elastoplastic constitutive model and a tensile failure criterion are defined for the SPH particles to obtain a hail model with material properties.

[0014] Furthermore, the construction of the explicit dynamic analysis model of the hail-radome coupling system also includes: In the global coordinate system, the hail model with material properties is positioned at a specified impact position relative to the radome composite structure model with material properties, obtaining the component positioning result; a first tie constraint is created between the upper surface of the honeycomb core material with material properties and the lower surface of the upper composite skin with material properties, and a second tie constraint is created between the lower surface of the honeycomb core material with material properties and the upper surface of the lower composite skin with material properties, obtaining the internal connection result; the contact interaction between the hail model and the radome upper skin model is defined using a general contact algorithm and a penalty function method, obtaining the external contact definition result; based on the component positioning result, the internal connection result, and the external contact definition result, an explicit dynamic analysis model of the static hail-radome coupled system is obtained; Based on the component positioning results, the internal connection results, and the external contact definition results, the analysis steps, loads, and boundary condition settings are defined, including: An explicit dynamic analysis step is established to simulate a brief impact event and set its time increment control parameters. Displacement constraints under actual working conditions are applied to the boundary of the radome composite structure model with material properties, and an initial velocity field is defined for the hail model with material properties, specifying the impact velocity and direction. This yields the explicit dynamic analysis model of the dynamic hail-radome coupled system, which is the complete explicit dynamic analysis model of the hail-radome coupled system.

[0015] Furthermore, the final cumulative damage state includes: the fiber / matrix tensile and compressive damage distribution of the upper and lower composite material skins, the crushed area of ​​the honeycomb core material, and the overall residual deformation.

[0016] Furthermore, the structural field variables at the end of the (N-1)th impact are imported into the explicit dynamic analysis model of the Nth impact through field variable mapping, specifically including: Using the result file of the final moment of the N-1th impact analysis as the source data, the structural field variables stored in it and located at the grid integration points are extracted; the structural field variables include: nodal displacement field defining the structural geometry, element stress field and plastic strain field defining the internal forces of the material, and damage variable field defining the degradation of material properties; By using state variable import and numerical interpolation algorithms, the structural field variables are mapped from the grid integration points corresponding to the data source to the grid positions corresponding to the explicit dynamic analysis model of the Nth impact, thus obtaining the mapped field variable data. The mapped field variable data is then used as the initial conditions for the Nth impact analysis and imported into the explicit dynamic analysis model of the Nth impact.

[0017] The advantages of this application are as follows: Achieving high-precision prediction of cumulative damage from multiple impacts: This invention pioneers a "multiple impact simulation method based on initial state transfer." By completely and accurately using all key state variables (including stress field, strain field, damage variables, plastic deformation, etc.) after the previous impact as the initial conditions for the next impact, it for the first time realistically reproduces the "history dependence" and "irreversibility" of composite material damage in numerical simulation. This overcomes the idealized assumptions of traditional independent analysis methods, enabling unprecedented accuracy in predicting the residual strength, stiffness, and damage propagation path of structures.

[0018] The simulation of impact physics processes is improved in terms of realism and numerical stability: By employing the smoothed particle hydrodynamics (SPH) meshless method to model hail, the mesh distortion problem in traditional finite element methods when simulating large deformation and fragmentation of hail is fundamentally solved. This method can more physically simulate the fragmentation and splashing behavior of hail, ensuring the stability of the calculation process and energy conservation, thus obtaining more realistic impact force time history curves and energy transfer processes. In the composite material model, a progressive damage evolution model based on fracture energy is introduced. This model binds material damage evolution to energy (the intrinsic property of the material) rather than mesh size, effectively eliminating the mesh dependency of simulation results and making the damage prediction results more objective and reliable.

[0019] This invention establishes an efficient and standardized automated analysis process, significantly improving engineering application efficiency: It develops a fully automated simulation system integrating parametric modeling, automatic solving, and intelligent post-processing. Users can complete all parameter settings through a user-friendly graphical interface (GUI), and the system automatically calls the solver and generates standardized reports. This transforms what was originally complex and error-prone repetitive work into a one-click operation, allowing researchers to focus on results analysis and solution optimization, improving analysis efficiency several times over. It is particularly suitable for large-scale, multi-variable condition screening and optimization design.

