A method and system for simulating lightning damage to composite materials based on Direct FE2

Abstract

This invention provides a method and system for simulating lightning damage to composite materials based on Direct FE2, comprising: step S1, constructing a macroscopic finite element model and a microscopic Resonant Velocity (RVE) model of the composite material; step S2, calculating the scaling factor and adjusting the volume of the microscopic RVE model based on the extended Hill-Mandel energy equivalence condition; step S3, establishing direct constraints between the boundary nodes of the microscopic RVE model and the element nodes of the macroscopic finite element model, coupling the microscopic RVE model and the macroscopic finite element model to obtain the Direct FE2 model; and step S4, setting the lightning strike conditions required for lightning strike simulation on the Direct FE2 model and applying loads to obtain the potential field distribution and temperature field distribution. Therefore, this invention can preserve the microscopic properties of the fiber and matrix, and achieve accurate coupling and transmission of multiple physical fields and high-precision prediction at the microscopic scale.

Description

Technical Field

[0001] This invention relates to the field of composite material performance evaluation technology, specifically to a method and system for simulating lightning damage to composite materials based on Direct FE2. Background Technology

[0002] Advanced composite materials, with their high specific strength, high specific stiffness, excellent corrosion resistance, and high designability, have been increasingly widely used in cutting-edge fields such as aerospace, automotive manufacturing, and new energy. However, these materials also bring new challenges, with lightning strikes posing one of the most destructive natural threats. Unlike traditional metallic materials with excellent electrical conductivity, composite materials typically have low and significantly anisotropic electrical and thermal conductivity. This means that the huge current generated by a lightning strike cannot dissipate quickly, resulting in instantaneous extreme high temperatures in localized areas due to the Joule heating effect. This can cause severe damage such as resin matrix vaporization, fiber breakage, and even explosive delamination. To ensure flight safety and meet stringent airworthiness certification standards, accurate assessment of the lightning strike resistance of composite material structures is crucial.

[0003] Currently, evaluation methods mainly include physical experiments and numerical simulations. Physical experiments are the final verification standard, but they are costly and struggle to capture the internal transient physical details of the damage process. Numerical simulations mostly use homogenized models for multiphysics coupling analysis, but they are all based on the assumption of macroscopic homogenization, ignoring the geometric characteristics of the microstructure and failing to accurately capture key microscopic damage mechanisms such as stress concentration and debonding at the fiber / matrix interface. Using the traditional FE2 method to directly embed the material's microstructural response into the analysis of the macrostructure requires writing specific control scripts, presenting certain technical barriers and hindering its widespread application. Summary of the Invention

[0004] This invention is made to solve the above-mentioned problems, and aims to provide a method and system for simulating lightning damage to composite materials based on Direct FE2.

[0005] This invention provides a method for simulating lightning damage to composite materials based on Direct FE2, characterized by the following steps: Step S1, constructing a macroscopic finite element model and a microscopic Resonant Velocity (RVE) model of the composite material; Step S2, calculating the scaling factor and adjusting the volume of the microscopic RVE model based on the extended Hill-Mandel energy equivalence condition; Step S3, establishing direct constraints between the boundary nodes of the microscopic RVE model and the element nodes of the macroscopic finite element model, coupling the microscopic RVE model and the macroscopic finite element model to obtain the Direct FE2 model; Step S4, setting the lightning strike conditions required for lightning strike simulation on the Direct FE2 model, applying loads, and obtaining the potential field distribution and temperature field distribution.

[0006] The composite material lightning damage simulation method based on Direct FE2 provided by this invention may also have the following feature: the scaling factor is expressed as follows:

[0007]

[0008] in, The Gaussian integral weighting coefficients at the macroscopic integration point are given. Let be the determinant of the Jacobian matrix at the macroscopic integration point. For the point of integration The volume of the microscopic RVE model.

[0009] The composite material lightning damage simulation method based on Direct FE2 provided by this invention can also have the following features: when adjusting the volume of the microscopic RVE model, the principle of thermal scale separation is followed, and the characteristic diffusion time is much smaller than the characteristic load time.

