# An Enhanced Three-Dimensional Auxetic Lattice Structure with Improved Property

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental

#### 2.1. Structure Design

_{1}; the angle of inner strut with side strut, θ; the angle of connecting strut with the horizontal direction, θ

_{1}; the diameter of side and inner struts, D; and the connecting strut diameter, d (Figure 2). It is noteworthy that the value of L

_{1}and θ

_{1}depend on other parameters which cannot be changed independently. As shown in Figure 2, the lattice geometric parameters have the relationship as follows:

_{0}is the density of all struts in a unit cell, ρ

_{s}is the apparent density of a unit cell and α is the designed length ratio of side strut to inner strut, i.e., α = H/L.

#### 2.2. Fabrication of Lattice Samples

#### 2.3. Mechanical Measurement

_{zy}could be calculated by the following formula:

## 3. Results and Discussion

#### 3.1. Parameter Studies of the Structures

#### 3.1.1. Effect of Strut Diameter d

#### 3.1.2. Effect of θ Angle

#### 3.2. Effect of Compression Direction

#### 3.3. Effect of Material

#### 3.4. Analysis of Enhanced Mechanical Properties

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Design route of the enhanced auxetic lattice structure: (

**a**) 2D unit cell, (

**b**) 3D unit cell of re-entrant lattice structure, (

**c**) 2D enhanced unit cell, (

**d**) unit cell of the enhanced 3D structure, (

**e**) enhanced 3D auxetic structure based on corresponding unit cell, (

**f**) three views of the unit cell of the 3D re-entrant structure, (

**g**) three views of the unit cell of the enhanced 3D structure.

**Figure 3.**(

**a**) 3D auxetic structure based on a photosensitive resin and (

**b**) lattice sample based on aluminum.

**Figure 4.**(

**a**) Stress–strain curves of enhanced lattice structures with different connecting strut diameters d based on Al, (

**b**) Poisson’s ratios of enhanced structures with different connecting strut diameters d based on Al.

**Figure 6.**(

**a**) Stress–strain curves of enhanced structures with different θ angles based on Al, (

**b**) Poisson’s ratios of enhanced structures and 3D re-entrant lattice structures with different θ angles based on Al.

**Figure 7.**Stress–strain curves of 3D re-entrant lattice structures with different θ angles based on Al.

**Figure 9.**Stress–strain curves of (

**a**) sample 3 and (

**b**) sample 4 based on Al in different compression directions.

**Figure 11.**The enhancement of the specific stiffness and strength of the structures with different (

**a**) connecting strut diameters and (

**b**) θ angles.

Sample | H (mm) | L (mm) | θ (°) | D (mm) | d (mm) | Relative Density | |
---|---|---|---|---|---|---|---|

$\mathbf{Theoretical}\text{}{\overline{\mathit{\rho}}}_{\mathit{t}}$ | $\mathbf{Experimental}\text{}{\overline{\mathit{\rho}}}_{\mathit{e}}$ | ||||||

1 | 7.0 | 3.5 | 70 | 1.4 | 0.7 | 0.27 | 0.25 |

2 | 0.6 | 0.25 | 0.23 | ||||

3 | 0.5 | 0.23 | 0.22 | ||||

4 | 7.0 | 3.5 | 60 | 1.4 | 0.5 | 0.28 | 0.26 |

5 | 70 | 0.25 | 0.22 | ||||

6 | 80 | 0.19 | 0.18 |

Sample | H (mm) | L (mm) | θ (°) | D (mm) | Relative Density | |
---|---|---|---|---|---|---|

$\mathbf{Theoretical}\text{}{\overline{\mathit{\rho}}}_{\mathit{t}}$ | $\mathbf{Experimental}\text{}{\overline{\mathit{\rho}}}_{\mathit{e}}$ | |||||

7 | 7.0 | 3.5 | 60 | 1.4 | 0.24 | 0.24 |

8 | 70 | 0.20 | 0.20 | |||

9 | 80 | 0.16 | 0.15 |

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**MDPI and ACS Style**

Xue, Y.; Gao, P.; Zhou, L.; Han, F.
An Enhanced Three-Dimensional Auxetic Lattice Structure with Improved Property. *Materials* **2020**, *13*, 1008.
https://doi.org/10.3390/ma13041008

**AMA Style**

Xue Y, Gao P, Zhou L, Han F.
An Enhanced Three-Dimensional Auxetic Lattice Structure with Improved Property. *Materials*. 2020; 13(4):1008.
https://doi.org/10.3390/ma13041008

**Chicago/Turabian Style**

Xue, Yingying, Peixin Gao, Li Zhou, and Fusheng Han.
2020. "An Enhanced Three-Dimensional Auxetic Lattice Structure with Improved Property" *Materials* 13, no. 4: 1008.
https://doi.org/10.3390/ma13041008