[0020] This invention provides a comprehensive assessment capability from microscopic damage to macroscopic response: It integrates the Hashin failure criterion and refined honeycomb modeling to clearly distinguish and visualize the occurrence and evolution of different failure modes, such as fiber fracture, matrix cracking, delamination, and honeycomb core crushing. Simultaneously, by outputting macroscopic responses such as stress cloud maps, pit depth evolution, and energy history curves, it constructs a complete assessment chain from material microscopic damage to structural macroscopic performance degradation, providing a powerful tool for a comprehensive understanding of the impact resistance and failure mechanisms of structures. Attached Figure Description Figure 1 The main technical roadmap of the composite material radome cumulative damage prediction method proposed in this application; Figure 2This application presents a technical roadmap for establishing an explicit dynamic analysis model of a hail-radome coupling system. Figure 3 This application presents a technical roadmap for repeated impacts. Figure 4 The GUI interface diagram of the hail impact composite honeycomb sandwich panel of this application; Figure 5 A folder diagram showing the simulation results of single-point multiple impacts in this application; Figure 6 The GUI diagram of the post-processing sub-interface for simulation results in this application; Figure 7. Results of multiple single-point impacts (a. First single-point impact, b. Second single-point impact, c. Third single-point impact, d. Fourth single-point impact) Figure 8 Evolution of maximum crater depth under single-point impact; Figure 9. Results of multiple random impacts (a. First random impact, b. Second random impact, c. Third random impact, d. Fourth random impact). Figure 10 Evolution of maximum crater depth under random impact; Figure 11. CAI test images after multiple impacts (a. front after compression, b. side after compression, c. panel, d. honeycomb structure). Figure 12 Load-displacement curves of a composite honeycomb sandwich structure under compression after being impacted by hail at different speeds.

[0021] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] Example 1: like Figure 1As shown, this application uses a constructed hail-radome coupled system model to conduct explicit dynamic simulation analysis of the damage accumulation process of the radome honeycomb sandwich composite material structure under multiple hail impacts. The main process includes: Step 1: Explicit dynamic analysis model and parameter setting of the hail-radome coupled system, such as... Figure 2 As shown: S101: Construct a finite element model of the radome composite structure and a hail finite element model. The finite element model of the radome composite structure includes: upper and lower composite material skins and a honeycomb core material; the upper and lower composite material skins are modeled using continuous shell elements to obtain the upper and lower composite material skin models; the honeycomb core material is modeled using continuous shell elements to obtain the honeycomb core material model; the hail finite element model is obtained by creating a spherical geometric model and discretizing the spherical geometric model into a series of interacting SPH particles using the smoothed particle hydrodynamics method. For example, the elastoplastic finite element model discretizes hailstones using traditional solid element meshes and assigns an elastoplastic constitutive model to simulate their deformation upon impact. Its drawback lies in mesh distortion: hailstones undergo extreme plastic deformation under high-speed impact, and traditional Lagrangian elements cause severe mesh distortion, drastically reducing the time step or even interrupting the computation. Furthermore, severely distorted meshes significantly reduce computational accuracy. To address the distortion problem, an erosion criterion is sometimes introduced, where elements are removed when their strain reaches a certain critical value. However, this is a non-physical, numerical process that artificially sacrifices mass and affects energy conservation; moreover, the parameters of the erosion criterion are difficult to determine.

[0024] SPH (Skewing Particle Hierarchy) is a meshless Lagrangian method that represents a continuum as a series of interacting particles. Each particle carries physical quantities such as mass, velocity, and stress, and the governing equations are solved using kernel function approximation. We chose SPH because of its meshless distortion problem: the absence of a mesh in the SPH method perfectly avoids numerical problems caused by extreme deformations, making it ideal for simulating processes such as impact, fracturing, and large deformations. Furthermore, it is physically more realistic: hail is essentially an aggregate of ice crystals, and its fracturing behavior is more physically intuitively consistent with the discrete particle characteristics of SPH. SPH can naturally simulate the fragmentation, splashing, and interaction of hail with structures. It also has good compatibility with explicit algorithms: SPH is well-suited for coupling with explicit dynamics solvers.

[0025] First, a geometric model of a sphere is created. Then, the Mesh module of the finite element method software is used to discretize it into SPH particles, typically using single-point integral particles. The particle spacing is a key parameter controlling the model's accuracy, determining the smooth length of the particles. Therefore, convergence analysis is required to achieve a balance between computational resources and accuracy.

[0026] For example, a typical radome is a composite honeycomb sandwich structure; the panels are generally treated as laminates, given anisotropic elastic constitutive properties and interlayer interfaces. The composite panel is modeled using continuous shell elements (SC8R) because, like solid elements, continuous shell elements have multiple integration points in the thickness direction, allowing for accurate simulation of thickness-direction stress and interlayer stress, which is crucial for predicting delamination failure. Simultaneously, it possesses translational and rotational degrees of freedom like traditional shell elements, resulting in higher computational efficiency than pure solid elements. In the element section properties, the material orientation, thickness, and number of integration points for each layup are defined layer by layer according to the actual design. Material orientation is achieved by defining a local coordinate system to ensure the correct fiber orientation in each layer.

[0027] Mesh size is one of the most critical factors affecting the accuracy of damage prediction. Too small a mesh results in high computational costs; too large a mesh fails to accurately capture stress gradients. Therefore, a fine mesh is used in the impact center region, the core area for damage initiation and propagation. In regions farther from the impact center, a gradually coarser mesh is used to save computational costs.

