A design and manufacturing method of a constant cross-section explosion load simulator based on gradient elastic metamaterials
By using gradient elastic metamaterial design and additive manufacturing, the problems of single-failure and local buckling in existing simulators have been solved, enabling non-destructive reuse and high-precision waveform simulation of the equal-section simulator, which is suitable for simulating various explosion waveforms.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-27
- Publication Date
- 2026-06-26
AI Technical Summary
Existing explosive load simulators are irreversibly damaged after a single use or prone to local buckling instability under high-speed impact, resulting in high cost, low testing efficiency and severe waveform distortion, making it difficult to achieve high-precision reusability and stable launch.
A uniform cross-section explosion load simulator based on gradient elastic metamaterials is designed. By using the one-dimensional elastic wave propagation inverse design theory and combining the impedance gradient correction factor, a three-dimensional metamaterial model with a continuous gradient distribution is generated. The simulator is manufactured using recoverable elastic materials through additive manufacturing to ensure that it maintains pure elastic deformation and can be reused without damage under strong impact.
It enables the simulator to be reused without damage under strong dynamic loads, maintains waveform accuracy, reduces experimental costs, improves testing efficiency, and ensures stable fit and sealing with the launching device. It is suitable for simulating various explosion waveforms.
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Figure CN122287222A_ABST
Abstract
Description
Technical Field
[0001] In the field of impact loading, this specifically relates to a reusable, constant-section explosive load simulator based on gradient elastic metamaterials and its design method. Background Technology
[0002] In fields such as vehicle and personnel protection, components may be subjected to strong dynamic loads such as explosions during service. To improve protective capabilities, researchers have developed numerous novel high-strength, high-toughness, lightweight composite structures (such as lattice sandwich structures and honeycomb sandwich structures) in recent years, necessitating extensive explosive impact testing to evaluate their actual protective performance. However, real explosive explosion experiments are extremely dangerous, require stringent site conditions, and are extremely expensive, making them difficult to conduct widely in conventional laboratories. Real explosive loads (such as the initial shock wave in air or underwater) are characterized by "instantaneous strong dynamics," meaning they reach peak pressure instantaneously and then decay in an approximately exponential manner. To safely and economically test novel structures in the laboratory, using lightweight gas cannons or Hopkinson bar-fired simulated projectiles to accurately reproduce this nonlinear decaying explosion waveform has become a core research method in this field.
[0003] Existing methods for simulating explosive loads mainly suffer from the following technical bottlenecks: The first type uses gradient foam metal or plastic multicellular bullets. These simulators simulate load attenuation through the gradient distribution of internal pores, but their deformation mechanism is plastic crushing failure. Therefore, these simulators suffer irreversible permanent damage after a single impact, making them unusable and resulting in high per-test costs and low testing efficiency for blast resistance experiments. The second type uses variable impedance elastic rods designed based on the reverse propagation of elastic waves. These simulators achieve reusability through recoverable elastic materials, but their geometry is typically a solid conical rod with a variable cross-section and a thinner tail, or a cavity with a constant outer diameter but a variable cross-section inside. The former is difficult to fit snugly into the barrel of a gas cannon, leading to air leakage and yaw problems during firing. The latter, while perfectly fitting into the barrel, has an extremely thin tail wall and lacks radial support. When the shock wave generated by the simulator impacts the target, it easily causes local yielding when transmitted to the extremely thin tail, resulting in an instantaneous loss of structural stiffness and severe waveform distortion.
[0004] In summary, there is an urgent need in this field for a high-precision explosive load simulator that can achieve elastic, non-destructive, and reusable operation, maintain a standard constant cross-sectional shape to adapt to stable air gun firing, and whose internal structure has strong resistance to buckling instability under high-speed impact. Summary of the Invention
[0005] To address the problems of high single-use cost and severe distortion of load waveform caused by local buckling instability of thin tubes with variable cross-section elastic rods under high-speed impact, this invention provides a design method for a uniform cross-section explosive load simulator based on gradient elastic metamaterials. This method not only enables lossless, purely elastic reusability but also allows for perfectly stable launch with a standard uniform cross-section shape, exhibiting excellent anti-instability capability and waveform fidelity under strong dynamic loads.