[0010] The composite material lightning damage simulation method based on Direct FE2 provided by this invention may also have the following features: Step S3 includes the following sub-steps: Step S31, by using multi-point constraints, the difference of the generalized displacements of the microscopic RVE model relative to the two boundary nodes is linearly correlated with the nodal displacements of the macroscopic finite element model; Step S32, an additional constraint is added to directly correlate the generalized displacement of the center point of the microscopic RVE model with the generalized displacement field of the macroscopic finite element model.

[0011] The composite material lightning strike damage simulation method based on Direct FE2 provided by this invention may also have the following features: the lightning strike center region of the macroscopic finite element model adopts a refined mesh, while the region far from the center adopts a coarse mesh.

[0012] The composite material lightning damage simulation method based on Direct FE2 provided by this invention may also have the following features: the lightning strike conditions include electrical boundary conditions and thermal boundary conditions.

[0013] The composite material lightning damage simulation method based on Direct FE2 provided by this invention may also have the following feature: the electrical boundary condition is: the potential of the bottom, left and right boundaries of the Direct FE2 model is uniformly set to 0V.

[0014] The composite material lightning damage simulation method based on Direct FE2 provided in this invention also has the following characteristics: the thermal boundary conditions are as follows: thermal radiation follows the Stefan-Boltzmann law, and the heat flux density is calculated by the following formula:

[0015]

[0016] in, The surface emissivity of the composite material. It is the Stefan-Boltzmann constant. The instantaneous surface temperature of the Direct FE2 model. The ambient temperature.

[0017] This invention also provides a composite material lightning damage simulation system based on Direct FE2, characterized by the following features: a model building module for constructing a macroscopic finite element model and a microscopic Resonant Velocity (RVE) model; a scaling module for calculating a scaling factor and adjusting the volume of the microscopic RVE model based on the extended Hill-Mandel energy equivalence condition; a constraint module for establishing direct constraints between the boundary nodes of the microscopic RVE model and the element nodes of the macroscopic finite element model, coupling the microscopic RVE model and the macroscopic finite element model to obtain the Direct FE2 model; and a boundary condition application module for setting the lightning strike conditions required for lightning strike simulation on the Direct FE2 model and applying loads to obtain the potential field distribution and temperature field distribution.

[0018] The role and effect of invention

[0019] The method and system for simulating lightning damage to composite materials based on Direct FE2 according to the present invention includes the following steps: Step S1, constructing a macroscopic finite element model and a microscopic Resonant Velocity Variable (RVE) model of the composite material; Step S2, calculating the scaling factor and adjusting the volume of the microscopic RVE model based on the extended Hill-Mandel energy equivalence condition; Step S3, establishing direct constraints between the boundary nodes of the microscopic RVE model and the element nodes of the macroscopic finite element model, coupling the microscopic RVE model and the macroscopic finite element model to obtain the Direct FE2 model; Step S4, setting the lightning strike conditions required for lightning strike simulation on the Direct FE2 model, applying loads, and obtaining the potential field distribution and temperature field distribution. Therefore, the method and system for simulating lightning damage to composite materials based on Direct FE2 of the present invention can retain the microscopic characteristics of the fiber and matrix, and achieve accurate coupling and transmission of multiple physical fields and high-precision prediction at the microscopic scale. Attached Figure Description

[0020] Figure 1 This is a schematic flowchart of a composite material lightning damage simulation method based on Direct FE2 in an embodiment of the present invention.

[0021] Figure 2 These are standard current waveform diagrams and simplified current waveform diagrams in embodiments of the present invention.

[0022] Figure 3 This is a schematic diagram of the Direct FE2 model and the DNS model in an embodiment of the present invention.

[0023] Figure 4 This is a comparison diagram of the potential of some lightning strike maximum moment models in embodiments of the present invention.

[0024] Figure 5 This is a temperature change diagram at the lightning strike center point in an embodiment of the present invention.

[0025] Figure 6 This is an isotherm diagram at 300°C for the Direct FE2 model and the DNS model in an embodiment of the present invention.

[0026] Figure 7 This is a comparison chart of the computation time of the Direct FE2 model and the DNS model in an embodiment of the present invention.