[0028] The honeycomb core material is modeled using refined geometric modeling, which involves creating a detailed geometric model based on the actual shape of the honeycomb cells (e.g., regular hexagons). While homogeneous solid models are more computationally efficient, they cannot accurately simulate the complex nonlinear failure processes of honeycomb panels, such as buckling and crushing. Therefore, we employ refined modeling to study the energy absorption mechanism and failure modes of the core material. Conventional shell elements (S4R) are selected as the element type, with the shell element thickness defined as the actual thickness of the honeycomb foil. The honeycomb panel is discretized in its width direction using 1-2 elements, with the mesh size matching the size of the fine mesh region of the panel.

[0029] The radome structure is usually connected to the main structure of the aircraft through its base or connecting ring. Therefore, in the simulation, we apply fixed support constraints on the node set at the edge of the model to simulate its actual installation conditions. In general, the modeling of the radome structure should take into account both the anisotropic damage of the laminate and the anisotropic compressive buckling behavior of the core material.

[0030] S102: Define anisotropic elastic parameters for each ply of the upper and lower composite material skin models, and integrate the Hashin damage initiation criterion and the progressive damage evolution model based on fracture energy to obtain upper and lower composite material skin models with material properties; assign an anisotropic constitutive model of Nomex material to the honeycomb core material model, and define its crushing characteristics to obtain a honeycomb core material model with material properties; define a strain rate-related elastoplastic constitutive model and a tensile failure criterion for the SPH particles to obtain a hail model with material properties.

[0031] For example, in the constitutive model construction of hail materials, the damage mode and severity of hail impact are considered to vary significantly with different impact velocities or energies. Because hail exhibits a strong strain rate effect and undergoes a transition from ductile to brittle, it fragments under significant deformation during impact. A strain rate-dependent elastoplastic model is used for hail. Since the compressive strength of hail increases with increasing strain rate, exhibiting a significant rate effect, tensile failure and compressive failure are two typical failure criteria in hail failure models. This application adopts the tensile failure model. For example, in the constitutive model of a composite panel, continuous shell elements or traditional shell elements are used for layup modeling, and the material is glass fiber reinforced. In the finite element simulation, if the damage model is based solely on the strength criterion (Hashin's criterion determines damage initiation), the stiffness of the elements will drop to zero instantaneously or very quickly after damage occurs. This abrupt change causes the calculation results to be heavily dependent on the mesh size. The denser the mesh and the smaller the elements, the less energy is required for failure, and the more brittle the structure becomes. To address this issue, fracture energy is introduced, which binds the damage evolution process to energy; regardless of the mesh size, the total energy consumed to expand a crack of the same area is constant. ABAQUS automatically adjusts the rate of stiffness degradation based on the characteristic length of the elements, thus greatly reducing the dependence of the simulation results on the mesh and making them more objective.

[0032] For example, in the constitutive model of the honeycomb core material, the panels primarily resist impact damage, while the core material absorbs energy. To accurately capture its mechanical behavior, a detailed shell model of the hexagonal structure of the honeycomb cell wall is performed, with Nomex selected as the material.

[0033] S103: In the global coordinate system, the hail model with material properties is positioned at a specified impact position relative to the radome composite structure model with material properties, obtaining the component positioning result; a Tie constraint is created between the upper surface of the honeycomb core material with material properties and the lower surface of the upper composite skin with material properties, and another Tie constraint is created between the lower surface of the honeycomb core material with material properties and the upper surface of the lower composite skin with material properties, obtaining the internal connection result; the contact interaction between the hail model and the radome upper skin model is defined using a general contact algorithm and a penalty function method, obtaining the external contact definition result; based on the component positioning result, the internal connection result, and the external contact definition result, an explicit dynamic analysis model of the static hail-radome coupled system is obtained; For example, the upper and lower composite panels are connected to the honeycomb core material via adhesive. Therefore, in the finite element model, the most common and efficient approach is to use Tie constraints. This involves binding the master and slave surfaces of the panel to the core material together, eliminating all relative degrees of freedom between them. In Abaqus software, a Tie constraint is created by selecting the upper surface of the core material and the lower surface of the upper panel, and this operation is repeated for the lower panel and the lower surface of the core material. Assuming the adhesive strength is high and its failure is not the focus of the analysis, the adhesive layer itself can be ignored, and Tie constraints are used to simulate perfect bonding behavior. This is a reasonable and efficient simplification. The contact definition between hail and the panel is the most critical interaction in the impact simulation. A general contact algorithm is used, which defaults to a penalty function contact method. The normal behavior is set to hard contact, meaning that normal pressure is only transmitted when the master and slave surfaces are in contact, and the pressure is zero upon separation. The tangential behavior defines the friction coefficient, which is set to 0 between the hail and the composite material surface. The default "penalty stiffness" scaling factor is typically used. If excessive penetration is observed at the contact surface, this factor can be increased appropriately, but excessively large factors can lead to calculation instability. Furthermore, the slip formula uses finite slip, allowing arbitrary relative sliding and separation between the contact surfaces, which is suitable for impact problems.