[0006] To achieve the above objectives, the first aspect of the present invention provides a design method for a uniform cross-section explosion load simulator based on a gradient elastic metamaterial, comprising the following steps:
[0007] S1, obtain the pressure-time evolution parameters of the target explosive load, the initial impact velocity parameters, and the impedance parameters of the impacted target plate; while keeping the macroscopic cross-sectional area of the simulator constant, based on the one-dimensional elastic wave propagation reverse design theory, derive the ideal equivalent wave impedance gradient distribution law required for the equal cross-section simulator to realize the target explosive load along the axial direction.
[0008] S2, Select the unit cell configuration of the three-dimensional elastic metamaterial, calculate and establish the mechanical mapping relationship between the relative density of the unit cell and its equivalent elastic modulus and equivalent density; Substitute the ideal equivalent wave impedance gradient distribution law into the mechanical mapping relationship, and solve the spatial relative density distribution function of the simulator along the axial direction; By continuously changing the geometric characteristic parameters of the unit cell along the axial direction, generate the initial geometric model of the three-dimensional metamaterial with an outer contour of a uniform cross-section cylinder and an internal pore distribution of continuous gradient.
[0009] S3. Based on the initial geometric model of the three-dimensional metamaterial generated in S2, a finite element model is constructed, and explicit dynamic analysis is performed to extract the simulated load waveform of the impact contact interface. The simulated load waveform is compared with the target explosion pressure-time curve and the waveform difference is calculated. If the waveform difference does not meet the preset tolerance requirements, an impedance gradient correction factor containing a relaxation factor is generated. The spatial relative density distribution function is nonlinearly iteratively corrected using this correction factor. The three-dimensional geometric model is regenerated based on the corrected spatial relative density distribution function and the dynamic analysis is returned to be performed until the waveform difference meets the preset tolerance requirements. The final three-dimensional metamaterial geometric model is then output.
[0010] Furthermore, in step S1, the pressure-time evolution parameters are used to characterize the explosive load waveform, which includes instantaneous surge and nonlinear decay characteristics, including peak overpressure, positive phase time, and decay constant.
[0011] Furthermore, in step S1, the macroscopic cross-sectional area being constant means that the outer contour of the simulator, i.e., the part in contact with the launching device such as the air cannon, maintains a constant diameter.
[0012] Furthermore, in step S1, the core calculation formula of the elastic wave propagation reverse design theory is as follows:
[0013] In the formula, λ is a dimensionless position parameter, and ξ(0) is the initial wave impedance at the impact end.
[0014] Furthermore, in step S2, the unit cell configuration of the three-dimensional elastic metamaterial is a three-period minimal surface (TPMS) structure without abrupt changes in cross-sectional area.
[0015] Furthermore, in step S2, the geometric characteristic parameters of the unit cell refer to parameters such as the wall thickness and rod diameter of the unit cell, but do not include the unit cell size. The wall thickness can be gradually changed along the axial direction by parametric 3D design software or implicit surface equations.
[0016] Furthermore, in step S2, the axial gradient distribution must conform to the ideal equivalent wave impedance gradient distribution law obtained in step S1.
[0017] Further, in step S3, the hyperelastic constitutive material properties such as Mooney-Rivlin or Ogden models generated in step S2 are assigned to the geometric model in the dynamic analysis, and a dynamic contact pair based on the penalty function method is set between the impact end face of the geometric model and the surface of the target plate.
[0018] Furthermore, the normal contact force history curve of the central region of the target plate is extracted and converted into a simulated load waveform.
[0019] Furthermore, the simulated load waveform obtained from the simulation is extracted, filtered, and a smooth simulated pressure-time curve characterizing the propagation law of the elastic main wave is obtained.
[0020] Furthermore, in step S3, the waveform difference includes both the "peak overpressure difference" and the "impulse difference", and the relative error of both needs to be less than the tolerance threshold.
[0021] Furthermore, in step S3, considering the lateral inertia and nonlinear coupling effect of the three-dimensional lattice under high-speed impact, an impedance gradient correction factor K, which includes a relaxation factor, is introduced for the peak overpressure. Its update formula is as follows: Among them, K old This is the correction factor for the previous iteration, initially set to 1; P target The peak overpressure of the target explosive load; P sim The peak overpressure of the simulated load is extracted from the dynamic simulation; α is the impedance compensation relaxation factor to ensure the stability of numerical iteration convergence, and its value range is 0 < α < 1.
[0022] Furthermore, in step S3, the spatial relative density distribution function is corrected using a power function relationship, and the corrected relative density distribution law is obtained. satisfy: in, This is the set upper limit critical value for the relative density of a single cell. This is the relative density distribution calculated in the previous iteration.
