Optimization Calculation Method for Finite Element Model of High-Speed Dynamic Loading of Gradient Composites

Abstract

The present invention relates to the technical field of finite element simulation calculation, and proposes a finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials, comprising the following steps: establishing a two-dimensional axisymmetric structural model of a layered gradient configuration; describing the material properties of the two-dimensional axisymmetric structural model to obtain material parameters, and segmentally describing the shock adiabat to obtain a segmented mathematical relationship; correcting the shock wave velocity and particle velocity based on the shear modulus and yield strength to obtain a corrected shock wave velocity and a corrected particle velocity; fitting through the segmented mathematical relationship, the corrected shock wave velocity and the corrected particle velocity to obtain a corrected segmented mathematical relationship between the corrected shock wave velocity and the corrected particle velocity, and based on the material parameters and the corrected segmented mathematical relationship, generating a large number of sample data by using the Latin hypercube sampling method and the central composite design sampling method, evaluating the data points of the sample data through a multi-objective genetic algorithm to obtain optimized sample data; modeling based on the optimized sample data to obtain an initial optimal finite element model, and repeatedly verifying the initial optimal finite element model to obtain an optimal finite element model. The present invention realizes the automation of the modeling process, increases the final particle velocity, reduces the computational time cost at the same time, and improves the accuracy and computational efficiency of the model.

Description

Technical Field

[0001] The present invention relates to the technical field of finite element simulation calculations, and particularly relates to an optimized calculation method for a finite element model of high-speed dynamic loading of gradient composite materials. Background Art

[0002] The high-speed dynamic loading process of gradient composite materials often appears in the research on collision protection in the aerospace field. For example, the high-speed collision between the skin of an aircraft and high-speed flying objects such as birds, and the hypervelocity collision between space debris and satellites. Gradient composite materials are composed of multiple layers of different materials, and each layer of material has different physical and mechanical properties, enabling the material to absorb energy layer by layer when subjected to impact, reducing the impact on the next layer. In high-speed collisions, such as the collision between an aircraft and a bird or the collision between space debris and a satellite, the material needs to withstand extremely high instantaneous impact forces. Gradient composite materials effectively disperse and absorb these impact forces through their multi-layer structure.

[0003] In the existing finite element calculation models for high-speed dynamic loading of composite materials, for the mechanical description part of gradient composite materials, only the influence of the equation of state on the dynamic loading process is considered, and mainly rely on manually building finite element models strictly according to the experimental configuration. However, for the deformation simulation calculation of gradient composite materials in high-speed dynamic loading, there are problems of repeated and cumbersome modeling, resulting in low modeling accuracy. Summary of the Invention

[0004] In view of this, the present invention proposes an optimized calculation method for a finite element model of high-speed dynamic loading of gradient composite materials, which solves the problems of repeated and cumbersome modeling in the prior art for the deformation simulation calculation of gradient composite materials in high-speed dynamic loading.

[0005] The technical solution of the present invention is implemented as follows: The present invention provides an optimized calculation method for a finite element model of high-speed dynamic loading of gradient composite materials, including the following steps:

[0006] S1, establish a two-dimensional axisymmetric structure model of a layered gradient configuration;

[0007] S2, describe the material properties of the two-dimensional axisymmetric structure model through the equation of state and the constitutive model to obtain the material parameters of the two-dimensional axisymmetric structure model, the material parameters including shear modulus and yield strength, and segmentally describe the Hugoniot adiabat to obtain the segmented mathematical relationship between the shock wave velocity and the particle velocity;

[0008] S3, correct the shock wave velocity and the particle velocity based on the shear modulus and the yield strength to obtain the corrected shock wave velocity and the corrected particle velocity;

[0009] S4. Fit using the piecewise mathematical relationship, the corrected shock wave velocity, and the corrected particle velocity to obtain a corrected piecewise mathematical relationship between the corrected shock wave velocity and the corrected particle velocity. Based on the material parameters and the corrected piecewise mathematical relationship, use the Latin hypercube sampling method and the central composite design sampling method to generate a large number of sample data points, and evaluate the data points of the sample data through a multi-objective genetic algorithm to obtain optimized sample data;

[0010] S5. Based on the optimized sample data, perform modeling to obtain an initial optimal finite element model, and repeatedly verify the initial optimal finite element model to obtain a final optimal finite element model.

