泡沫基负有效质量超材料抗爆性能的数值模拟

doi:10.12382/bgxb.2025.0505

摘要/Abstract

摘要： 负有效质量超材料的带隙特性是实现冲击波衰减的有效途径之一。对以“泡沫-振子”为芯层构建的夹芯复合结构开展了爆炸载荷下动力响应的数值模拟研究,分析了不同几何与载荷参数下结构的变形过程、接触力的时域与频域特征以及能量耗散规律。结果表明:振子尺寸的增大能有效减少芯层的压缩量;增加振子质量能降低结构局域共振频率,抑制中高频冲击波的传播,从而提高结构的抗爆能力;然而由于冲击波引发的振子惯性阻抗效应,前面板接触力峰值随振子尺寸的增大显著提升;在重力作用下,不同的加载方向对结构的爆炸响应影响较小。研究为负有效质量超材料的抗爆性能优化提供了有效参考。

关键词: 负有效质量超材料, EVA泡沫, 抗爆性能, 数值模拟, 能量耗散

Abstract:

The bandgap characteristics of negative effective mass metamaterials provide an effective approach for shock wave attenuation. In this study, a sandwich composite structure incorporating a foam-resonator core was numerically investigated to evaluate its dynamic response under explosive loading. The structural deformation, time-and frequency-domain characteristics of contact forces, and energy dissipation behavior under various geometric configurations and loading conditions were systematically examined. The results demonstrate that increasing the resonator size effectively reduces core layer compression. Moreover, enlarging the resonator mass lowers the local resonance frequency, thereby suppressing the propagation of mid-to-high frequency shock waves and enhancing the overall blast resistance. However, as the resonator size increases, the inertial impedance effect induced by shock loading significantly amplifies the peak contact force on the front panel, potentially leading to local damage or failure of the foam matrix. Furthermore, the analysis reveals that the structural response exhibits minimal sensitivity to different loading directions under gravity. This study provides valuable insights for optimizing the blast resistance of negative effective mass metamaterials.

Key words: negative effective mass metamaterials, EVA foam, blast resistance, numerical simulation, energy dissipation

贾迪, 陈传庆, 李鑫. 泡沫基负有效质量超材料抗爆性能的数值模拟[J]. 兵工学报, 2025, 46(10): 250505-.

JIA Di, CHEN Chuanqing, LI Xin. Numerical Simulation Study on the Blast Resistance of Foam Matrix Negative Effective Mass Metamaterials[J]. Acta Armamentarii, 2025, 46(10): 250505-.

图/表 15

图1 模型尺寸示意图

Fig.1 Schematic diagram of model size

表1 结构几何参数表

Table 1 Structural geometric parameter table

模型	纯EVA	R2	R4	R6	R8
振子半径/mm	0	2	4	6	8
泡沫尺寸/mm	308×60×50 (长度×高度×厚度)

图2 有限元网格模型

Fig.2 Mesh of finite element model

表2 不锈钢304与铝6063材料参数

Table 2 Material properties of stainless steel 304 and aluminum 6063

材料	密度/ (kg·m^-3)	弹性模量/ GPa	屈服应力/ MPa	泊松比	应变率参数 C/s^-1	应变率参数 P
不锈钢304	7900	193	310	0.3	100	10
铝6063	2730	70	48.7	0.33	128800	4

图3 EVA应力应变曲线

Fig.3 EVA stress-strain curve

表3 TNT状态方程参数

Table 3 Parameters of TNT equation of state

参数	A/ Pa	B/ Pa	R₁	R₂	ω	E₀/ (J·m^-3)	V
数值	3.71×10¹¹	3.21×10⁹	4.15	0.95	0.3	7×10⁹	1.0

表4 空气状态方程参数

Table 4 Parameters of air equation of state

参数	C₀、C₁、C₂、C₃、C₆	C₄、C₅	E₀/(J·m^-3)	V
数值	0	0.4	2.58×10⁵	1.0

图4 结构响应过程的数值模拟与实验结果对比

Fig.4 Comparison of numerical simulation and experimental results of structural response process

图5 纯EVA泡沫模型与R2、R4、R6、R8模型的最大压缩量对比

Fig.5 Comparison of the maximum compression of pure EVA foam model and R2, R4, R6, and R8 models

表4 前、后面板与芯层的接触力峰值

Table 4 The peak contact force between face sheets and core

模型	纯EVA	R2	R4	R6	R8
前面板峰值/kN	8.04	13.5	13.6	18	24.8
后面板峰值/kN	3.85	4.06	3.13	3.02	2.97
传递率/%	47.9	30.1	23.0	16.7	12.0

图6 纯EVA模型与R2~R8模型前、后面板的时域接触力

Fig.6 The time-domain contact force between the front and back panels of pure EVA model and R2~R8 model

图7 纯EVA模型与R2~R8模型前、后面板的接触力频域谱

Fig.7 Frequency domain spectrum of contact force between the front and back panels of pure EVA model and R2~R8 model