[0023] A second aspect of the present invention provides a method for manufacturing a uniform cross-section explosion load simulator based on a gradient elastic metamaterial, comprising the following steps:
[0024] Based on the final metamaterial simulator model verified by the above design method, a polymer elastic material or a hyperelastic alloy material with recoverable elastic properties is selected, and additive manufacturing technology is used for integrated printing to obtain the final pure elastic reusable explosive load simulator entity.
[0025] Furthermore, the material with recoverable elastic properties includes, but is not limited to, thermoplastic polyurethane elastomer (TPU) or flexible photosensitive resin; the additive manufacturing includes, but is not limited to, selective laser sintering (SLS) or digital light processing (DLP).
[0026] The beneficial effects of this invention include:
[0027] 1. This invention selects materials with recoverable elastic properties (such as TPU) and, through gradient design, enables the simulator to undergo only pure elastic deformation under strong impact loads, and to completely recover its original shape after a single impact, achieving non-destructive reuse, greatly reducing the cost of related explosion-proof experiments and improving experimental efficiency.
[0028] 2. While designing a continuously gradient structure internally, this invention maintains the simulator's macroscopic outline as a constant-diameter, uniform-section cylinder, which can perfectly fit the barrel of a light air cannon or other launching device, ensuring good sealing and launching stability, and laying the foundation for accurate and repeatable impact experiments.
[0029] 3. This invention is based on the one-dimensional elastic wave propagation reverse design theory and introduces an impedance gradient correction factor to perform nonlinear iterative correction of the density function. This design method is not only applicable to Friedlander waves, but also applicable to the simulator design of any strongly dynamic load waveform with a specific time evolution law (such as triangular waves, step waves, half-sine waves, etc.). It has strong versatility and broad application prospects. Attached Figure Description
[0030] Figure 1 The present invention provides a flowchart of a design method for an equal-section explosion load simulator based on gradient elastic metamaterials.
[0031] Figure 2 This is a schematic diagram simulating an explosive load.
[0032] Figure 3 This is a schematic diagram of a model simulating explosive loads.
[0033] Figure 4 This is a schematic diagram simulating a rectangular wave.
[0034] Figure 5 This is a schematic diagram of a model simulating a rectangular wave. Detailed Implementation
[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0036] This invention provides a design method for a uniform cross-section explosion load simulator based on gradient elastic metamaterials. (See attached diagram) Figure 1 As shown, the specific implementation process of this general design and manufacturing method is as follows:
[0037] (1) First, it is necessary to determine the pressure-time evolution parameters of the target explosive load. In this example, the Friedlander wave is chosen as the theoretical model. It is characterized by an instantaneous peak overpressure followed by nonlinear decay. The theoretical model expression is:
[0038] p(t) = P0(1-t / t0)exp(-bt / t0)
[0039] Where p0 is the target peak overpressure, t0 is the positive phase time, and b is the dimensionless decay constant. Simultaneously, the initial impact velocity V0 set by the launching device and the macroscopic cross-sectional area A of the impacted target plate are obtained. t With wave impedance ξ t In this example, the waveform parameters are selected as follows: P0 = 0.67 MPa, t0 = 0.37 ms, b = 4.
[0040] (2) Under the boundary condition that the simulator is a uniform cross-section cylinder (i.e., the macroscopic cross-sectional area A is constant), based on the continuity equation and momentum conservation equation of a one-dimensional elastic wave crossing the impact interface, the ideal equivalent wave impedance gradient distribution law ξ(X) at the axial Lagrangian position X of the uniform cross-section simulator is derived, and its calculation formula is as follows:
[0041]
[0042] The expression for the dimensionless position parameter λ is:
[0043]
[0044] The expression for the initial wave impedance ξ(0) at the impact end is:
[0045]
[0046] In the formula, E and ρ are the equivalent elastic modulus and equivalent density of the simulator, respectively. Through this inverse design analytical theory, a mapping relationship between the time-domain waveform attenuation characteristics and the spatial axial impedance distribution can be established.
[0047] (3) Select a three-dimensional elastic metamaterial with no abrupt change in cross-sectional area (such as TPMS three-period minimum surface) as the unit cell configuration, and determine the matrix material density ρ. s With modulus E s The relative density of this unit cell was established through mechanical calibration. Its equivalent elastic modulus E eff Equivalent density ρ eff The nonlinear mechanical mapping function between them.