[0027] Figure 8 This is a schematic diagram of a composite material lightning damage simulation system based on Direct FE2 in an embodiment of the present invention. Detailed Implementation

[0028] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the method and system for simulating lightning damage to composite materials based on Direct FE2.

[0029] Example

[0030] Figure 1 This is a schematic flowchart of a composite material lightning damage simulation method based on Direct FE2 in an embodiment of the present invention.

[0031] like Figure 1 As shown, this invention provides a method for simulating lightning damage to composite materials based on Direct FE2, comprising:

[0032] Step S1: Construct the macroscopic finite element model and the microscopic RVE model of the composite material. The macroscopic finite element model is used to characterize the structural information of the composite material, and the microscopic RVE model is used to characterize the microscopic material information. The material properties of the macroscopic finite element model are set to values ​​close to 0 so that its stiffness contribution can be ignored. For the microscopic RVE model, independent material properties are defined for different components.

[0033] Step S2 involves calculating the scaling factor and adjusting the volume of the microscopic RVE model based on the extended Hill-Mandel energy equivalence condition. The extended Hill-Mandel energy equivalence condition requires that the virtual work in the thermal and electrical domains at the macroscopic scale equals the volume average sum of the virtual work of all microscopic RVE models. By comparing the virtual work expressions calculated at the two scales, the coefficient of difference between them is obtained and defined as the scaling factor.

[0034] For two-dimensional problems, this goal can be achieved by scaling the thickness of the microscopic RVE model; while for three-dimensional problems, the microscopic RVE model needs to be scaled uniformly in three directions.

[0035] The scaling factor is expressed as follows:

[0036]

[0037] in, The Gaussian integral weighting coefficients at the macroscopic integration point are given. Let be the determinant of the Jacobian matrix at the macroscopic integration point. For the point of integration The volume of the microscopic RVE model.

[0038] Just make An expression equal to 1 satisfies the Hill-Mandell energy equivalence condition.

[0039] When adjusting the volume of the microscopic RVE model, the principle of thermal scale separation is followed, ensuring that the feature diffusion time is much smaller than the feature loading time, as shown in the following formula:

[0040] = <<

[0041] in, Characteristic diffusion time, This represents the feature length of the micro-RVE model. Indicates thermal conductivity, Indicates the characteristic load time.

[0042] In one embodiment, satisfying the Hill-Mandel condition can also be achieved by modifying the material constitutive equations. In the user-defined material subroutine, the homogenized stiffness matrix or thermoelectric conduction matrix of the calculated microscopic RVE model is multiplied by a scaling factor and then returned to the macroscopic integration point. This method is mathematically equivalent to scaling geometry and also satisfies the Hill-Mandel condition.

[0043] If the size of the microscopic RVE model is too large, the microscopic thermal inertia is significant, leading to uneven temperature distribution inside the microscopic RVE model. In this case, the true temperature field at the microscopic scale is defined as follows:

[0044]

[0045] in, Represents microscopic local coordinates. This represents the true temperature field at the microscopic scale. Represents the macroscopic temperature field. This represents the linear change term caused by the macroscopic temperature gradient. This represents a microscopic perturbation. In a microscopic RVE model that violates the scale separation criterion, the enforced center point constraint ( This will cause non-physical temperature distortions near the constraint points, which will prevent the model from accurately reflecting the average temperature response of the microscopic RVE model, ultimately leading to the failure of macroscopic temperature prediction.

[0046] Compared to heat conduction, the electric potential field can reach equilibrium in a very short time, and the size of the microscopic RVE model has a negligible impact on the accuracy of electric field calculations. Therefore, for lightning strike problems, a smaller-sized microscopic RVE model should be selected to satisfy the thermal scale separation assumption.

[0047] Step S3: Establish direct constraints between the boundary nodes of the micro RVE model and the element nodes of the macro finite element model, and couple the micro RVE model with the macro finite element model to obtain the Direct FE2 model.

