RETRACTED: The Nonlinear Compressive Response and Deformation of an Auxetic Cellular Structure under In-Plane Loading

Wei Zhang,Ping Hu,Wenbin Hou,Zhengdong Ma

doi:10.1155/2014/214681

Abstract

At the request of the Author, the following article Zhang, W, Hou, W, Hu, Ping and Ma, Z (2014) The Nonlinear Compressive Response and Deformation of an Auxetic Cellular Structure under In-Plane Loading Advances in Mechanical Engineering published 17 November 2014. doi: 10.1155/2014/214681has been retracted due to errors discovered by the authors. On Page 3, the definition of component force in Equation 4 is incorrect. (2) On Page 4, the definition of component force in Equation 11 is incorrect. Moreover this equation should not have parameterM(length of cell wall), because a mistake was made in the process of calculation. Because of the above reasons, the conclusion obtained from the mechanical model is incorrect and should instead state that the Elastic Buckling and Plastic Collapse are both yield modes of this structure (3) On Page 5, the FEA model used in this article is not appropriate, because the deformation of single cell is not homogeneous, which means that the geometrical non-linear effect on single cell model is greater. So in the actual whole structure we may not obtain the results that were described in Page 6 Paragraph 2. (4) The data in figures 8 (page 6) and 9 (page 7) is incorrect and the values of effective Young’s modulus and plateau stress are much larger than reasonable values. The definition of effective stress is wrong in the FEA model, which means the effective stress should be calculated by the total width of cell instead of length of horizontal cell wall. For example, in Figure 8, the plateau stress can reach 140Mpa, this is not reasonable because there are many holes in this cellular structure, and its mechanical properties should be much lower than material properties of cell wall. The reasonable plateau stress should be around 2Mpa. The authors takes responsibility for these errors and regret the publication of invalid results. The nonlinear compressive response and deformation of an auxetic cellular structure that has periodic negative Poisson's ratio (NPR) cell were studied through theoretical and numerical method. The in-plane deformation and process of absorbing energy of this NPR cellular structure were discussed. The relative density of NPR cell was determined by geometric parameters and a theoretical approach to the strength of NPR cell was carried out to analyze the failure process under in-plane compression. Thus, to prove the effective of unit cell mechanical model, the size effect of this NPR cellular structure was discussed. The simulations of two different NPR cellular structures under in-plane compression were generated and their effective properties, strain-stress curves, and absorbed energy were analyzed. It can be concluded that the NPR cell that has lower relative density may have better capability of absorbing energy with enhanced Young's modulus. Finally the parametric analyses related to relative density were presented with NPR unit cell model and a set of quasistatic compressive experiments was carried out, which can be used to reveal the nonlinear properties of NPR cellular structure and to prove the effectiveness of theoretical method.

Highlights

E The cellular structure plays an important role in most high performance racing cars, which attracts more and more sci-R entists to study its topological structure and properties [1, 2].performance of energy absorption by limit compressive stress [7].The traditional honeycomb structure has some disadvantages such as high peak stress, unstable plateau stress, and short duration
The plateau failure mode and plateau stress are mainly discussed in this stress is a very important indication to evaluate the perfor- paper
When the negative Poisson’s ratio (NPR) cellular structure is under geometric parameters and plateau stress and evaluated the loading, the effective Poisson’s ratio is less than zero, and the εy Structure core εx

Summary

Introduction

E The cellular structure plays an important role in most high performance racing cars, which attracts more and more sci-. Gibson’s research presented that cellular structure made up of these two-dimensional cells the cellular structure which has excellent crashworthiness has negative effective Poisson’s ratio and enhanced Young’s should have high, stable, and long-duration plateau stress modulus as well as the common advantages of traditional [6]. Due to negative Poisson’s ratio and enhanced Young’s modulus, the NPR cell may reach higher limit compressive stress presenting higher plateau stress with lower density. Comparing ρ2 with ρ3, the structure of ρ3 has lower density, but it has higher plateau stress by negative Poisson’s ratio and enhanced Young’s modulus It can be concluded from the above analysis that the cell should have lower final stress and higher plateau stress to improve the crashworthiness, and the NPR cellular structure that has lower density may have higher plateau stress. The strain-stress curve of NPR cellular structure is shown, which can be divided into three stages: elastic density, which is shown in the shadow area of Figure 4. The Euler critical load of cell is given by: Stress σ∙2

D Figure 3

D Elastic buckling

E Figure 9

In-Plane Compressive Experiments

D Figure 10

Conclusion