Research on Dynamic Impact Response and Energy Dissipation Mechanisms of Auxetic Metamaterial Sandwich Structures with Negative Poisson’s Ratio Based on Material Point Method

doi:10.12382/bgxb.2025.0507

Abstract

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

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-.

Figures/Tables 23

Fig.1 Dual discretization framework of material point method

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

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

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

Fig.3 Schematics of three cell configurations

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)

Fig.5 Triangular cell sandwich structure model

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

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

Fig.7 Velocity deceleration curve of the incident cylinder

Fig.8 Drop-weight impact testing machine

Fig.9 3D printed sandwich specimen

Fig.10 Geometry of 3D printed sandwich specimen

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

Fig.12 Simulated and experimental deformation patterns of sandwich structure

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

Fig.14 Material point models of three cellular sandwich structures

Fig.15 Vertical displacement contours of three cellular sandwich structures

Fig.16 Vertical displacement history curves of the impact loaction

Fig.17 Vertical deceleration history of the incident cylinder

Fig.18 Reaction force history curves of the structure bottom

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

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

References 11

[12]	KUMAR V, RAMAMURTHY K. Meshfree and finite element modelling of impact: A comparative study[J]. International Journal of Impact Engineering, 2016, 90: 146-153. doi: 10.1016/j.ijimpeng.2015.10.017 URL
[13]	SAMBASIVAN S, KAPAHI A, UDAYKUMAR H S. Simulation of high speed impact, penetration and fragmentation problems on locally refined Cartesian grids[J]. Journal of Computational Physics, 2013, 235: 334-370. doi: 10.1016/j.jcp.2012.10.031 URL
[14]	USTA F, TÜRKMEN H S, SCARPA F. Low-velocity impact resistance of composite sandwich panels with various types of auxetic and non-auxetic core structures[J]. Thin-Walled Structures, 2021, 163: 107738. doi: 10.1016/j.tws.2021.107738 URL
[15]	SULSKY D, CHEN Z, SCHREYER H L. A particle method for history-dependent materials[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 118(1-2): 179-196. doi: 10.1016/0045-7825(94)90112-0 URL
[16]	ZHANG X, SZE K Y, MA S. An explicit material point finite element method for hypervelocity impact[J]. International Journal for Numerical Methods in Engineering, 2006, 66(4): 689-706. doi: 10.1002/nme.v66:4 URL
[17]	WANG Y, BEOM H G, SUN M, et al. Numerical simulation of explosive welding using the material point method[J]. International Journal of Impact Engineering, 2011, 38(1): 51-60. doi: 10.1016/j.ijimpeng.2010.08.003 URL
[18]	GONG W, LIU Y, ZHANG X, et al. Numerical investigation on dynamical response of aluminum foam subject to hypervelocity impact with material point method[J]. Computer Modeling in Engineering & Sciences(CMES), 2012, 83(5): 527-545.
[19]	DE VAUCORBEIL A, NGUYEN V P, MANDAL T K. Mesh objective simulations of large strain ductile fracture: A new nonlocal Johnson-Cook damage formulation for the Total Lagrangian Material Point Method[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 389: 114388. doi: 10.1016/j.cma.2021.114388 URL
[20]	JOHNSON G R, COOK W H. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures[J]. Engineering fracture mechanics, 1985, 21(1): 31-48. doi: 10.1016/0013-7944(85)90052-9 URL
[1]	蒋伟忠, 张毅, 朱一林, 等. 功能性负泊松比超材料研究进展与展望[J]. 应用力学学报, 2025, 43(3): 494-510.
	JIANG W Z, ZHANG Y, ZHU Y L, et al. Research progress and prospect of functional auxetic metamaterials[J]. Chinese Journal of Applied Mechanics, 2025, 43(3): 494-510. (in Chinese)
[2]	PAYUNGPISIT K, CHUEATHONG P, PONGTHONGPASUK T, et al. Quasi-static and dynamic responses of bio-inspired auxetic structures[J]. International Journal of Impact Engineering, 2025, 201: 105285. doi: 10.1016/j.ijimpeng.2025.105285 URL