[0011] On the basis of the above technical solutions, preferably, step S2 includes:

[0012] The calculation formula of the equation of state is:

[0013]

[0014] where p is the pressure, p k (V) is the cold pressure, γ(V) is the equation-of-state coefficient, V is the specific volume, E is the specific internal energy, E k (V) is the cold energy, p T is the thermal pressure, E T is the thermal energy.

[0015] On the basis of the above technical solutions, preferably, step S2 further includes:

[0016] The calculation formula of the constitutive model is:

[0017]

[0018] where G is the shear modulus, G0 is the shear modulus at atmospheric pressure, G' p is the first derivative of the shear modulus with respect to pressure, G' T is the first derivative of the shear modulus with respect to temperature, p is the pressure, η is the material compressibility, T is the temperature, Y is the yield strength, Y0 is the yield strength at atmospheric pressure, Y' p is the first derivative of the yield strength with respect to pressure, Y' T is the first derivative of the yield strength with respect to temperature, β is the first correction parameter for the work hardening effect, n is the second correction parameter for the work hardening effect, and ε is the third correction parameter for the work hardening effect.

[0019] On the basis of the above technical solutions, preferably, step S2 further includes:

[0020] The piecewise mathematical relationship between the shock wave velocity and the particle velocity is:

[0021]

[0022] Among them, D is the shock wave velocity, u is the particle velocity, x is the critical velocity, and u 0,1 is the initial particle velocity before loading when the particle velocity is less than the critical velocity, and C 0,1 is the first linear fitting constant of the measured shock wave velocity and the particle velocity when the particle velocity is less than the critical velocity, λ1 is the second linear fitting constant of the measured shock wave velocity and the particle velocity when the particle velocity is less than the critical velocity, and u 0,2 is the initial particle velocity before loading when the particle velocity is not less than the critical velocity, and C 0,2 is the first non-linear fitting constant when the particle velocity is not less than the critical velocity, λ2 is the second non-linear fitting constant when the particle velocity is not less than the critical velocity, and τ is the quadratic term coefficient of the parabola when the particle velocity is not less than the critical velocity.

[0023] Based on the above technical solutions, preferably, step S3 includes:

[0024] The calculation formulas for the corrected shock wave velocity and the corrected particle velocity are:

[0025]

[0026] Among them, D' is the corrected shock wave velocity, D is the shock wave velocity, G0 is the shear modulus at atmospheric pressure, and G' p is the first derivative of the shear modulus with respect to pressure, and G' T is the first derivative of the shear modulus with respect to temperature, p is the pressure, η is the material compressibility, T is the temperature, m is the first correction parameter, a is the second correction parameter, l is the third correction parameter, k is the fourth correction parameter, b is the fifth correction parameter, u' is the corrected particle velocity, u is the particle velocity, x is the critical velocity, Y0 is the yield strength at atmospheric pressure, and Y' p is the first derivative of the yield strength with respect to pressure, and Y' T is the first derivative of the yield strength with respect to temperature, β is the first correction parameter for the work hardening effect, n is the second correction parameter for the work hardening effect, and ε is the third correction parameter for the work hardening effect.

[0027] Based on the above technical solutions, preferably, step S4 includes:

[0028] S41, designing multiple groups of geometric models of laminated gradient composites by using the Latin hypercube sampling method and the central composite design sampling method;

[0029] S42, establishing a non-linear regression response surface model, and evaluating all sample points through the multi-objective genetic algorithm to obtain optimized sample data.

[0030] Based on the above technical solutions, preferably, step S41 includes:

[0031] Taking the material parameters, the modified shock wave velocity, and the modified particle velocity as design variables, sampling design is carried out by using the Latin hypercube sampling method and the central composite design sampling method to generate multiple groups of geometric models of laminated gradient composites, and batch finite element simulation calculations are performed.