[0034] S104: Based on the component positioning results, internal connection results, and external contact definition results, the analysis steps, loads, and boundary conditions are set; including: establishing an explicit dynamic analysis step, simulating a brief impact event, and setting its time increment control parameters; applying displacement constraints of actual working conditions to the boundary of the radome composite structure model with material properties, and defining an initial velocity field for the hail model with material properties, specifying the impact velocity and direction, to obtain the explicit dynamic analysis model of the dynamic hail-radome coupling system, i.e., the complete explicit dynamic analysis model of the hail-radome coupling system.

[0035] Step 2: Explicit dynamic simulation of the first impact condition; In the above coupled system model, the hail parameters and working conditions for the first impact are set, including the initial velocity, diameter, incident direction and impact location of the hail. The initial hail impact process was simulated using explicit dynamics, and the response results of the radome structure at the end of the initial impact were obtained, including structural field variables such as full-field displacement, stress and strain, damage variables, plastic strain and energy history, as well as the deformation and fragmentation state of the hail itself.

[0036] Step 3: Simulation process of multiple impact accumulation for the Nth impact (N≥2), as follows: Figure 3 As shown; For the Nth hail impact, where N is an integer ≥ 2, perform the following loop steps: Initial field import and Nth impact analysis model construction; The structural field variables (including geometric deformation, residual stress and strain fields, damage variables of each failure mode, plastic strain and other historically relevant internal variables) at the end of the N-1th impact simulation are extracted from the results file of the previous working condition and imported into the new explicit dynamic analysis model as the initial state field. While maintaining the consistency of the radome structure mesh topology, a hail-radome coupled system model for the Nth impact analysis is constructed through field variable mapping, so that the radome structure is in an accurate state of cumulative damage and residual deformation at the beginning of the Nth impact.

[0037] Nth impact condition setting and explicit dynamic analysis; In the explicit dynamic analysis model for the Nth impact, hail parameters corresponding to the Nth impact are set, including the initial velocity, diameter, and impact location of the hail. The impact location can be a single-point impact the same as the previous impact, or a random impact location generated according to preset rules within a given area. The explicit dynamic analysis model for the Nth impact is solved explicitly to simulate the hail re-impact process based on existing damage and residual stress / deformation. The structural field variables at the end of the Nth impact simulation are obtained, thereby achieving a further accumulation and expansion description of the evolution of panel hashin damage, crushing of honeycomb core material, and overall stiffness degradation.

[0038] Step 4: Obtaining the cumulative damage status after multiple impact cycles; Repeat the simulation steps for the Nth impact, incrementing N from 2 to a preset number M, to complete M hail impact simulation cycles, where M is an integer ≥ 1. After the Mth impact simulation, obtain the final cumulative damage state of the radome honeycomb sandwich structure under multiple impacts, including: the distribution and evolution of tensile and compressive damage to the upper and lower panel fibers / matrix, the crushing and buckling areas of the honeycomb core material, the evolution of overall residual deformation and pit depth, and energy absorption characteristics.

[0039] For example, to accurately simulate the cumulative damage effect under multiple hail impacts, a simulation strategy based on initial field introduction was adopted. The core of this method lies in fully considering the irreversibility and historical dependence of composite material damage, breaking the idealized assumption in traditional independent simulations that each impact starts from an intact state, thereby significantly improving the physical realism and prediction accuracy of the simulation results.

[0040] The specific operation procedure is as follows: After completing the explicit dynamic calculation of the first impact event, all key state variables contained in the solver output file (the .odb file in Abaqus) are used as initial conditions and completely imported into the simulation model of the next impact. These state variables constitute a complete field defining the initial state of the system, mainly including: Deformation and geometry: The permanent plastic deformation and displacement field of the structure after the first impact. This ensures that the structure is in the correct pre-deformed geometry at the onset of the second impact, rather than in its original undeformed state, which is crucial for accurately calculating the contact area and energy transfer.

[0041] Stress-strain field: The distribution of residual stress and strain within a structure. These residual stress fields significantly affect the subsequent mechanical response of the material, for example, they may exacerbate or delay the initiation of new damage, and are the basis for simulating stiffness reduction and load redistribution.

[0042] Material damage state: This is the most critical information. It includes all damage variables calculated according to the selected damage criterion, such as fiber tensile damage, fiber compressive damage, matrix tensile damage, and matrix compressive damage. The values ​​of these damage variables at each integration point are accurately transferred to the new model, thus fully recording the stiffness degradation history of the material due to the previous impact.

[0043] Other historically relevant variables: such as plastic strain, energy absorption, and all other internal state variables related to the material's historical response.

[0044] In terms of technical implementation, this process involves specifying the result file from the previous analysis in the predefined field of subsequent analysis steps and selecting the field variables to be mapped. The solver then uses a mapping algorithm to accurately interpolate the result data stored on the old mesh onto the mesh of the new model. Through the continuous application of this method, we can seamlessly connect multiple impact events in a single simulation flow, dynamically and progressively simulating the further expansion of existing damage zones, the initiation of new damage in stress concentration areas, the change in load paths due to local stiffness reduction, and the gradual degradation of the overall stiffness and load-bearing capacity of the structure.

