# A Modified Three-Dimensional Negative-Poisson-Ratio Metal Metamaterial Lattice Structure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design and Manufacture of a Modified 3D NPR Structure

#### 2.1. Modified 3D NPR Structural Design

_{2}. The values of the three model plane parameters are shown in Table 1.

_{x}in the X direction, width is the length in the Z direction is L

_{z}, and thickness is in “t”. In this paper, the mechanical properties of the negative-Poisson-specific metamaterial were studied by taking the three types of honeycomb types (A, B, and C of 3 × 3 × 3), i.e., ∅

_{2}= 50°, ∅

_{2}= 60°, and ∅

_{2}= 70°. The 2D plane composition is shown in Figure 4, and the main parameters of the honeycomb structure of the three types are shown in Table 2.

#### 2.2. Manufacture of a Modified 3D NPR Structure

## 3. Modified 3D Negative-Poisson-Specific Lattice Test

## 4. Finite Element Numerical Simulation Analysis

#### 4.1. Performance of 316 L Stainless Steel

#### 4.2. Finite Element Model Establishment

_{2}were established as 50°, 60°, and 70° (type A; type B; type C) and the corresponding three control models (control A; control B; control C). These were saved in IGES file format, imported into Abaqus CAE commercial software, and quasi-static compression simulation experiments were performed to study the mechanical properties at different angles.

#### 4.3. Analysis and Discussion of Mechanical Responses of Finite Element Models

#### 4.4. Finite Element Poisson’s Ratio Analysis and Discussion

#### 4.5. Energy Absorption

## 5. Finite Element Model Comparison between Experiments

## 6. Conclusions

- The modified NPR structure designed here can effectively improve the stiffness of the structure and make up for the low stiffness of the negative Poisson relative to the metamaterial model;
- Increasing the modified NPR structure of the star can effectively improve the stability of the structure and can avoid the phenomenon of “convexity” during destruction. The macroscopic stability of the structure is worse with increasing the ∅ angle of the star structure;
- The energy absorption effect of the modified structure depends on the ∅ angle of the star structure rather than the concave angle ${\varnothing}_{2}$. The energy absorption effect of the modified NPR structure is the best when ∅ = 70.9°.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Modified NPR 2D and 3D structure configurations. (

**a**) Modified 3D NPR structure configuration; (

**b**) Schematic diagram of the 3D component unit structure of the control model; (

**c**) Geometric structure configuration of 2D star structure components; (

**d**) geometric structure configuration of 2D concave structure components.

**Figure 4.**Different 2D plane compositions: (

**a**) type A, face-up and overhead composition; (

**b**) type B, face-up and overhead composition; (

**c**) type C, face-up and overhead composition.

**Figure 15.**Three types of load–displacement curves. (

**a**) Comparative load–displacement curve of type A; (

**b**) Comparative load–displacement curve of type B; (

**c**) Comparative load–displacement curve of type C.

**Figure 16.**Load–displacement curve of numerical analogue: (

**a**) type A load–displacement curve; (

**b**) type B load–displacement curve; (

**c**) type C load–displacement curve; (

**d**) three types of fitting simulation load–displacement curves.

**Figure 17.**Schematic diagram of the lateral strain points of the simulated structure negative-Poisson-specific space.

**Figure 18.**Simulation Poisson’s ratio comparison: Poisson’s ratio–strain curve comparison for type A, type B, and type C, as well as control A, control B, and control C.

Type | A (mm) | B (mm) | ∅ (°) | ∅_{2} (°) | L (mm) |
---|---|---|---|---|---|

A | 18.82 | 39.70 | 38.14 | 50 | 70 |

B | 18.82 | 36.03 | 70.90 | 60 | 70 |

C | 18.82 | 33.88 | 105.77 | 70 | 70 |

Type | ∅_{2} | H (mm) | L_{x} | L_{z} | T (mm) |
---|---|---|---|---|---|

A | 50 | 231.66 | 154.05 | 154.05 | 5 |

B | 60 | 231.66 | 168.38 | 168.38 | 5 |

C | 70 | 231.66 | 180.37 | 180.37 | 5 |

Classification | Elastic Modulus (GPa) | Yield Limit (MPa) | Tensile Strength (MPa) | $\mathbf{Density}(\mathbf{Kg}/{\mathbf{m}}^{3})$ | Poisson Ratio |
---|---|---|---|---|---|

SLM Specimen1 | 183.99 | 505 | 665 | 8.737 | 0.317 |

SLM Specimen2 | 197.51 | 500 | 665 | 8.791 | 0.316 |

SLM Specimen3 | 200.74 | 510 | 665 | 8.816 | 0.318 |

Ordinary 316 L | 206 | 269.17 | 603.50 | 8.027 | 0.3 |

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**MDPI and ACS Style**

Li, F.; Zhang, Q.; Shi, H.; Liu, Z.
A Modified Three-Dimensional Negative-Poisson-Ratio Metal Metamaterial Lattice Structure. *Materials* **2022**, *15*, 3752.
https://doi.org/10.3390/ma15113752

**AMA Style**

Li F, Zhang Q, Shi H, Liu Z.
A Modified Three-Dimensional Negative-Poisson-Ratio Metal Metamaterial Lattice Structure. *Materials*. 2022; 15(11):3752.
https://doi.org/10.3390/ma15113752

**Chicago/Turabian Style**

Li, Fangyi, Qiang Zhang, Huimin Shi, and Zheng Liu.
2022. "A Modified Three-Dimensional Negative-Poisson-Ratio Metal Metamaterial Lattice Structure" *Materials* 15, no. 11: 3752.
https://doi.org/10.3390/ma15113752