[3]	KOOHBOR B, UDDIN K Z, HERAS M, et al. Strain rate sensitivity of rotating-square auxetic metamaterials[J]. International Journal of Impact Engineering, 2025, 195: 105128. doi: 10.1016/j.ijimpeng.2024.105128 URL
[4]	杨德庆, 马涛, 张梗林. 舰艇新型宏观负泊松比效应蜂窝舷侧防护结构[J]. 爆炸与冲击, 2015, 35(2): 243-248.
	YANG D Q, MA T, ZHANG G L. A novel auxetic broadside defensive structure for naval ships[J]. Explosion and Shock Waves, 2015, 35(2): 243-248. (in Chinese)
[5]	吴文旺, 肖登宝, 孟嘉旭, 等. 负泊松比结构力学设计、抗冲击性能及在车辆工程应用与展望[J]. 力学学报, 2021, 53(3): 611-638. doi: 10.6052/0459-1879-20-333
	WU W W, XIAO D B, MENG J X, et al. Mechanical design, impact energy absorption and applications of auxetic structures in automobile lightweight engineering[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 611-638. (in Chinese)
[6]	贺锋, 梁一鸣, 李季, 等. 异型陶瓷负泊松比复合结构的防弹防爆性能数值模拟研究[J]. 安全与环境学报, 2024, 24(8): 2919-2928.
[21]	HEUZÉ O. General form of the Mie-Grüneisen equation of state[J]. Comptes Rendus Mecanique, 2012, 340(10): 679-687. doi: 10.1016/j.crme.2012.10.044 URL
[22]	辛春亮, 薛再清, 涂建, 等. 有限元分析常用材料参数手册[M]. 北京: 机械工业出版社, 2020.
	XIN C L, XUE Z Q, TU J, et al. Handbook of common material parameters for finite element analysis[M]. Beijing: China Machine Press, 2020. (in Chinese)
[23]	王宇新. 爆炸冲击动力学数值分析物质点法[M]. 北京: 中国建筑工业出版社, 2014.
	WANG Y X. Numerical analysis on explosion and impact dynamics by material point method[M]. Beijing: China Architecture & Building Press. 2014. (in Chinese)
[24]	ZHU Y, WANG Z P, POH L H. Auxetic hexachiral structures with wavy ligaments for large elasto-plastic deformation[J]. Smart Materials and Structures, 2018, 27(5): 055001. doi: 10.1088/1361-665X/aab33d URL
[25]	SARVESTANI H Y, AKBARZADEH A H, NIKNAM H, et al. 3D printed architected polymeric sandwich panels: Energy absorption and structural performance[J]. Composite Structures, 2018, 200: 886-909. doi: 10.1016/j.compstruct.2018.04.002 URL
[26]	DANG W, LIU X T, SUN B H. Bending response of integrated multilayer corrugated sandwich panels[J]. Applied Composite Materials, 2023, 30(5): 1493-1512. doi: 10.1007/s10443-023-10133-9
[27]	WANG Y, ZHAO W, ZHOU G, et al. Optimization of an auxetic jounce bumper based on Gaussian process metamodel and series hybrid GA-SQP algorithm[J]. Structural and Multidisciplinary Optimization, 2018, 57(6): 2515-2525. doi: 10.1007/s00158-017-1869-z URL
[28]	MILLER W, SMITH C W, SCARPA F, et al. Flatwise buckling optimization of hexachiral and tetrachiral honeycombs[J]. Composites Science and Technology, 2010, 70(7): 1049-1056. doi: 10.1016/j.compscitech.2009.10.022 URL
[6]	HE F, LIANG Y M, LI J, et al. Numerical simulation study on ballistic and blast resistance of heterotypic ceramic negative Poisson’s ratio composite structures[J]. Journal of Safety and Environment, 2024, 24(8): 2919-2928. (in Chinese)
[7]	廖瑜, 蒋新生, 田镇华, 等. 泡沫铝弹冲击下柱面负泊松比蜂窝夹芯结构防护钢板动态响应特性[J/OL]. 兵工学报, 2025: 1-14. DOI: 10.12382/bgxb.2025.0025.
	LIAO Y, JIANG X S, TIAN Z H, et al. Dynamic response characteristics of cylindrical auxetic honeycomb sandwich-structured protective steel plates under foam aluminum projectile impact[J/OL]. Acta Armamentarii, 2025: 1-14. DOI: 10.12382/bgxb.2025.0025. (in Chinese)
[8]	庄晟逸, 李成伟, 向文超, 等. 负泊松比结构的改进设计及其在航空航天中的应用[J]. 化工学报, 2024, 75(11): 3951-3972. doi: 10.11949/0438-1157.20240878
	ZHUANG S Y, LI C W, XIANG W C, et al. Improved designs of negative Poisson’s ratio structure and their applications in aerospace engineering[J]. CIESC Journal, 2024, 75(11): 3951-3972. (in Chinese)
[9]	FU T, WANG X, HU X, et al. Impact dynamic response of stiffened porous functionally graded materials sandwich doubly-curved shells with Arc-type auxetic core[J]. International Journal of Impact Engineering, 2024, 191: 105000. doi: 10.1016/j.ijimpeng.2024.105000 URL
[10]	CAVENAGH R, HAZELL P J, WEERASINGHE D, et al. Influence of the cover plate thickness on the ballistic penetration of re-entrant auxetic structures[J]. International Journal of Impact Engineering, 2024, 186: 104890. doi: 10.1016/j.ijimpeng.2024.104890 URL
[11]	金泽华, 刘清洋, 马文朝, 等. 新型星形负泊松比抗冲击结构设计与入水冲击[J]. 兵工学报, 2024, 45(5): 1497-1513. doi: 10.12382/bgxb.2022.1212
	JIN Z H, LIU Q Y, MA W C, et al. Design of anti-impact structure with novel star-shaped negative poisson’s ratio and research on water-entry impact[J]. Acta Armamentarii, 2024, 45(5): 1497-1513. (in Chinese) doi: 10.12382/bgxb.2022.1212