[0045] Ultimately, this initial field introduction method successfully constructed a continuously evolving damage path that spans multiple impact events, providing a powerful analytical tool for evaluating the durability and damage tolerance of honeycomb sandwich composite radomes in real service environments.

[0046] Step 5: Assessment of Residual Load-Bearing Capacity Based on Cumulative Damage State Based on the final cumulative damage state obtained from M-cycle impact simulations, a post-damage mechanical analysis model of the radome structure is constructed, or quasi-static / low-speed load conditions are applied to perform stiffness and strength analysis. Based on the overall force-displacement response, equivalent stiffness degradation ratio, ultimate bearing capacity, and stress-strain levels in key areas, the residual stiffness and residual strength of the radome after multiple hail impacts are evaluated. If necessary, the cumulative damage area is further mapped to an electromagnetic simulation model to analyze the degradation trend of the radome's wave transmission performance, thereby providing a basis for damage tolerance design and life assessment of the radome in real service environments.

[0047] For example, the quantitative assessment of residual stiffness and residual strength from the final accumulated damage state includes: Obtaining the final cumulative damage state: After multiple impact simulations, the structure gradually accumulates damage. Each impact induces damage of varying degrees (such as matrix cracking, fiber tensile fracture, and honeycomb core material crushing). This damage is quantified using the Hashin damage criterion and progressive damage model, and reflected in every part of the structure. The final cumulative damage state includes: Local damage: For example, local damage areas near the impact point, which may include fiber tensile fracture or matrix cracking. Overall damage: Reflecting the damage development of the entire structure, such as honeycomb core material crushing, interlaminar failure, and delamination. Residual stress and deformation: Permanent geometric deformation caused by multiple impacts, and the distribution of residual stress within the structure.

[0048] A post-damage mechanical model is established based on the cumulative damage state, or a load is applied. Once the final cumulative damage state is obtained, the next objective is to evaluate the radome's remaining load-bearing capacity under this state. This can be analyzed using one of the following two methods: (1) Constructing a mechanical analysis model after damage A new post-damage mechanical analysis model is established by redefining the material properties of the structure based on the damage. This model needs to consider the following factors: Damage-degraded material properties: Damage leads to a decrease in material stiffness, which may include degradation of elastic modulus, shear modulus, strength, etc. The more severe the damage, the more significant the degradation of stiffness and strength. Damage evolution: As loading progresses, the damage will further extend or develop, and it is necessary to simulate the further evolution of damage based on factors such as fracture energy and plastic deformation. Stiffness degradation: Based on the previous damage evolution model, the structural stiffness will degrade as the damage intensifies. The quantification of stiffness degradation can be achieved by establishing a degradation coefficient. For example, for damage to composite laminates, the post-damage stiffness can be calculated using the following method: D eff =(1− D ) D in,D eff It is the stiffness matrix after damage. D It is a damage variable (between 0 and 1, where 0 represents no damage and 1 represents complete failure).

[0049] (2) Apply quasi-static / low-velocity loads directly to the explicit dynamic model corresponding to the final cumulative damage state; apply quasi-static loads or low-velocity loads directly to the explicit dynamic model after damage. This method is suitable for considering the overall structural response, rather than solely relying on local stiffness degradation. By applying loads to the explicit dynamic model after damage, the force-displacement response of the structure can be obtained, and its influence on the residual stiffness and strength after impact can be analyzed. This method is particularly suitable for simulating the mechanical response under dynamic conditions, such as how a structure responds to external loads and withstands more deformation under multiple impacts.

[0050] 3. Obtain overall force-displacement response data; Through the above analysis method, the model will output overall force-displacement response data, which includes information such as stress, displacement, and deformation at various points of the structure during loading. Force-displacement response data can be used to analyze: the overall deformation of the structure: Through the force-displacement curve, we can see how the structure deforms as the load increases. Damage propagation: By analyzing the deformation under different loading conditions, we can determine whether the damage has further propagated.

[0051] 4. Calculate the equivalent stiffness degradation ratio and ultimate bearing capacity: From the force-displacement response data, the equivalent stiffness degradation ratio and ultimate bearing capacity of the structure can be calculated to quantify the remaining performance of the radome.

[0052] (1) Equivalent stiffness degradation ratio The stiffness degradation ratio is an important indicator for measuring the degree of stiffness loss in a structure after damage. It can be expressed as the ratio of the structure's initial stiffness to its stiffness after damage: η k = K eff / K 0 in, η k It is the equivalent stiffness degradation ratio. K eff It is the stiffness of the structure after damage. K 0 represents the stiffness in the undamaged state.

