# 3D Printing of Flexible Mechanical Metamaterials: Synergistic Design of Process and Geometric Parameters

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Parameterized Structural Design

_{G}) structure is defined as:

_{solid}and V

_{void}, respectively. Simultaneously, when the fixed value T in the TPMS structural function equation is replaced by a new function T(x,y,z) [33], a gradient change in the volume fraction in a specified direction within the same lattice structure arrangement can be achieved.

#### 2.2. Synergistic Design of the Process and Geometric Parameters

_{1}obtained via experimental measurements in 3D printing.

_{1}. This can indicate the local change trend of the elastic modulus around the volume fraction V

_{1}. Based on this, ΔV is defined as follows:

_{solid}+ V

_{void}is unchanged. What needs to be specifically noted is that △V is a parameter dependent on V

_{1}, and thus the control of elastic anisotropy in 3D-printed lattice structures is also centered around the fixed volume fraction lattice structure. Then, the mapping curvature value T ± ΔT can be determined using the equation F(T, V), and then the gradient function T(x,y,z) can be constructed using the first function through two points (T − ΔT, l) and (T + ΔT, l), the independent variable is the direction of the gradient, the other variables are constants, and l is the gradient length. The gradient range of the gradient structure can be determined using the above method.

#### 2.3. Experiment and Simulation

_{11}= C

_{22}= C

_{33}, C

_{12}= C

_{13}= C

_{23}, and C

_{44}= C

_{55}= C

_{66}. The remaining constants are zero. The stiffness matrix of Gyroid [C] can be simplified as follows: To calculate the values of C

_{11}, C

_{12}, and C

_{44}, at each step, one of the strains is 1, and the others are 0. Using this numerical homogenization method, the normal strain and shear strain are realized using finite element analysis to calculate the corresponding stress. For normal strain ɛ

_{11}= 1, the boundary condition is set to:

_{31}= 1, the boundary condition is set to:

## 3. Results

#### 3.1. Influence of Interlayer Bonding on Mechanical Properties

#### 3.2. Collaborative Optimization Design of Process and Structural Parameters

#### 3.3. Functional Analysis of Gradient Lattice Structure

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**3D-printing model and sample. (

**a**) Lattice structure unit cell model. (

**b**) Lattice structure model. (

**c**) Lattice structure sample preparation.

**Figure 5.**The homogenization theory simulates the results of three-dimensional elastic modulus surface (unit: MPa).

**Figure 6.**The elastic modulus of the uniform Gyroid structure. (

**a**) The theoretical simulation value of homogenization. (

**b**) The sample preparation test value of SLS process.

**Figure 7.**Uniform and gradient Gyroid structure SLS sample preparation. (

**a**) Comparison of uniform and gradient structure printed samples. (

**b**) Comparison of the variation in the distribution of integrals in the Z direction between uniform and gradient structures (

**c**).Three-dimensional modulus surfaces of uniform structure and gradient structure.

**Figure 8.**Compression load force and displacement curve. (

**a**) Stress–strain curves of uniform lattice structure in x, y, and z directions. (

**b**) Stress–strain curves of gradient lattice structure in x, y, and z directions.

Process Parameter | Value |
---|---|

Laser power | 20 w |

Laser scan speed | 2500 mm/s |

Laser hatch spacing | 0.1 mm |

Powder deposition thickness | 0.15 mm |

Type | Weight (g) | Dimension (X × Y × Z mm) | |
---|---|---|---|

Gradient Gyroid structure | Sample 1 | 14.31 | 39.38 × 39.44 × 40.51 |

Sample 2 | 13.57 | 39.33 × 39.55 × 40.50 | |

Sample 3 | 13.18 | 39.64 × 39.89 × 40.32 | |

Uniform Gyroid structure | Sample 1 | 13.78 | 39.32 × 39.22 × 40.12 |

Sample 2 | 14.26 | 39.53 × 39.23 × 40.48 | |

Sample 3 | 13.54 | 39.25 × 39.64 × 40.33 |

Uniform Gyroid | Gradient Gyroid | ||||
---|---|---|---|---|---|

Modulus of Elasticity E (MPa) | Modulus of Elasticity E (MPa) | ||||

X([100]) | Y([010]) | Z([001]) | X([100]) | Y([010]) | Z([001]) |

0.988 | 0.975 | 1.175 | 1.001 | 1.106 | 1.025 |

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**MDPI and ACS Style**

Li, N.; Xue, C.; Chen, S.; Aiyiti, W.; Khan, S.B.; Liang, J.; Zhou, J.; Lu, B.
3D Printing of Flexible Mechanical Metamaterials: Synergistic Design of Process and Geometric Parameters. *Polymers* **2023**, *15*, 4523.
https://doi.org/10.3390/polym15234523

**AMA Style**

Li N, Xue C, Chen S, Aiyiti W, Khan SB, Liang J, Zhou J, Lu B.
3D Printing of Flexible Mechanical Metamaterials: Synergistic Design of Process and Geometric Parameters. *Polymers*. 2023; 15(23):4523.
https://doi.org/10.3390/polym15234523

**Chicago/Turabian Style**

Li, Nan, Chenhao Xue, Shenggui Chen, Wurikaixi Aiyiti, Sadaf Bashir Khan, Jiahua Liang, Jianping Zhou, and Bingheng Lu.
2023. "3D Printing of Flexible Mechanical Metamaterials: Synergistic Design of Process and Geometric Parameters" *Polymers* 15, no. 23: 4523.
https://doi.org/10.3390/polym15234523