[0048] (4) The macroscopic cross-sectional area A of the constant cross-section simulator is constant, and its macroscopic wave impedance is determined only by the material equivalent properties, that is, it satisfies the equation:
[0049]
[0050]
[0051] In the formula, n and C are the deformation mechanism index and structural efficiency coefficient, respectively, which are related to the unit cell configuration selected in step (3). For the Gyroid structure selected in this example, n = 1.5 and C = 0.56. Substituting the ideal impedance ξ(X) obtained in step (2) into the above formula, and combining it with the mapping function in step (3), the spatial relative density distribution function that continuously varies along the simulator axis is solved.
[0052] (5) Using implicit surface modeling technology, the implicit mathematical equations of the selected unit cell configuration are extracted, and the level set bias threshold t and relative density are established. nonlinear mapping function In this example, the Gyroid structure is selected, but this design method can also select other parameterized model structures, including TPMS structures and BBC lattice structures. The spatial relative density distribution function obtained in step (4) is... Substituting these values into the implicit mathematical equation transforms the original constant threshold into a variable t(X) that continuously varies with the spatial coordinate X. Subsequently, the Marching Cubes algorithm is used to extract isosurfaces, thereby implementing a parameterized field-driven geometric modeling module. Based on the zeroth-order isosurfaces extracted from the implicit equation, a seamless, smoothly varying 3D metamaterial geometric model of this instance is directly generated. Figure 3 As shown.
[0053] (6) Import the three-dimensional geometric model into the finite element analysis software and assign it a hyperelastic constitutive model. Set the simulator to impact the target plate with an initial velocity V0, establish a dynamic surface-to-surface contact pair, and calculate the impact response using an explicit dynamic solver. Extract the interface normal contact force and, after low-pass filtering, convert it into a simulated load waveform. Extract the simulated peak overpressure P of this waveform. sim And the impulse, and calculate the waveform difference with the target waveform.
[0054] (7) If the waveform difference extracted in step (6) exceeds the preset tolerance, the density distribution function will be corrected in the following way:
[0055] For peak overpressure, considering the lateral inertia and nonlinear coupling effect of the three-dimensional lattice under high-speed impact, an impedance gradient correction factor K, which includes a relaxation factor, is introduced, and its update formula is as follows:
[0056]
[0057] Among them, K old This is the correction factor for the previous iteration, initially set to 1; P target The peak overpressure of the target explosive load; P sim The peak overpressure of the simulated load is extracted from the dynamic simulation; α is the impedance compensation relaxation factor to ensure the stability of numerical iteration convergence, and its value range is 0 < α < 1.
[0058] The spatial relative density distribution function is corrected using a power function relationship, and the corrected relative density distribution pattern is shown below. satisfy:
[0059]
[0060] in, This is the set upper limit critical value for the relative density of a single cell. This is the relative density distribution calculated in the previous iteration. Based on the corrected... Repeat steps (5) and (6) until the error index meets the requirements, and output the final three-dimensional geometric model. The simulated peak overpressure P of the waveform in this example is... sim The value is 0.65432 MPa, which is 2.3% different from the target waveform.
[0061] (8) Export the final 3D model optimized and converged in step (7) into a file format recognizable by the additive manufacturing equipment (such as STL, AMF, or 3MF format). Use a flexible polymer material with excellent recoverable elasticity and high strain rate impact resistance for integrated additive manufacturing. The flexible polymer material includes, but is not limited to: thermoplastic polyurethane elastomer (TPU), thermoplastic elastomer (TPE), flexible photosensitive resin, or printable silicone elastomer. The additive manufacturing process is matched according to the selected material, including but not limited to: selective laser sintering (SLS), photopolymerization molding process (DLP, SAL), fused deposition modeling (FDM), etc. After fabrication, post-processing such as powder removal and cleaning is performed according to the process type to obtain a structurally complete, immune to local buckling instability, and highly accurate waveform simulation pure elastic reusable constant cross-section explosion load simulator.