[0032] On the basis of the above technical solutions, preferably, step S42 includes:

[0033] Data fitting and accuracy verification are performed on the non-linear regression response surface model. Taking the peak velocity of the rear interface of the loaded sample as the output variable, all sample points are evaluated by a multi-objective genetic algorithm to obtain optimized sample data.

[0034] On the basis of the above technical solutions, preferably, step S5 includes:

[0035] S51, performing finite element simulation calculations on the optimized sample data, establishing the initial optimal finite element model in combination with boundary condition setting, mechanical description setting, and mesh generation, and carrying out explicit dynamics calculations;

[0036] S52, repeatedly verifying and performing performance evaluation on the initial optimal finite element model through the final particle velocity and the computational time cost to obtain the final optimal finite element model.

[0037] On the basis of the above technical solutions, preferably, step S1 includes:

[0038] S11, designing a multi-layer laminated gradient configuration according to the mechanical properties of the material under high-speed dynamic loading conditions, and determining the type, thickness, and arrangement order of each layer of material;

[0039] S12, simplifying the three-dimensional model by using a two-dimensional axisymmetric structure, and the two-dimensional axisymmetric structure model includes a gun barrel and multi-layer gradient composites.

[0040] The finite element model optimization calculation method for high-speed dynamic loading of a gradient composite material of the present invention has the following beneficial effects compared with the prior art:

[0041] (1) By combining the equation of state and the constitutive model to describe the mechanical material properties, and combining the response surface optimization method with the finite element calculation model, introducing the constitutive model and parameter correction, the comprehensive optimization of the finite element model for high-speed dynamic loading of gradient composite materials is realized, so that the comprehensive error of the particle velocity curve in each key area is controlled. Using the Latin hypercube sampling method to design multiple groups of models and evaluate a large number of sample points, the automation of the modeling process is realized. By simplifying the two-dimensional axisymmetric structure, the final particle velocity is increased, and at the same time the computational time cost is reduced, improving the accuracy and computational efficiency of the model;

[0042] (2) By establishing a piecewise mathematical relationship between the shock wave velocity and the particle velocity, using linear fitting and non-linear fitting methods to process different working conditions before and after the critical velocity respectively, and combining multiple physical quantities such as shear modulus, yield strength, pressure, and temperature to perform multi-parameter correction on the shock wave velocity and the particle velocity, the accurate description of the velocity change characteristics of gradient composites during high-speed dynamic loading is realized, and the accuracy of model calculation is improved;

[0043] (3) By introducing a constitutive model on the basis of introducing the equation of state, the material properties of gradient composites under high-speed dynamic loading are described. Especially, the accuracy of material parameters is improved in terms of pressure, specific volume, and specific internal energy, etc., and the behavior characteristics of shear modulus and yield strength under the changes of pressure and temperature are described in detail, thereby enhancing the reliability of the finite element model in simulating the high-speed dynamic loading process and realizing the accurate description of the mechanical properties of gradient composites under different environmental conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0045] Figure 1 It is a flow chart of an optimization calculation method for a finite element model of high-speed dynamic loading of a gradient composite material of the present invention;

[0046] Figure 2 It is a schematic diagram of an automated optimization calculation process for dynamic loading of a gradient composite material of the present invention;

[0047] Figure 3 It is a comparative curve graph of simulation calculation results after the constitutive model of the present invention is corrected;

[0048] Figure 4 It is a curve graph of the effect of improved simulation accuracy during the high-speed dynamic loading process of the present invention;

[0049] Figure 5 It is a schematic diagram of a dynamic loading simulation model of a multi-layer gradient composite material of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] The following will describe the technical solutions in the embodiments of the present invention clearly and completely in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0051] Please refer to Figure 1 , the present invention provides a finite element model optimization calculation method for high-speed dynamic loading of gradient composites, including the following steps:

[0052] S1. Establish a two-dimensional axisymmetric structural model with a layered gradient configuration;