[0048] Step S3 includes the following sub-steps:

[0049] Step S31: Through multi-point constraints, the difference in generalized displacements of the microscopic RVE model relative to the two boundary nodes is linearly correlated with the nodal displacements of the macroscopic finite element model, as shown in the following formula:

[0050]

[0051]

[0052]

[0053]

[0054] in, Indicates temperature. Represents electric potential, , , , These represent the right, left, upper, and lower boundaries of the microscopic RVE model, respectively. Let be the length of the microscopic RVE model in the 1 direction (from left to right). This represents the length of the microscopic RVE model in two directions (from bottom to top). Subscript and These represent the partial derivatives of the variable in directions 1 and 2, respectively.

[0055] Among them, multi-point constraints are implemented using the multi-point constraint (MPC) function commonly used in commercial finite element software.

[0056] Step S32 adds an additional constraint, directly relating the generalized displacement of the center point of the microscopic RVE model to the generalized displacement field of the macroscopic finite element model, as shown in the following formula:

[0057]

[0058]

[0059] in, The coordinates of the center point of the microscopic RVE model. These are the coordinates of the corresponding Gaussian point in the macroscopic finite element model.

[0060] In the macroscopic finite element model, a fine mesh is used in the central region of the lightning strike, while a coarse mesh is used in the region far from the center.

[0061] Step S4: Set the lightning strike conditions required for the lightning strike simulation for the Direct FE2 model, and apply the load to obtain the electric potential field distribution and temperature field distribution.

[0062] The lightning strike conditions include electrical boundary conditions and thermal boundary conditions.

[0063] The electrical boundary conditions are as follows: the potentials of the bottom, left, and right boundaries of the Direct FE2 model are uniformly set to 0V. This is equivalent to grounding these boundaries, allowing lightning current injected from the top to flow smoothly out of the Direct FE2 model.

[0064] The thermal boundary conditions are as follows: thermal radiation follows the Stefan-Boltzmann law, and the heat flux density is calculated by the following formula:

[0065]

[0066] in, The surface emissivity of the composite material. It is the Stefan-Boltzmann constant. The instantaneous surface temperature of the Direct FE2 model. The ambient temperature.

[0067] This invention automates the modeling process by processing input text files using a Python script. First, a macroscopic model input file and a microscopic model input file are input into the Python script. The script collects macroscopic-scale grid node information and calculates the coordinates of integration points. Then, the microscopic RVE model is scaled down at the Gaussian point of the macroscopic-scale grid to satisfy the homogenization condition. Next, a set of boundary nodes for the microscopic RVE model is established, paired with face, edge, and vertex node sets. Multi-point constraint equations are applied to the boundary nodes and centroid (i.e., the geometric center of the microscopic RVE model) of each microscopic RVE model. Finally, the input file for generating the Direct FE2 model is output. The specific steps include the following processing logic, and its pseudocode implementation is as follows:

[0068]

[0069] The automated modeling process described above can also be implemented in other ways. Besides Python, other programming languages ​​such as MATLAB, Fortran, or C++ can be used to generate input files containing complete model information and constraint relationships. Furthermore, this embodiment is not limited to ABAQUS software; it can also be applied to other commercial finite element software platforms that support multi-point constraints and script programming, such as ANSYS and COMSOL.

[0070] Figure 2 These are standard and simplified current waveform diagrams from embodiments of the present invention. Figure 2 As shown, this waveform is already specified in MIL (Military Standard) and SAE (Society of Automotive Engineers Standard). Figure 2 Figure (a) shows the typical segmented lightning strike current, where component A is the initial return stroke current, characterized by a high peak value, steep rise time, and short duration, significantly impacting material damage. Component B is the intermediate current, providing some charge transfer after the return stroke. Component C is the continuous current, transferring the main charge over a longer period with a smaller amplitude, typically leading to heat accumulation and ablation. Component D is the second strike current, appearing as a short pulse with a relatively high peak value. Subsequent results verification primarily focuses on the linearly simplified segment A current. Figure 2 In (b), the peak current of segment A is taken as 40 kA and the duration is 30 μs. Since directly applying the original standard waveform would increase the requirements for time step and convergence in transient solutions, this paper simplifies the current of segment A linearly. By keeping the peak current and the duration consistent, the influence of the waveform on numerical stability is reduced, thereby improving computational efficiency without changing the current path and relative distribution.