[0053] (2) Ultimate bearing capacity Ultimate bearing capacity is the maximum load a structure can withstand; exceeding this load will cause structural failure or severe damage. The maximum bearing point, or ultimate bearing capacity, can be found using a force-displacement curve. These calculations allow for the quantification of the radome's remaining stiffness and strength after multiple impacts, thus enabling the evaluation of its performance in practical applications.

[0054] 5. Remaining Functionality Assessment: Electromagnetic Transmission Performance: Besides mechanical properties, damage can also affect the electromagnetic transmission performance of the radome. By establishing an electromagnetic simulation model based on the damage state, the change in electromagnetic transmittance of the radome after multiple impacts can be predicted. Electromagnetic transmission performance assessment: The electromagnetic transmittance and operational performance of the radome are evaluated based on the damage state under different impact cycles. Severely damaged areas may lead to a significant decrease in the radome's transmittance, thereby affecting its radar performance.

[0055] Example 2: In one exemplary implementation, to improve the efficiency of large-scale, multi-condition simulation, this application has developed a parametric modeling and automated simulation process based on Abaqus.

[0056] Parametric Modeling: Through a developed graphical user interface (GUI), users can easily input geometric and material parameters for hail, panels, and honeycomb cores. A customized front-end was developed for Abaqus simulation, enabling parametric modeling. Users can define the working directory, hail radius, and detailed parameters of the honeycomb sandwich panels (such as panel thickness, number of layers, layup angle, honeycomb height, wall thickness, etc.) here. The GUI interface is accessed as follows: Figure 4 As shown, select the working directory for storing simulation results and enter various simulation parameters as prompted. After selecting the simulation mode as "single-point impact" and entering the number of impacts as "5", click the "Build Model and Run Abqus Simulation" button. The program will automatically model and complete the simulation. This GUI uses a scripting language to convert the user-input parameters into the modeling instructions required by Abaqus, greatly simplifying the complex process of repeatedly modeling different parameters and improving research efficiency.

[0057] Automatic calculation: The program automatically calls the Abaqus solver to perform calculations. After the simulation is completed, a prompt will be displayed in the GUI interface, and various simulation result files will be generated in the specified working directory, such as... Figure 4 As shown, the .odb file is a database file containing all simulation results, the .inp file is the input file, the .log file is the log file, and the .py file is the relevant Python script.

[0058] Automated post-processing: Dedicated scripts are written to automatically extract key data such as stress, displacement, and energy from the results database (.odb files) and generate charts and contour plots. To view detailed simulation results, the .odb files can be opened within the Abaqus CAE interface. For simulation results of interest, such as maximum stress values, the evolution of impact crater depth over time, and impact result contour plots, click on the GUI interface... Figure 5 The "View Simulation Post-Processing Results" button is located in the center. Clicking it will take you to a sub-interface as shown below. Figure 6 As shown, selecting the corresponding .odb file will automatically generate various post-processing results.

[0059] In one exemplary embodiment, Figure 7 shows the results of multiple single-point impacts, taking the center point of four impacts as an example: This set of figures shows the equivalent stress distribution inside the structure at the end of the first four impacts. The red area represents the high-stress zone, mainly concentrated directly below the impact point. As the number of impacts increases, the range of the red high-stress zone gradually expands, and the peak stress also shows an upward trend (approximately 176 MPa for the first impact and 198 MPa for the fourth impact).

[0060] The initial impact causes plastic deformation and initial damage to the panel. Subsequent impacts occur on the already damaged area, reducing the material's load-bearing capacity and requiring greater stress to resist the same impact load. Simultaneously, the damage extends further to surrounding areas, a typical phenomenon of damage accumulation.

[0061] Evolution of maximum crater depth under single-point impact as follows Figure 8 As shown in the figure, this diagram records the maximum displacement of the structure over time during multiple impacts. It can be clearly seen that each impact produces a peak displacement, followed by a rebound after the impact, but leaving a permanent residual deformation. With the increase in the number of impacts, both the peak displacement generated by each impact and the residual displacement after the impact increase in a stepwise manner.

[0062] The stepped rise of the curve visually illustrates the accumulation of plastic deformation. Each impact creates a deeper, more permanent dent than the previous one. The increase in peak displacement may indicate that the local stiffness of the structure at the impact point is reduced due to material damage and plastic deformation, making it more susceptible to large deformations in subsequent impacts.

[0063] As the number of impacts increases, the high-stress region at the impact point gradually expands, and the peak stress also shows an upward trend. This is because the damage caused by the previous impact reduces the material's load-bearing capacity, requiring greater stress to resist subsequent impacts. Each impact leaves a permanent residual deformation. With increasing impact count, the residual deformation increases in a stepwise manner, visually demonstrating the accumulation of plastic deformation.

[0064] Figure 9 shows the results of multiple random impacts, again using four impacts as an example: This set of figures illustrates the stress distribution after four random impacts. Each impact creates an independent stress concentration area at a different location. In (c) and (d), it can be seen that the new impact (left) coexists with the stress area left by the previous impact (right). Unlike single-point impacts, the damage from random impacts is distributed over a wider area. If two impacts are close enough, their stress fields and damage areas may overlap, resulting in "bridging" damage between the two craters, which can cause more severe structural performance degradation than two isolated impacts.