图8 R4模型重力正向、反向及侧向加载的最大压缩量对比

Fig.8 Comparison of maximum compression under forward, reverse, and lateral gravity loading for the R4 model

图9 R4模型重力反向及侧向加载接触力对比

Fig.9 Comparison of contact forces under reverse and lateral gravity loading for the R4 model

图10 R4模型重力反向及侧向加载的前、后面板接触力频域谱

Fig.10 Frequency-domain spectra of front and back panel contact forces under reverse and lateral gravity loading for the R4 model

参考文献 20

[1]	CHEN C, AIROLDI A, CAPORALE A M, et al. Impact response of composite energy absorbers based on foam-filled metallic and polymeric auxetic frames[J]. Composite Structures, 2024, 331:117916.
[2]	CHEN C, HE Y, XU R, et al. Dynamic behaviors of sandwich panels with 3D-printed gradient auxetic cores subjected to blast load[J]. International Journal of Impact Engineering, 2024, 188:104943.
[3]	LIU Z, ZHANG X, MAO Y, et al. Locally resonant sonic materials[J]. Science, 2000, 289:1734-1736.
[4]	MILTON G W, WILLIS J R. On modifications of newton’s second law and linear continuum elastodynamics[J]. Proceedings: Mathematical, Physical and Engineering Sciences, 2007, 463:855-80.
[5]	HUANG H H, SUN C T, HUANG G L. On the negative effective mass density in acoustic metamaterials[J]. International Journal of Engineering Science, 2009, 47:610-617.
[6]	TAN K T, HUANG H H, SUN C T. Blast-wave impact mitigation using negative effective mass density concept of elastic metamaterials[J]. International Journal of Impact Engineering, 2014, 64:20-29.
[7]	TAN K T, HUANG H H, SUN C T. Optimizing the band gap of effective mass negativity in acoustic metamaterials[J]. Applied Physics Letters, 2012, 101:241902.
[8]	CHEN Y Y, BARNHART M V, CHEN J K, et al. Dissipative elastic metamaterials for broadband wave mitigation at subwavelength scale[J]. Composite Structures, 2016, 136:358-371.
[9]	VO N H, PHAM T M, BI K, et al. Stress wave mitigation properties of dual-meta panels against blast loads[J]. International Journal of Impact Engineering, 2021, 154:103877.
[10]	VO N H, PHAM T M, HAO H, et al. Blast resistant enhancement of meta-panels using multiple types of resonators[J]. International Journal of Mechanical Sciences, 2022, 215:106965.
[11]	VO N H, PHAM T M, BI K, et al. Model for analytical investigation on meta-lattice truss for low-frequency spatial wave manipulation[J]. Wave Motion, 2021, 103:102735.
[12]	张恩, 路国运, 杨会伟, 等. 超材料混凝土的带隙特征及对冲击波的衰减效应[J]. 爆炸与冲击, 2020, 40(6): 66-74.
	ZHANG E, LU G Y, YANG H W, et al. The band gap characteristics and attenuation effect of shock waves in metamaterial concrete[J]. Explosive and Shock, 2020, 40(6):66-74. (in Chinese)
[13]	方鑫. 非线性声学超材料中弹性波传播理论及其减振应用研究[J]. 机械工程学报, 2020, 56(5): 79.
	FANG X. Research on the propagation theory of elastic waves and its vibration reduction application in nonlinear acoustic metamaterials[J]. Journal of Mechanical Engineering, 2020, 56(5):79. (in Chinese)
[14]	HUANG H H, SUN C T. Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density[J]. New Journal of Physics, 2009, 11(1):013003.
[15]	LIU C, HUANG Y, WU J H. Dissipative stratified elastic metamaterials for broadband blast-wave impact mitigation[J]. Mechanics of Advanced Materials and Structures, 2025, 32(5):815-825.
[16]	周广盼, 王荣, 王明洋, 等. 涂覆聚脲混凝土自锚式悬索桥主梁抗爆性能试验与数值模拟[J]. 兵工学报, 2023, 44(S1):9-25.
	ZHOU G P, WANG R, WANG M Y, et al. Experimental and numerical simulation of blast resistance of the main beam of a self-anchored suspension bridge with coated polyurea concrete[J]. Journal of Ordnance Science, 2023, 44(S1):9-25. (in Chinese)
[17]	CHEN C, HE Y, XU R, et al. Dynamic behaviors of sandwich panels with 3D-printed gradient auxetic cores subjected to blast load[J]. International Journal of Impact Engineering, 2024, 188:104943.
[18]	FAREGH S S H, HASSANI A. Stress and strain distribution in twist extrusion of AA6063 aluminum alloy[J]. Int J Mater Form, 2018, 11:175-184.
[19]	KARAGIOZOVA D, NURICK G N, CHUNG KIM YUEN S. Energy absorption of aluminium alloy circular and square tubes under an axial explosive load[J]. Thin-Walled Structures, 2005, 43:956-982.
[20]	CHANG F S, SONG Y, LU D X, et al. Unified constitutive equations of foam materials[J]. Journal of Engineering Materials and Technology, 1998, 120:212-217.