[0071] This embodiment uses a two-dimensional finite element model of the cross-section of the lightning strike area as an example for detailed explanation. In this embodiment, the macroscopic finite element model is a two-dimensional square plate with a geometric dimension of 8×4 mm, and the element used is a four-node coupled electro-thermal quadrilateral element (DC2D4E). A microscopic RVE model is also established simultaneously.

[0072] Figure 3 This is a schematic diagram of the Direct FE2 model and the DNS model in an embodiment of the present invention. Figure 3 The fiber volume fraction in the Direct FE2 model is set to 28.27%. It should be noted that the Direct FE2 method is not limited to a single fiber arrangement. For RVE models with different fiber arrangements that satisfy periodic patterns (e.g., random distribution, hexagonal distribution, central distribution, etc.) and different fiber volume fractions, the same process can be used to establish micro-units and embed them into the macroscopic finite element solution framework. When the microstructure is extended to a three-dimensional model, the Direct FE2 method remains applicable, but the computational cost increases significantly.

[0073] Based on the above considerations, to ensure the effectiveness of the method while also considering computational efficiency, this embodiment of the invention selects a two-dimensional RVE model with a central arrangement for comparative verification. The fibers and matrix inside the RVE are given independent material properties, and the specific material parameters are shown in Table 1.

[0074]

[0075] This embodiment additionally establishes a direct numerical simulation (DNS, as shown in the example). Figure 3 The model shown is used to verify the accuracy of the DirectFE2 method. In the DNS model, the fibers are distributed in a periodic circular array within the cross-section, with the remaining area serving as the matrix. The DirectFE2 model achieves macro- and micro-scale coupling. At the macro level, the overall electrothermal response is described using a finite element mesh of the cross-sectional structure, while at the meso level, the Resonant Vessel (RVE) is embedded at the macro-integration point. The 0.08 mm marked in the figure represents the characteristic scale of the microstructure, used to determine the RVE size, fiber geometry, and the corresponding mesh generation datum.

[0076] The same loads and boundary conditions were applied to both the Direct FE2 and DNS models. The mesh size of the DNS model was set to be the same as that of the original microscopic RVE model (the mesh count should remain unchanged after scaling down the microscopic RVE model). The initial temperature field of the entire model was set to 25℃. Thermal radiation boundary conditions were applied to the top and left and right boundaries of the model, with a surface emissivity of 0.9. The lightning load was represented by a linearly distributed current and acted within a 2mm radius in the middle of the model. The lightning current was injected from a designated location on the upper boundary of the cross section, and the potential of the bottom, left, and right boundaries of the model was uniformly set to 0 V, equivalent to grounding boundaries, so that the current injected from the upper boundary could flow out smoothly through these boundaries. Thermal radiation was also added to the top, left, and right sides of the model.

[0077] To verify the effectiveness and accuracy of the method proposed in this invention, the simulation results obtained by the Direct FE2 method will be directly compared and analyzed with the results of the DNS model.

[0078] Figure 4 This is a comparison diagram of the potential of some lightning strike maximum moment models in embodiments of the present invention.

[0079] like Figure 4 As shown, the potential fields of the DNS model and the Direct FE2 model at the maximum moment of lightning strike are compared. Figure 4 (a) shows the potential field distribution of the DNS model, (b) shows the potential field distribution of the Direct FE2 model for a large-size RVE, and (c) shows the potential field distribution of the Direct FE2 model for a small-size RVE. It can be clearly seen from the figures that the overall distribution of the potential field predicted by the two methods is almost identical. From a numerical perspective, using… Figure 4 The result of (a) is used as the benchmark solution for peak comparison. Figure 4 The peak potential of (a) is approximately 3.184 V. Figure 4 (b) has a peak potential of approximately 3.173 V and a relative error of approximately 0.35%. Figure 4 The peak potential of (c) is 3.171 V, with a relative error of approximately 0.41%. The deviations of both Direct FE2 models from the DNS model in peak potential are less than 0.5%. Given the material conductivity and electrical boundary conditions, the consistency of the potential field directly determines the consistency of the spatial distribution of the potential gradient and current density. The Joule heating in subsequent thermal analysis is also controlled by the potential gradient. The consistency of the baseline solutions of the Direct FE2 and DNS models indicates their effectiveness for lightning strike problems. Conversely, significant deviations in the potential distribution will lead to the accumulation of errors in the current density and heat source terms, thus affecting damage prediction.