[0065] Evolution of maximum crater depth under random impact as follows Figure 10 As shown in the figure, this diagram illustrates the variation over time of the maximum dent depth that appeared on the entire structure under multiple random impacts. Figure 8 Unlike other impacts, the peak displacements here vary in magnitude, and the growth of residual displacement is not uniform and step-like. Because the location of each impact differs, as do the underlying support conditions (e.g., whether it falls at the center of a cell or at a wall panel junction), the impact responses differ, resulting in different maximum displacements and residual deformations for each impact. This figure reflects the deepest crater depth observed in all impacts across the entire model, rather than the depth evolution at a fixed point.

[0066] The residual strength of the structure was assessed using a post-impact compression (CAI) simulation method. This method first performs an impact simulation, then uses the results with the damage field as the initial state before performing compression calculations. Figure 11 shows (CAI test after multiple impacts): It can be seen that significant stress concentration occurs near the original impact damage area, and buckling deformation begins from this location. The structure undergoes overall flexural buckling, with the damage area being the weak point leading to buckling. High-stress areas are concentrated in the most severely bent parts of the structure, i.e., the original impact damage area. The honeycomb core layer also bears the load during compression and wrinkles and crushes when the structure becomes unstable, especially in the area where the panel buckling deformation is most severe.

[0067] The initial damage caused by the impact disrupts the structural integrity, creating a stress concentration point. Under subsequent compressive loading, the stiffness of this weak area decreases, leading to premature local buckling and rapid evolution into overall instability, thereby reducing the structure's ultimate load-bearing capacity.

[0068] The load-displacement curves of the composite honeycomb sandwich structure under compression after being impacted by hail at different velocities are shown below. Figure 12 As shown: Linear loading stage: The load increases approximately linearly with increasing displacement. The slope of the curve represents the compressive stiffness of the specimen. From... Figure 12As can be seen, the slopes of the two curves are almost identical in this stage, indicating that impact damage does not significantly affect the overall stiffness of the material in the initial stage. Peak Load Stage: The load reaches its maximum value; this point is called the peak load or post-impact residual compressive strength, a key indicator of a material's damage tolerance. Specimens subjected to higher velocity impacts have significantly lower peak loads than those subjected to lower velocity impacts. Catastrophic Failure Stage: After reaching the peak load, the load drops sharply and almost vertically. This indicates that the specimen has suffered structural and catastrophic damage, and its load-bearing capacity is lost instantaneously. Post-Failure Stage: After the load drops to a lower level, it tends to stabilize, but with slight fluctuations.

[0069] The load at this stage is called residual friction bearing. At this point, the specimen has completely failed, and the load is mainly borne by friction and compression between the fracture surfaces. The load levels of the two curves are also basically the same at this stage. Initial damage occurs upon impact. When a composite material is subjected to a transverse impact, even if the surface shows only minor dents, complex damage modes develop internally, primarily including matrix cracking, fiber breakage, and delamination. Higher impact velocity means greater impact energy, resulting in a wider and more severe internal damage area. Damage propagation and failure during compression: In the initial stages of compression, the load is primarily borne by the undamaged portions of the material. At this time, although internal impact damage exists, it has not yet deteriorated, so the overall stiffness is almost unaffected. Peak load and failure: As the compressive load increases, stress concentrates in the internal damage area. When the load reaches a critical value, the pre-existing delamination area becomes unstable due to local buckling and begins to rapidly propagate outwards. This coupling effect of delamination propagation and local buckling leads to the instability of the entire structure, ultimately causing compressive fracture of the fibers, resulting in catastrophic, global damage, manifested as a sharp drop in load.

[0070] The severity of initial damage determines residual strength; high-energy impacts cause larger areas and more severe delamination damage. During subsequent compression, this larger damaged area acts like a larger defect, more easily reaching the critical condition for instability propagation at lower load levels. Therefore, the greater the initial damage, the lower the ultimate load the specimen can withstand under compression. Internal damage caused by impact is the decisive factor affecting the residual compressive strength of a material. The greater the impact energy, the more severe the internal damage, and the more prone the material is to instability and failure under subsequent compressive loads, resulting in lower load-bearing capacity.

[0071] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0072] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for predicting the cumulative damage from repeated hail impacts on composite material radomes, characterized in that, The method includes: After establishing an explicit dynamic analysis model of the hail-radome coupling system, the hail parameters for the first impact and the material parameters of the radome honeycomb sandwich panel are set, and the explicit dynamic analysis model is solved to obtain the structural field variables of the radome at the end of the first impact. For the Nth hail impact, N≥2; execute the following loop steps: The structural field variables at the end of the (N-1)th impact are imported into the explicit dynamic analysis model of the Nth impact through field variable mapping. An explicit dynamic analysis model of the Nth impact containing historical damage states is constructed. The updated structural field variables at the end of the Nth impact are obtained by setting the hail parameters and the material parameters of the radome honeycomb sandwich panel of the Nth impact. Repeat the impact process multiple times until the preset M impact simulations are completed, M≥1; obtain the final cumulative damage state of the radome structure after M impacts.

