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In-Plane Dynamics Characteristics and Multi-Objective Optimization of Negative Poisson’s Ratio Honeycomb Structure with Power Function Curve

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Abstract

As an alternative to the conventional concave hexagonal honeycomb structure (CHHS), a negative Poisson’s ratio honeycomb structure with power function curve (NHPC) was devised. The relationship between the power function exponent (PFE) and normalized power function coefficient (NPFC) of honeycomb structure and its equivalent Poisson’s ratio (EPR) was explored to identify the range of variables required for the negative Poisson’s ratio effect. To investigate the in-plane mechanical properties and energy absorption characteristics of NHPC, the deformation mode, dynamic response, and energy absorption characteristics under various impact velocities were studied by constructing an in-plane impact simulation model. The results showed that NHPC obviously exhibited a negative Poisson’s ratio effect on medium and low impact velocities, and the deformation was primarily uniform. As the NPFC increased, the honeycomb structure was less prone to stress concentration, while the peak crushing force (PCF) and the specific energy absorption (SEA) declined and the plateau stress increased. A multi-objective optimization experiment was operated with low PCF and high SEA as the targets within the range of design variables in order to generate the optimal NHPC. According to the experimental findings, the improved NHPC showed a 25.48 % reduction in PCF and a 19.29 % increase in SEA. This paper provides theoretical recommendations for improving the energy absorption and structural optimization of the honeycomb structure.

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Abbreviations

CHHS:

concave hexagonal honeycomb structure

NHPC:

negative Poisson’s ratio honeycomb structure with power function curve

PFE:

power function exponent

NPFC:

normalized power function coefficient

EPR:

equivalent Poisson’s ratio

PCF :

peak crushing force

SEA :

specific energy absorption

FE:

finite element

l :

distance between the cell’s two straight arms, mm

h :

length of the straight arms on either side of the cell, mm

A :

power function coefficient

A n :

normalized power function coefficient

α :

power function exponent

ν :

impact velocity, m/s

ε :

nominal strain

μ :

Poisson’s ratio of the material

ε x :

transverse strain

ε y :

longitudinal strain

ΔX :

transverse compression of the material, m

L 1 :

transverse length of the material, m

ΔY :

average value of the boundary displacement on both sides of the material, m

L 2 :

longitudinal length of the material, m

μ e :

equivalent Poisson’s ratio of the material

F:

impact force, N

b :

out-plane thickness of the honeycomb structure, m

δ :

compression displacement, m

σ p :

plateau stresses, MPa

ε cr :

yield strain, i.e. the nominal strain value when the nominal stress reaches the initial peak stress, m

σ(ε):

nominal stress

ε d :

locking strain, i.e., the nominal strain corresponding to the honeycomb structure when it enters the densification stage

Δρ :

relative density of the honeycomb material

ρs :

density of the matrix material, kg/m3

E m :

SEA of the honeycomb structure, J/kg

E v :

energy absorbed per unit volume of the honeycomb structure, J/m3

R 2 :

determination coefficient

RMSE :

root mean square error value

f i :

analysis value of the i sample point

f′i :

response face value of the i sample point

\({\bar f}\) :

average analysis value of all sample points

N :

total number of sample points

p:

number of the polynomial

\(\overline {{f_i}} \) :

mean deviation of all solutions to the objective function fi in the Pareto solution set Ψ

ρ(f i):

standard deviation of all solutions to the objective function fi in the Pareto solution set Ψ

Nf :

number of optimization objectives

f i(i):

initial values of the objective function fi

\(f_i^Z(i)\) :

regularized values of the objective function fi

\(g_i^Z(i)\) :

weighted results of \(f_i^Z(i)\)

\(g_i^{Z*}\) :

corresponding ideal points

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Acknowledgement

This work was supported by the National Natural Science Foundation of China (51975438, U1564202); the 111 Project (B17034) and the Industrialization Project of Xiangyang Technology Transfer Center of Wuhan University of Technology (WXCJ-20220020).

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Authors and Affiliations

  1. Hubei Key Laboratory of Advanced Technology of Automotive Components, Wuhan University of Technology, Wuhan, 430070, China

    Yifan Zhu, Fengxiang Xu, Yijie Guan & Zhen Zou

  2. Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan, 430070, China

    Yifan Zhu, Fengxiang Xu, Yijie Guan & Zhen Zou

  3. Institute of Lightweight and Safety of New Energy Vehicle, School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, 212013, China

    Libin Duan & Zhanpeng Du

  4. Jiangsu XCMG State Key Laboratory Technology Co., Ltd., Xuzhou, 221000, China

    Hongfeng Ma

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  1. Yifan Zhu
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Zhu, Y., Xu, F., Guan, Y. et al. In-Plane Dynamics Characteristics and Multi-Objective Optimization of Negative Poisson’s Ratio Honeycomb Structure with Power Function Curve. Int.J Automot. Technol. 24, 1285–1303 (2023). https://doi.org/10.1007/s12239-023-0104-8

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