[0080] Figure 5This is a temperature change diagram at the lightning strike center point in an embodiment of the present invention. For example... Figure 5 As shown, Figure 5 (a) shows the temperature change at the lightning strike center within 0.05 s, and (b) shows the temperature change at the lightning strike center during the lightning strike process, used to compare the prediction performance of different models. The temperature change at the lightning strike center is shown for the DNS model and three different Direct FE2 models. D-FE-L represents a large-size RVE with a 0.1 mm macro-grid in the lightning strike center region; D-FE-S represents a small-size RVE with a 0.1 mm macro-grid in the lightning strike center region; and D-FE-SS represents a small-size RVE with a refined 0.05 mm macro-grid. The results show that: D-FE-L, due to its large RVE size, exhibits significant microscopic thermal inertia effects, leading to an underestimation of the peak temperature; D-FE-S uses a small-size RVE to eliminate thermal inertia, but the 0.1 mm macro-grid is relatively coarse and cannot accurately describe the lightning strike center temperature, resulting in a still low peak prediction; D-FE-SS simultaneously satisfies both small-size RVE and refined grid, and its calculation results are highly consistent with the DNS benchmark solution. To provide an objective and quantitative comparison, the peak temperature at the end of the lightning strike was used as the evaluation index, and the DNS model results were used as the benchmark solution. The relative error of the D-FE-L model was approximately 17.0%; the relative error of the D-FE-S model was approximately 8.8%; and the relative error of the D-FE-SS model was approximately 2.1%. The dominant heat source for lightning strike heating is Joule heating, and the lightning strike center point is usually the region with the largest potential gradient and the most concentrated Joule heating. The peak temperature, heating rate, and decay characteristics at this point are most sensitive to the model and mesh size. Based on this, this embodiment selects the temperature history at the lightning strike center point as the comparison index, mainly to verify the scale separation hypothesis and the necessity of macroscopic mesh refinement in the lightning strike region. Furthermore, the Direct FE2 model can simultaneously match the benchmark results during both the short-term rapid heating phase and the long-term decay phase, proving the reliability of the Direct FE2 model.

[0081] Figure 6 This is an isotherm diagram at 300°C for the Direct FE2 model and the DNS model in an embodiment of the present invention. Figure 6 As shown, Figure 6 (a) shows the 300℃ isotherm plot of the DNS model, and (b) shows the 300℃ isotherm plot of the Direct FE2 model. The regions corresponding to the 300℃ isotherms are also marked in the figures to compare the differences in the range and shape of the high-temperature influence areas predicted by the two models. Furthermore, the areas within the 300℃ isotherms of the DNS and Direct FE2 models are compared, with an error of approximately 1.78% in width and approximately 3.67% in depth. Figure 6The temperature field prediction results are transformed into a meaningful threshold boundary, and based on this, the predictive ability of the Direct FE2 model for lightning thermal damage is initially evaluated. Comparing the isotherm positions, envelope areas, and shapes obtained from the DNS model and the Direct FE2 model essentially compares whether the two models' predictions of the high-temperature influence zone resulting from the combined effects of Joule heating and thermal diffusion are consistent. If the two models show a high degree of agreement in terms of range and shape, the Direct FE2 model's prediction of the lightning thermal damage area can be preliminarily considered reliable.

[0082] The lightning damage simulation method for composite materials based on Direct FE2 of this invention is applicable not only to two-dimensional models but also to three-dimensional models. This characteristic makes the method widely applicable and valuable in engineering applications, providing strong support for the assessment of lightning damage to composite materials.

[0083] In a further embodiment, the composite material lightning damage simulation method based on Direct FE2 of the present invention may also include the coupling of mechanical fields. The constraints include not only degrees of freedom such as temperature and electric potential, but also degrees of freedom of displacement, thereby enabling the prediction of mechanical damage such as matrix cracking and delamination caused by thermal expansion and gas pressure.