2. The method for predicting the cumulative damage from repeated hail impacts on a composite material radome according to claim 1, characterized in that, After obtaining the final cumulative damage state, based on the final cumulative damage state, a post-damage mechanical analysis model of the radome honeycomb sandwich panel is constructed, or a quasi-static / low-speed load is directly applied to the explicit dynamic model corresponding to the final cumulative damage state to obtain the overall force-displacement response data of the radome structure. Based on the overall force-displacement response data, the equivalent stiffness degradation ratio and ultimate bearing capacity are calculated to obtain a quantitative evaluation result of the remaining stiffness and remaining strength of the structure.

3. The method for predicting the cumulative damage from repeated hail impacts on a composite material radome according to claim 1, characterized in that, The hail parameters include: initial velocity, diameter, incident direction and impact position of the hail, and the sandwich panel parameters include: panel thickness, number of layers, layup angle, honeycomb height and wall thickness.

4. The method for predicting the cumulative damage from repeated hail impacts on a composite material radome according to claim 1, characterized in that, The construction of the explicit dynamic analysis model of the hail-radome coupling system includes: A finite element model of the radome composite structure and a hail finite element model were constructed. The radome composite structure finite element model includes upper and lower composite material skins and a honeycomb core material. The upper and lower composite material skins were modeled using continuous shell elements to obtain the upper and lower composite material skin models. The honeycomb core material was modeled using continuous shell elements to obtain the honeycomb core material model. The hail finite element model was obtained by creating a spherical geometric model and discretizing the spherical geometric model into a series of interacting SPH particles using the smoothed particle hydrodynamics method. Anisotropic elastic parameters are defined for each ply of the upper and lower composite material skin models, and the Hashin damage initiation criterion and the progressive damage evolution model based on fracture energy are integrated to obtain upper and lower composite material skin models with material properties; the anisotropic constitutive model of Nomex material is applied to the honeycomb core material model, and the crushing characteristics are defined to obtain a honeycomb core material model with material properties; a strain rate-related elastoplastic constitutive model and a tensile failure criterion are defined for the SPH particles to obtain a hail model with material properties.

5. The method for predicting the cumulative damage from repeated hail impacts on a composite material radome according to claim 4, characterized in that, The construction of the explicit dynamic analysis model of the hail-radome coupling system also includes: In the global coordinate system, the hail model with material properties is positioned at a specified impact position relative to the radome composite structure model with material properties, obtaining the component positioning result; a first tie constraint is created between the upper surface of the honeycomb core material with material properties and the lower surface of the upper composite skin with material properties, and a second tie constraint is created between the lower surface of the honeycomb core material with material properties and the upper surface of the lower composite skin with material properties, obtaining the internal connection result; the contact interaction between the hail model and the radome upper skin model is defined using a general contact algorithm and a penalty function method, obtaining the external contact definition result; based on the component positioning result, the internal connection result, and the external contact definition result, an explicit dynamic analysis model of the static hail-radome coupled system is obtained; Based on the component positioning results, the internal connection results, and the external contact definition results, the analysis steps, loads, and boundary conditions are set, including: An explicit dynamic analysis step is established to simulate a brief impact event and set its time increment control parameters. Displacement constraints under actual working conditions are applied to the boundary of the radome composite structure model with material properties, and an initial velocity field is defined for the hail model with material properties, specifying the impact velocity and direction. This yields the explicit dynamic analysis model of the dynamic hail-radome coupled system, which is the complete explicit dynamic analysis model of the hail-radome coupled system.

6. The method for predicting the cumulative damage from repeated hail impacts on a composite material radome according to claim 1, characterized in that, The final cumulative damage state includes: the fiber / matrix tensile and compressive damage distribution of the upper and lower composite material skins, the crushed area of ​​the honeycomb core material, and the overall residual deformation.

7. The method for predicting the cumulative damage from repeated hail impacts on a composite material radome according to claim 1, characterized in that, The structural field variables at the end of the (N-1)th impact are imported into the explicit dynamic analysis model of the Nth impact through field variable mapping, specifically including: Using the result file of the final moment of the N-1th impact analysis as the source data, the structural field variables stored in it and located at the grid integration points are extracted; the structural field variables include: nodal displacement field defining the structural geometry, element stress field and plastic strain field defining the internal forces of the material, and damage variable field defining the degradation of material properties; By using state variable import and numerical interpolation algorithms, the structural field variables are mapped from the grid integration points corresponding to the data source to the grid positions corresponding to the explicit dynamic analysis model of the Nth impact, thus obtaining the mapped field variable data. The mapped field variable data is then used as the initial conditions for the Nth impact analysis and imported into the explicit dynamic analysis model of the Nth impact.

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