基于物质点法的负泊松比胞元夹层结构动态冲击响应及能量耗散机制

doi:10.12382/bgxb.2025.0507

摘要/Abstract

摘要： 负泊松比结构因其拉胀变形行为,在冲击载荷下展现出优异的能量分散与应力均匀化能力,在军事防护领域具有广阔应用前景。然而,传统网格类数值方法(如有限元法)在模拟大变形时易因网格畸变导致计算精度下降甚至中断。采用物质点法系统研究了三种典型胞元(正六边形蜂窝、内凹六边形和波浪形手性)夹层结构在冲击载荷下的动态响应与能量耗散机制,并通过网格独立性检验和实验验证,证实该方法具有良好的网格收敛性与物理保真度。结果表明,负泊松比结构抗冲击性能显著优于常规结构:相较于正六边形蜂窝结构,内凹六边形和波浪形手性结构的峰值反力分别降低27.9%和61.9%。机理分析表明,波浪形手性结构通过“环链旋转-韧带延展-孔隙闭合”的多级耗能机制,促使能量沿胞元网络均匀耗散,从而有效抑制应力集中与结构失效。本研究为舰艇防爆、单兵装甲等防护装备的轻量化抗冲击设计提供了理论依据与仿真工具。

关键词: 物质点法, 负泊松比结构, 动态冲击, 能量耗散机制, 轻量化防护

Abstract:

Structures with negative Poisson’s ratios (NPR) exhibit superior energy dispersion and stress homogenization capabilities under impact loading due to their unique auxetic deformation behavior, demonstrating broad application prospects in military protection. However, conventional mesh-based numerical methods such as the Finite Element Method (FEM) often suffer from reduced accuracy or even computational interruption due to mesh distortion when simulating extreme nonlinear behaviors like large deformation and fracture. To address this, the present study employs the Material Point Method (MPM) to systematically investigate the dynamic response and energy dissipation mechanisms of three typical cellular sandwich structures (regular hexagonal honeycomb, re-entrant hexagon, and chiral wave core) under impact loading. Through mesh convergence analysis and experimental validation, the MPM is demonstrated to possess good numerical convergence and physical fidelity in simulating such extreme deformation scenarios. The results indicate that the NPR effect significantly improves the impact resistance of the structures: compared to the conventional hexagonal honeycomb structure (positive Poisson’s ratio), the re-entrant hexagonal structure exhibits a 27.9% reduction in peak reaction force, while the chiral wave cellular structure achieves a reduction of 61.9%. Further mechanistic analysis reveals that the chiral structure facilitates uniform dissipation of impact energy throughout the cellular network via a multi-stage energy absorption mechanism—comprising ring rotation, ligament extension, and pore closure—thereby effectively mitigating local stress concentration and structural failure. This study provides theoretical support and simulation tools for the lightweight anti-impact design of protective equipment such as naval blast protection and personal armor.

Key words: material point method, auxetic structure, impact dynamics, energy dissipation, lightweight protection

杨晨琛, 刘骏, 韩芳灏, 梅跃. 基于物质点法的负泊松比胞元夹层结构动态冲击响应及能量耗散机制[J]. 兵工学报, 2025, 46(10): 250507-.

YANG Chenchen, LIU Jun, HAN Fanghao, MEI Yue. Research on Dynamic Impact Response and Energy Dissipation Mechanisms of Auxetic Metamaterial Sandwich Structures with Negative Poisson’s Ratio Based on Material Point Method[J]. Acta Armamentarii, 2025, 46(10): 250507-.