[0084] Figure 7 This is a comparison chart of the computation time of the Direct FE2 model and the DNS model in an embodiment of the present invention.

[0085] like Figure 7As shown in the figure, the computation time of the DNS, D-FE-S, and D-FE-SS models under the same working conditions is compared to characterize the computational efficiency improvement of the proposed method compared to DNS. Compared to direct numerical simulation, which requires extremely detailed micro-mesh division of the full-size structure, this embodiment significantly reduces the overall degrees of freedom by using a fine mesh in the lightning strike area and a coarser mesh in the area far from the center, thereby shortening the computation time. Under the condition of comparable computational accuracy, the actual computation time (Wallclock Time) of the DNS model is 1552 seconds, while that of the D-FE-SS model is only 230 seconds. The proposed method improves computational efficiency by approximately 6.7 times while maintaining high accuracy. The DNS model needs to distinguish the fiber and matrix microstructures and perform fine mesh discretization throughout the entire computational domain, resulting in a large number of degrees of freedom, numerous time steps, and high solution cost per step. In contrast, the Direct FE2 model significantly reduces the global degrees of freedom and the size of the linear equation system by using a coarser structural mesh at the macroscopic level and calling RVE only at selected macroscopic integration points to provide an equivalent response, thereby improving computational efficiency. Furthermore, this embodiment does not simplify the composite material into a single anisotropic material, but instead performs real-time calculations by calling RVE at the integration point. This preserves the non-homogeneity information at the microscale, providing a clear physical explanation and quantitative prediction for the initiation and evolution of microscopic damage within the material, overcoming the limitations of traditional homogenization models that cannot reveal microscopic failure mechanisms.

[0086] Figure 8 This is a schematic diagram of a composite material lightning damage simulation system based on Direct FE2 in an embodiment of the present invention.

[0087] like Figure 8 As shown, this embodiment also provides a composite material lightning damage simulation system 100 based on Direct FE2, including: a model building module 10, a scaling module 20, a constraint module 30, and a boundary condition application module 40.

[0088] The model building module 10 uses the above step S1 to build the macroscopic finite element model and the microscopic RVE model.

[0089] The scaling module 20 uses step S2 described above to calculate the scaling factor and adjust the volume of the microscopic RVE model based on the extended Hill-Mandel energy equivalence condition.

[0090] The constraint module 30 uses the above step S3 to establish direct constraints between the boundary nodes of the micro RVE model and the element nodes of the macro finite element model, thereby coupling the micro RVE model and the macro finite element model to obtain the Direct FE2 model.

[0091] The boundary condition application module 40 uses the above step S4 to set the lightning strike conditions required for lightning strike simulation of the Direct FE2 model and apply loads to obtain the electric potential field distribution and temperature field distribution.

[0092] The role and effect of the embodiments

[0093] According to the Direct FE2-based composite material lightning damage simulation method and system involved in this embodiment, it includes: step S1, constructing a macroscopic finite element model and a microscopic RVE model of the composite material; step S2, calculating the scaling factor and adjusting the volume of the microscopic RVE model based on the extended Hill-Mandel energy equivalence condition; step S3, establishing direct constraints between the boundary nodes of the microscopic RVE model and the element nodes of the macroscopic finite element model, coupling the microscopic RVE model and the macroscopic finite element model to obtain the Direct FE2 model; step S4, setting the lightning strike conditions required for lightning strike simulation on the Direct FE2 model, applying loads, and obtaining the potential field distribution and temperature field distribution. Therefore, the Direct FE2-based composite material lightning damage simulation method and system of this invention can retain the microscopic characteristics of fibers and matrix, and achieve accurate coupling and transmission of multiple physical fields and high-precision prediction at the microscopic scale.

[0094] This embodiment predicts the macroscopic behavior of composite materials based solely on the material properties of the basic components. For composite materials with different microstructures but the same material system, there is no need to repeatedly calibrate their macroscopic performance parameters. By changing the geometric features of the microscopic model, macroscopic thermoelectric coupling analysis can be achieved, thus reducing the simulation calculation cost.