[0053] S2. Describe the material properties of the two-dimensional axisymmetric structural model through the equation of state and the constitutive model to obtain the material parameters of the two-dimensional axisymmetric structural model. The material parameters include the shear modulus and the yield strength, and segmentally describe the shock adiabat to obtain the segmented mathematical relationship between the shock wave velocity and the particle velocity;

[0054] S3. Correct the shock wave velocity and the particle velocity based on the shear modulus and the yield strength to obtain the corrected shock wave velocity and the corrected particle velocity;

[0055] S4. Fit through the segmented mathematical relationship, the corrected shock wave velocity and the corrected particle velocity to obtain the corrected segmented mathematical relationship between the corrected shock wave velocity and the corrected particle velocity. Based on the material parameters and the corrected segmented mathematical relationship, use the Latin hypercube sampling method and the central composite design sampling method to generate a large number of sample data, and evaluate the data points of the sample data through the multi-objective genetic algorithm to obtain the optimized sample data;

[0056] S5. Build a model based on the optimized sample data to obtain the initial optimal finite element model, and repeatedly verify the initial optimal finite element model to obtain the final optimal finite element model.

[0057] Specifically, please refer to Figure 2, which is a schematic diagram of the dynamic loading process of the automated optimization calculation of gradient composites in the present invention. In this embodiment, according to the existing high-speed loading layered structure, the configuration of the gradient composite material is preliminarily designed through the automated calculation of the finite element model of the high-speed dynamic loading of the gradient composite material. The geometric configuration is established by inputting into the finite element simulation calculation program, and the preliminary establishment of the calculation model is completed by combining the boundary condition setting, advanced mechanical description setting, and mesh division. Further, explicit dynamics calculations are carried out in the finite element simulation calculation model, and the simulation calculation results of the material dynamic response behavior can be obtained through post-processing. For the results of the explicit dynamics simulation calculation, further automatic calculation of an enlarged sample can be carried out, and sampling design and evaluation can be performed. After optimization by the response surface method, taking the criterion of the maximum final velocity selected as an example, the optimal design of the gradient composite material structure can be carried out. Finally, repeated verification is carried out in cooperation with a model described by a high-precision and advanced mechanical model to ensure the correctness of the automated optimization.

[0058] In this embodiment, for the finite element simulation calculation of the dynamic deformation loading of multi-layer gradient composites, a suitable mechanical property description control equation is selected, and the structure of the gradient composite material is optimized by combining the response surface optimization method, so as to realize the establishment and simulation of a high-precision and automated finite element model.

[0059] In this embodiment, other types of suitable constitutive models can be selected for different materials, such as the Johnson-Cook constitutive model, the Zerilli–Armstrong constitutive model, etc. to correct the shock adiabatic line. In addition to the response surface optimization algorithm, simulated annealing algorithm, particle swarm algorithm, etc. can also be selected as alternative solutions for automated calculation.

[0060] Step S1 includes:

[0061] S11, design a multi-layered gradient configuration according to the mechanical properties of the material under high-speed dynamic loading conditions, and determine the type, thickness, and arrangement order of each layer of material;

[0062] S12, simplify the three-dimensional model by using a two-dimensional axisymmetric structure, and the two-dimensional axisymmetric structure model includes a gun barrel and multi-layer gradient composite materials.

[0063] Specifically, in this embodiment, a 20-layer laminated gradient configuration typical of the field is established. The finite element simulation model adopts a two-dimensional axisymmetric structure, which can save computing resources while ensuring overall accuracy. The Lagrangian algorithm calculates parameters with the deformation of the object, and the Eulerian algorithm extracts the state of the material at a fixed position, which are respectively applicable to the cases of small deformation and large deformation in high-speed dynamic loading. For the light gas gun launching device that generates high-speed dynamic deformation in the laboratory, where the deformation of the gun body is small and the deformation of the multi-layer gradient composite material is large, neither the pure Lagrangian algorithm nor the Eulerian algorithm is applicable. Therefore, the more advanced Lagrangian-Eulerian coupling algorithm is adopted in this embodiment.