图/表 23

图1 物质点法的双重离散框架

Fig.1 Dual discretization framework of material point method

图2 更新拉格朗日描述的物质点法计算流程

Fig.2 Computational procedure of Updated Lagrangian Material Point Method (ULMPM)

表1 Q235钢的材料模型参数[22]

Table 1 Material model parameters of Q235 steel

参数	数值	参数	数值
E/GPa	210	D₁	0.50
ν	0.3	D₂	3.44
ρ/(kg·m^-3)	7850	D₃	-2.12
c_p/(J·kg^-1·K^-1)	450	D₄	0.002
A/MPa	265	D₅	1.09
B/MPa	300	c/(m·s^-1)	5172
n	0.31	S₁	1.49
${\stackrel{·}{\epsilon }}_{0}$/s^-1	0.00001	S₂	0
C	0.014	S₃	0
T_r/K	293	γ₀	1.8
T_m/K	1795	E₀/(J·m^-3)	0
m	1.03

表2 用于3D打印的316L不锈钢材料模型参数[23]

Table 2 Material parameters of 316L stainless steel used for 3D printing

参数	数值	参数	数值
E/GPa	70	D₁	0.01241
ν	0.3	D₂	1.607
ρ/(kg·m^-3)	7850	D₃	4.133
c_p/(J·kg^-1·K^-1)	450	D₄	-0.01377
A/MPa	205	D₅	1.302
B/MPa	1064	c/(m·s^-1)	2986
n	0.5085	S₁	1.49
${\stackrel{·}{\epsilon }}_{0}$/s^-1	0.00001	S₂	0
C	0.02846	S₃	0
T_r/K	293	γ₀	1.8
T_m/K	1623	E₀/(J·m^-3)	0
m	0.662

图3 三种胞元构型示意图

Fig.3 Schematics of three cell configurations

图4 三种胞元构型的压缩泊松比极坐标图(左侧坐标轴代表有效泊松比,右上角Exx表示平均Biot应变)

Fig.4 Polar plots of the compressive Poisson’s ratio for three cell configurations (Left axis represents the effective Poisson’s ratio; Exx denotes the average Biot strain)

图5 三角形胞元夹层结构模型

Fig.5 Triangular cell sandwich structure model

表3 含不同背景网格尺寸的三组算例

Table 3 Three cases with different background mesh sizes

算例	背景网格尺寸	单个网格粒子数	粒子总数
网格1	1.25×1.25mm²	2×2	~3.83×10³
网格2	1.00×1.00mm²	2×2	~5.98×10³
网格3	0.50×0.50mm²	2×2	~23.94×10³

图6 三角形胞元夹层结构的冲击变形(t=1ms时刻)

Fig.6 Impact deformation of triangular cell sandwich structure (t=1ms)

图7 入射圆柱体的速度衰减曲线

Fig.7 Velocity deceleration curve of the incident cylinder

图8 落重冲击试验机

Fig.8 Drop-weight impact testing machine

图9 3D打印的夹层试件

Fig.9 3D printed sandwich specimen

图10 3D打印夹层试件的几何尺寸

Fig.10 Geometry of 3D printed sandwich specimen

图11 落重试验的二维平面物质点离散模型

Fig.11 Two-dimensional material point discrete model for the drop-weight test

图12 夹层结构变形模式的模拟和实验对比

Fig.12 Simulated and experimental deformation patterns of sandwich structure

图13 冲击点的垂向位移时程曲线

Fig.13 Vertical displacement-time curve at the impact location

图14 三种胞元夹层结构的物质点模型

Fig.14 Material point models of three cellular sandwich structures

图15 三种胞元夹层结构的纵向位移云图

Fig.15 Vertical displacement contours of three cellular sandwich structures

图16 冲击点的垂向位移时程曲线

Fig.16 Vertical displacement history curves of the impact loaction

图17 冲击圆柱体的垂向速度衰减曲线

Fig.17 Vertical deceleration history of the incident cylinder

图18 底部反力时程曲线

Fig.18 Reaction force history curves of the structure bottom

图19 三种胞元夹层结构的能量耗散时程曲线

Fig.19 Energy dissipation-time curves for three cellular sandwich structures

图20 三种胞元夹层结构在多个时刻的等效塑性应变云图

Fig.20 Contour plots of equivalent plastic strains for three cellular sandwich structures at various time instances

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