[0095] This embodiment constructs a scale separation criterion adapted to lightning strike simulation. At the macroscopic level, a variable-density mesh generation strategy is adopted, effectively solving the problem that linear interpolation shape functions cannot accurately capture the maximum electric potential and temperature gradient at the lightning strike center, balancing computational accuracy and efficiency. At the microscopic level, strict thermal scale separation requirements are established. By adjusting the RVE size, it is ensured that the diffusion time of microscopic features is much shorter than the macroscopic load time, greatly reducing the point-constrained temperature distortion caused by microscopic thermal inertia, and achieving high-precision prediction of the electric potential and temperature fields.

[0096] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for simulating lightning damage to composite materials based on Direct FE2, characterized in that, include: Step S1: Construct the macroscopic finite element model and the microscopic RVE model of the composite material; Step S2: Calculate the scaling factor based on the extended Hill-Mandel energy equivalence condition and adjust the volume of the microscopic RVE model; Step S3: Establish direct constraints between the boundary nodes of the microscopic RVE model and the element nodes of the macroscopic finite element model, and couple the microscopic RVE model with the macroscopic finite element model to obtain the Direct FE2 model; Step S4: Set the lightning strike conditions required for lightning strike simulation for the Direct FE2 model, and apply loads to obtain the potential field distribution and temperature field distribution.

2. The method for simulating lightning damage to composite materials based on Direct FE2 according to claim 1, characterized in that: in, The scaling factor is expressed as follows: in, The Gaussian integral weighting coefficients at the macroscopic integration point are given. Let be the determinant of the Jacobian matrix at the macroscopic integration point. For the point of integration The volume of the microscopic RVE model.

3. The method for simulating lightning damage to composite materials based on Direct FE2 according to claim 1, characterized in that: in, When adjusting the volume of the microscopic RVE model, the principle of thermal scale separation is followed to ensure that the feature diffusion time is much smaller than the feature loading time.

4. The method for simulating lightning damage to composite materials based on Direct FE2 according to claim 1, characterized in that: in, Step S3 includes the following sub-steps: Step S31: Through multi-point constraints, the difference of the generalized displacements of the microscopic RVE model relative to the two boundary nodes is linearly correlated with the nodal displacements of the macroscopic finite element model. Step S32: Add an additional constraint to directly associate the generalized displacement of the center point of the microscopic RVE model with the generalized displacement field of the macroscopic finite element model.

5. The method for simulating lightning damage to composite materials based on Direct FE2 according to claim 1, characterized in that: in, The macroscopic finite element model uses a fine mesh in the center region of the lightning strike and a coarse mesh in the region far from the center.

6. The method for simulating lightning damage to composite materials based on Direct FE2 according to claim 1, characterized in that: in, The lightning strike conditions include electrical boundary conditions and thermal boundary conditions.

7. The method for simulating lightning damage to composite materials based on Direct FE2 according to claim 6, characterized in that: in, The electrical boundary condition is as follows: the potential of the bottom, left and right boundaries of the Direct FE2 model is uniformly set to 0V.

8. The method for simulating lightning damage to composite materials based on Direct FE2 according to claim 6, characterized in that: in, The thermal boundary conditions are as follows: thermal radiation follows the Stefan-Boltzmann law, and the heat flux density is calculated by the following formula: in, The surface emissivity of the composite material. It is the Stefan-Boltzmann constant. The instantaneous surface temperature of the Direct FE2 model. The ambient temperature.

9. A composite material lightning strike damage simulation system based on Direct FE2, characterized in that, include: The model building module is used to build macroscopic finite element models and microscopic RVE models; A scaling module is used to calculate the scaling factor based on the extended Hill-Mandel energy equivalence condition and adjust the volume of the microscopic RVE model; The constraint module is used to establish direct constraints between the boundary nodes of the microscopic RVE model and the element nodes of the macroscopic finite element model, and to couple the microscopic RVE model and the macroscopic finite element model to obtain the Direct FE2 model. The boundary condition application module is used to set the lightning strike conditions required for lightning strike simulation on the Direct FE2 model and apply loads to obtain the electric potential field distribution and temperature field distribution.

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