[0064] When using the Lagrangian-Eulerian coupling algorithm to process the nodal stress-strain relationship, an appropriate time step is very important for describing the accuracy of numerical simulation. If the time step is too large, the accuracy of numerical simulation will be significantly reduced; if the time step is too small, it will increase the consumption of computing resources and lead to too long computing time. Therefore, preliminary calculations are required to determine the time step range to ensure the stable operation of the simulation program and guarantee the computing accuracy. For the model observation points for evaluating the loading effect, they are set at the rear interface of the gradient composite material loaded with the standard target material. The particle velocity profile curve measured here can well reflect the high-speed dynamic loading response characteristics of the gradient composite material.

[0065] Step S2 includes:

[0066] The calculation formula of the equation of state is:

[0067]

[0068] where p is the pressure, p k (V) is the cold pressure, γ(V) is the equation of state coefficient, V is the specific volume, E is the specific internal energy, E k (V) is the cold energy, p T is the thermal pressure, E T is the thermal energy.

[0069] The calculation formula of the constitutive model is:

[0070]

[0071] where G is the shear modulus, G0 is the shear modulus under normal pressure, G' p is the first derivative of the shear modulus with respect to pressure, G' T is the first derivative of the shear modulus with respect to temperature, p is the pressure, η is the material compressibility, T is the temperature, Y is the yield strength, Y0 is the yield strength under normal pressure, Y' p is the first derivative of the yield strength with respect to pressure, Y' Tis the first derivative of the yield strength with respect to temperature, β is the first correction parameter for the work-hardening effect, n is the second correction parameter for the work-hardening effect, and ε is the third correction parameter for the work-hardening effect.

[0072] The piecewise mathematical relationship between the shock wave velocity and the particle velocity is as follows:

[0073]

[0074] where D is the shock wave velocity, u is the particle velocity, x is the critical velocity, and u 0,1 is the initial particle velocity before loading when the particle velocity is less than the critical velocity, and C 0,1 is the first linear fitting constant between the measured shock wave velocity and the particle velocity when the particle velocity is less than the critical velocity, λ1 is the second linear fitting constant between the measured shock wave velocity and the particle velocity when the particle velocity is less than the critical velocity, and u 0,2 is the initial particle velocity before loading when the particle velocity is not less than the critical velocity, and C 0,2 is the first non-linear fitting constant when the particle velocity is not less than the critical velocity, λ2 is the second non-linear fitting constant when the particle velocity is not less than the critical velocity, and τ is the quadratic coefficient of the parabola when the particle velocity is not less than the critical velocity.

[0075] Specifically, in this embodiment, due to the strong empirical nature of traditional mechanical models, it is increasingly difficult to meet the ever-increasing simulation calculation requirements at the present stage, and there are the following two problems.

[0076] First, for materials such as Al, Ni, Zn, Cu, Pt, Pb, Ce, Ta, etc. that are tried in the high-speed dynamic loading of gradient composites, there is a situation where the material becomes more compressible or more difficult to compress as the impact pressure increases. At this time, the traditional linear relationship cannot well describe the mechanical behavior. Second, when the impact pressure is small and the particle velocity is low, the solid has a definite shape. To deform solid materials such as metals, a large external force must be applied. Especially when the impact pressure is small, simply considering the mechanical description of the equation of state of matter only reflects the response of the solid under hydrostatic pressure loading, and the low-pressure applicability of the "fluid approximation" model of materials has been questioned. Therefore, when the shock wave is very weak, the strength of the solid material in the shock adiabatic line cannot be ignored, and the empirical relationship obtained from medium- and high-pressure shock compression experiments may not be extrapolated to the low-pressure shock compression region. Therefore, in this embodiment, the shock adiabatic relationship of the material is described in a piecewise manner. When the velocity is less than the critical velocity, the traditional linear form is still used to describe the D-u relationship of the shock adiabatic line; when the velocity is greater than the critical velocity, the parabola equation form is used to describe the D-u relationship of the shock adiabatic line, and the mechanical behavior of the material under high impact pressure can be well described.