[0062] It should be noted that the target load demonstrated in the embodiments of this invention is mainly an explosive load with Friedlander nonlinear decay characteristics. However, the design method of this invention is not limited to this. By replacing the theoretical model of the target pressure-time evolution parameters in step S1, this invention is also applicable to the simulator design of any strong dynamic load waveform (e.g., triangular wave, step wave, half-sine wave, etc.) with a specific time evolution law, such as... Figure 4 The diagram shows a simulated rectangular waveform. Furthermore, the TPMS structure mentioned in this embodiment is only a preferred metamaterial unit cell configuration; other three-dimensional lattice structures without abrupt changes in cross-sectional area are also applicable. The listed materials such as polyurethane elastomer (TPU) and additive manufacturing processes are not unique limitations; any materials with recoverable elastic properties and corresponding molding processes are applicable to the technical solutions of this invention.
[0063] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention (e.g., equivalent substitution of the target waveform mathematical model, simple substitution of metamaterial configuration, equivalent substitution of elastic material, etc.) should be included within the protection scope of the present invention.
Claims
1. A design method for a reusable explosion load simulator based on gradient elastic metamaterials, characterized in that, Includes the following steps: S1. First, based on the pressure-time evolution parameters of the target explosive load, the impedance parameters of the impacted target plate, and the designed initial impact velocity, the ideal equivalent wave impedance gradient distribution law required for the equal cross-section simulator to realize the target explosive load along the axial direction is solved according to the elastic wave propagation reverse design theory. S2. Based on the calculated ideal equivalent wave impedance gradient distribution law, establish the mapping relationship between the relative density and equivalent mechanical parameters of the selected metamaterial unit cell; keep the macroscopic cross-sectional area of the outer shape unchanged, and generate the initial geometric model of the three-dimensional metamaterial with a uniform cross-section cylinder and continuous gradient change of the internal cell by changing the wall thickness or pillar size of the cell along the axial direction. S3. Based on the initial geometric model of the three-dimensional metamaterial described in S2, an explicit dynamic finite element model is constructed to simulate the dynamic response process of the metamaterial impacting the target plate at the initial impact velocity. The load-time history data of the contact interface is extracted and compared with the target explosion load. The relative density gradient parameters of the internal cells are iteratively corrected to obtain the final metamaterial simulator model whose load waveform matching error meets the requirements.
2. The design method according to claim 1, characterized in that, In step S1, the pressure-time evolution parameters are used to characterize the explosive load waveform, which includes instantaneous surge and nonlinear decay characteristics, including peak overpressure, positive phase time and decay constant.
3. The design method according to claim 1, characterized in that, In step S2, the three-dimensional elastic metamaterial unit cell configuration is a three-period minimal surface (TPMS) structure without abrupt changes in cross-sectional area; the geometric feature parameter of the unit cell is the wall thickness of the unit cell, and the wall thickness feature is gradually varied along the axial direction to generate a geometric model through parameterization.
4. The design method according to claim 1, characterized in that, In step S3, the Abaqus explicit dynamics solver is used for analysis to extract the interface contact force and convert it into the peak overpressure and impulse of the simulated load waveform; the waveform difference includes the peak overpressure difference and the impulse difference.
5. The design method according to claim 1, characterized in that, In step S3, if the preset tolerance requirements are not met, the specific method for generating the impedance gradient correction factor and the corrected spatial relative density distribution function is as follows: For peak overpressure, considering the lateral inertia and nonlinear coupling effect of the three-dimensional lattice under high-speed impact, an impedance gradient correction factor K, which includes a relaxation factor, is introduced, and its update formula is as follows: Among them, K old This is the correction factor for the previous iteration, initially set to 1; P target The peak overpressure of the target explosive load; P sim The simulated load peak overpressure is extracted from the dynamic simulation; α is the impedance compensation relaxation factor to ensure the stability of numerical iteration convergence, with a value range of 0 < α < 1; the spatial relative density distribution function is corrected using a power function relationship, and the corrected relative density distribution law is shown. satisfy: in, This is the set upper limit critical value for the relative density of a single cell. This is the relative density distribution calculated in the previous iteration.
6. A method for manufacturing a uniform cross-section explosion load simulator based on gradient elastic metamaterials, characterized in that, The final metamaterial simulator model verified by the design method according to any one of claims 1 to 5 is obtained by selecting a polymer elastic material or a superelastic alloy material with recoverable elastic properties and using additive manufacturing technology for integrated printing.
7. The manufacturing method according to claim 6, characterized in that: The material having recoverable elastic properties includes, but is not limited to, thermoplastic polyurethane elastomer (TPU) or flexible photosensitive resin; the additive manufacturing includes, but is not limited to, selective laser sintering (SLS) or digital light processing (DLP).