[0077] Step S3 includes:

[0078] The calculation formulas for the corrected shock wave velocity and the corrected particle velocity are as follows:

[0079]

[0080] Among them, D' is the corrected shock wave velocity, D is the shock wave velocity, G0 is the shear modulus at atmospheric pressure, G' p is the first derivative of the shear modulus with respect to pressure, G' T is the first derivative of the shear modulus with respect to temperature, p is the pressure, η is the material compressibility, T is the temperature, m is the first correction parameter, a is the second correction parameter, l is the third correction parameter, k is the fourth correction parameter, b is the fifth correction parameter, u' is the corrected particle velocity, u is the particle velocity, x is the critical velocity, Y0 is the yield strength at atmospheric pressure, Y p ' is the first derivative of the yield strength with respect to pressure, Y T ' is the first derivative of the yield strength with respect to temperature, β is the first correction parameter for the work hardening effect, n is the second correction parameter for the work hardening effect, and ε is the third correction parameter for the work hardening effect.

[0081] Specifically, in this embodiment, although the low-pressure region of the shock loading experiment is in the range less than 10 GPa, it still far exceeds the pressure range under civilian working conditions. Therefore, the SCG constitutive model, as a high-pressure constitutive model, still has good applicability for correcting the shock wave velocity and the particle velocity. The high-pressure yield effect of the material in high-speed dynamic loading will significantly change the high-pressure physical properties of the material, and has a greater impact on the shock wave velocity and the particle velocity during the high-speed dynamic loading process of the material. The shear modulus mainly affects the measurement of the particle velocity profile at the observation point. For the convenience of establishing the mechanical model, the above corrections are mainly made to the shock wave velocity and the particle velocity of the material, and the corrected corrected shock wave velocity and the corrected particle velocity are obtained. m is the first correction parameter, a is the second correction parameter, l is the third correction parameter, k is the fourth correction parameter, b is the fifth correction parameter, and their values are mainly determined by the material type and the shock pressure.

[0082] Step S4 includes:

[0083] S41, designing multiple groups of geometric models of laminated gradient composites by using the Latin hypercube sampling method and the central composite design sampling method;

[0084] Taking the material parameters, the corrected shock wave velocity, and the corrected particle velocity as design variables, using the Latin hypercube sampling method and the central composite design sampling method for sampling design, generating multiple groups of geometric models of laminated gradient composites, and performing batch finite element simulation calculations.

[0085] S42. Establish a non - linear regression response surface model, and evaluate all sample points through the multi - objective genetic algorithm to obtain optimized sample data;

[0086] Perform data fitting and accuracy verification on the non - linear regression response surface model. Using the peak velocity of the rear interface of the loaded sample as the output variable, evaluate all sample points through the multi - objective genetic algorithm to obtain optimized sample data.

[0087] Specifically, based on the simulation calculation of the high - speed dynamic loading finite - element model in this embodiment, an automated optimization calculation module is introduced and combined with the dynamic loading model. The ANSYS optimization design module is selected in this embodiment. After importing the finite - element simulation results into the ANSYS optimization design module, the structural characteristic parameters of the multi - layer gradient composite material are exported as design variables, and the peak velocity of the rear interface of the loaded sample is used as the output variable. Methods such as Latin hypercube sampling and central composite design sampling are used to design 780 geometric models of laminated gradient composite materials and perform batch automated finite - element calculations. Subsequently, after performing data fitting and verifying the accuracy of the non - linear regression response surface model, the simulation calculation results of any structural geometric model and the corresponding high - speed dynamic loading model can be obtained quickly and efficiently. The best results are obtained after evaluating 33,600 sample points through the multi - objective genetic algorithm. Manual modeling is carried out for the best optimization results and the calculation accuracy is fully guaranteed for result verification. The experimental results are as Figures 3 - 5 shown;

[0088] Please refer to Figure 3 , which is a comparison of the simulation calculation results after constitutive model correction under lower - speed and higher - speed loading, as Figure 3 shown. Whether under lower - speed or higher - speed loading conditions, in the high - speed dynamic loading condition of gradient composite materials, the gap between the simulation calculation results without constitutive model correction and the published experimental results is relatively large. The calculation model corrected by the SCG constitutive model has a comprehensive error of less than 5% in the first jump of the particle velocity curve, the elastic - plastic transition zone, the plastic rising zone, and the two platform velocity regions. However, the simulation calculation accuracy for the second particle velocity rising stage still needs to be improved, and this phenomenon will improve with the increase of the loading speed.

[0089] Step S5 includes:

[0090] S51. Perform finite - element simulation calculations on the optimized sample data, combine boundary condition setting, mechanical description setting, and mesh generation to establish the initial optimal finite - element model, and carry out explicit dynamics calculations;

[0091] S52. Repeatedly verify and perform performance evaluation on the initial optimal finite - element model through the final particle velocity and calculation time cost to obtain the final optimal finite - element model.

[0092] Specifically, please refer toFigure 4 , which is a graph showing the effect of improving the simulation accuracy during the high-speed dynamic loading process by combining the equation of state and the constitutive model to mechanically describe the two-dimensional axisymmetric structural model, as shown in Figure 4 . The results of the automated simulation calculation based on the high-precision model show that under the high-speed dynamic loading condition, the final particle velocity of the optimized gradient composite material structure increases from 7.54 km / s to 7.69 km / s. This indicates that it is difficult to significantly improve the final particle velocity by only performing assembly optimization on the original structure, but the time cost of the calculation can be reduced by 52.75%. By using the response surface optimization method in combination with the finite element calculation model, the automated modeling and calculation of the high-speed dynamic loading finite element model are realized, bringing the effects of simplifying the modeling process and improving the calculation efficiency. The results show that this method is correct and effective, and has strong operability. At the same time, the structure of the loaded sample can be manually designed to directly obtain the emission velocity of the loaded sample from the response surface, improving the calculation efficiency, saving time costs, and playing an important role in studying the propagation of shock waves in gradient flyers and realizing the research on the high-speed dynamic response mechanism of gradient composite materials. Please refer to Figure 5 , which is a schematic diagram of the dynamic loading simulation model of the gradient composite material in this embodiment.

[0093] The above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials, characterized in that: The following steps are involved: S1, establish a two-dimensional axisymmetric structural model of layered gradient configuration; S2, describing the material properties of the two-dimensional axisymmetric structure model by using the equation of state and the constitutive model to obtain material parameters of the two-dimensional axisymmetric structure model, wherein the material parameters include shear modulus and yield strength, and describing the impact adiabatic line in sections to obtain a section-wise mathematical relationship between the shock wave velocity and the particle velocity; S3, correcting the shock wave velocity and the particle velocity based on the shear modulus and the yield strength to obtain a corrected shock wave velocity and a corrected particle velocity; S4, fitting the piecewise mathematical relationship, the modified shock wave velocity and the modified particle velocity to obtain a modified piecewise mathematical relationship between the modified shock wave velocity and the modified particle velocity, generating a large amount of sample data by using a Latin hypercube sampling method and a central composite design sampling method based on the material parameters and the modified piecewise mathematical relationship, evaluating the data points of the sample data by using a multi-objective genetic algorithm to obtain optimized sample data; S5, modeling is performed based on the optimized sample data to obtain an initial optimal finite element model, and the initial optimal finite element model is repeatedly verified to obtain a final optimal finite element model.

2. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 1, characterized in that: Step S2 includes: The calculation formula of the equation of state is: Where p is pressure, p k (V) is the cold pressure, γ(V) is the coefficient of the equation of state, V is the specific volume, E is the specific internal energy, and E k (V) is the cold energy, p T is hot pressing, E T For thermal energy.

3. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 2, characterized in that: Step S2 also includes: The calculation formula of the constitutive model is: Where G is the shear modulus, G0 is the normal pressure shear modulus, G' p is the first derivative of shear modulus with respect to pressure, G' T is the first derivative of shear modulus with respect to temperature, p is pressure, η is material compression, T is temperature, Y is yield strength, Y0 is yield strength at normal pressure, and Y' p is the first-order derivative of yield strength with respect to pressure, Y T ' is the first derivative of yield strength with respect to temperature, β is the first correction parameter of work hardening effect, n is the second correction parameter of work hardening effect, and ε is the third correction parameter of work hardening effect.

4. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 3, characterized in that: Step S2 also includes: The piecewise mathematical relationship between the shock wave velocity and the particle velocity is: Where D is the shock wave velocity, u is the particle velocity, x is the critical velocity, and u 0,1 is the initial particle velocity before loading when the particle velocity is less than the critical velocity, C 0,1 is the first linear fitting constant of the measured shock wave velocity and particle velocity when the particle velocity is less than the critical velocity, λ1 is the second linear fitting constant of the measured shock wave velocity and particle velocity when the particle velocity is less than the critical velocity, u 0,2 is the initial particle velocity before loading when the particle velocity is not less than the critical velocity, C 0,2 is the first nonlinear fitting constant when the particle velocity is not less than the critical velocity, λ2 is the second nonlinear fitting constant when the particle velocity is not less than the critical velocity, and τ is the parabola quadratic term coefficient when the particle velocity is not less than the critical velocity.

5. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 4, characterized in that: Step S3 includes: The calculation formulas for the modified shock wave velocity and the modified particle velocity are: Where D' is the modified shock wave velocity, D is the shock wave velocity, G0 is the shear modulus at normal pressure, and G' p is the first derivative of shear modulus with respect to pressure, G' T is the first derivative of shear modulus with respect to temperature, p is pressure, η is material compression, T is temperature, m is the first correction parameter, a is the second correction parameter, l is the third correction parameter, h is the fourth correction parameter, b is the fifth correction parameter, u' is the corrected particle velocity, u is the particle velocity, x is the critical velocity, Y0 is the yield strength at normal pressure, Y p ' is the first-order derivative of yield strength to pressure, Y T ' is the first derivative of yield strength with respect to temperature, β is the first correction parameter of work hardening effect, n is the second correction parameter of work hardening effect, and ε is the third correction parameter of work hardening effect.

6. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 1, characterized in that: Step S4 includes: S41, designing multiple groups of layered gradient composite material geometric models using the Latin hypercube sampling method and the central composite design sampling method; S42, establishing a nonlinear regression response surface model, evaluating all sample points through the multi-objective genetic algorithm, and obtaining optimized sample data.

7. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 6, characterized in that: Step S41 includes: The material parameters, the modified shock wave velocity and the modified particle velocity are set as design variables, the Latin hypercube sampling method and the central composite design sampling method are used for sampling design, multiple groups of layered gradient composite material geometric models are generated, and batch finite element simulation calculations are performed.

8. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 7, characterized in that: Step S42 includes: The nonlinear regression response surface model was fitted with data and its accuracy was verified. The peak velocity of the rear interface of the loaded sample was used as the output variable. All sample points were evaluated by a multi-objective genetic algorithm to obtain the optimized sample data.

9. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 1, characterized in that: Step S5 includes: S51, performing finite element simulation calculation on the optimized sample data, establishing the initial optimal finite element model in combination with boundary condition setting, mechanical description setting and meshing, and carrying out explicit dynamics calculation; S52, repeatedly verifying and evaluating the performance of the initial optimal finite element model through final particle velocity and calculation time cost to obtain a final optimal finite element model.

10. The finite element model optimization calculation method for high-speed dynamic loading of gradient composite materials according to claim 1, characterized in that: Step S1 includes: S11, design a multi-layered gradient configuration according to the mechanical properties of the material under high-speed dynamic loading conditions, and determine the type, thickness and arrangement order of each layer of material; S12, using a two-dimensional axisymmetric structure to simplify the three-dimensional model, wherein the two-dimensional axisymmetric structure model includes a gun body and a multi-layer gradient composite material.

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