# FDM Layering Deposition Effects on Mechanical Response of TPU Lattice Structures

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fused Deposition Modeling on Lattice Structures

#### 2.1. Design

#### 2.2. Experimental Tests

#### 2.3. FDM Process in Conjunction with TPU

## 3. Finite Element Method on Lattice Structures

#### 3.1. Material: Models

_{B}is the effective stress. Table 3 shows the editable parameters in the Abaqus formulation for Equation (4), identified in the literature [29,30], and after an optimization procedure on cubic and cylindrical numerical models, S is the stress scaling factor, $m$ is an exponent usually bigger than $1$, $C$ is an exponent that can assume values from $-1$ to $0$, and $A$ and $E$ are constants.

#### 3.2. Simulations and Overviews

## 4. Results

## 5. Discussion

## 6. Conclusions

- By the traditional FE analysis, an anisotropic behavior of such structures was proven;
- Anisotropy was ascribed to the layering process of filament, not always quantifiable a priori;
- A phenomenological layering factor φ
_{l}was defined that tries to correlate the number of FDM contours, the deformation level, with the anisotropy degree; - On the basis of the layering factor, thin-walled cell structures were confirmed to be the less affected, whereas larger walled structures were negatively affected;
- The mechanical and functional behaviors of this kind of structure were confirmed to be influenced by many parameters, related to material and process, as well asa specific geometry.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Wang, P.; Zou, B.; Ding, S.; Li, L.; Huang, C. Effects of FDM-3D printing parameters on mechanical properties and microstructure of CF/PEEK and GF/PEEK. Chin. J. Aeronaut.
**2021**, 34, 236–246. [Google Scholar] [CrossRef] - Ziemian, C.; Sharma, M.; Ziemian, S. Anisotropic mechanical properties of ABS parts fabricated by fused deposition modelling. In Mechanical Engineer; Gokcek, M., Ed.; InTech: London, UK, 2017; pp. 159–180. [Google Scholar]
- Durgun, I.; Ertan, R. Experimental investigation of FDM process for improvement of mechanical properties and production cost. Rapid Prot. J.
**2014**, 20, 228–235. [Google Scholar] [CrossRef] - Pagac, M.; Schwarz, D.; Petru, J.; Polzer, S. 3D printed polyurethane exhibits isotropic elastic behavior despite its anisotropic surface. Rapid Prot. J.
**2020**, 26. [Google Scholar] [CrossRef] - Garzon-Hernandez, S.; Garcia-Gonzalez, D.; Jérusalem, A.; Arias, A. Design of FDM 3D printed polymers: An experimental-modelling methodology for the prediction of mechanical properties. Mater. Des.
**2020**, 188, 108414. [Google Scholar] [CrossRef] - Ahn, S.H.; Montero, M.; Odell, D.; Roundy, S.; Wright, P.K. Anisotropic material properties of fused deposition modeling ABS. Rapid Prot. J.
**2002**, 8, 248–257. [Google Scholar] [CrossRef] [Green Version] - Baich, L.; Manogharan, G.; Marie, H. Study of infill print parameters on mechanical strength and production cost-time of 3D printed ABS parts. Int. J. Rapid Manuf.
**2015**, 5, 308–319. [Google Scholar] [CrossRef] - Bhate, D.; Penick, C.A.; Ferry, L.A.; Lee, C. Classification and selection of cellular materials in mechanical design: Engineering and biomimetic approaches. Designs
**2019**, 3, 19. [Google Scholar] [CrossRef] [Green Version] - Kumar, A.; Verma, S.; Jeng, J.-Y. Supportless Lattice structures for energy absorption fabricated by fused deposition modeling. 3D Print. Add. Manuf.
**2020**, 7, 85–96. [Google Scholar] [CrossRef] - Askari, M.; Hutchins, D.A.; Thomas, P.J.L.; Astolfi, R.L.; Watson, M.; Abdi, M.; Ricci, S.; Laureti, L.; Nie, S.; Freear, R.; et al. Additive manufacturing of metamaterials: A. review. Add. Manuf.
**2020**, 36, 101562. [Google Scholar] [CrossRef] - Nazir, A.; Abate, K.M.; Kumar, A.; Jeng, J.-Y. A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures. Int. J. Adv. Manuf. Technol.
**2019**, 104, 3489–3510. [Google Scholar] [CrossRef] - Bartolomé, L.; Aginagalde, A.; Martínez, A.B.; Urchegui, M.A.; Tato, W. Experimental characterization and modelling of large-strain viscoelastic behavior of a thermoplastic polyurethane elastomer. Rubber Chem. Technol.
**2013**, 86, 146–164. [Google Scholar] [CrossRef] - Solomon, I.J.; Sevvel, P.; Gunasekaran, J. A review on the various processing parameters in FDM. Mater. Today Proc.
**2021**, 37, 509–514. [Google Scholar] [CrossRef] - Panda, B.; Leite, M.; Biswal, B.B.; Niu, X.; Garg, A. Experimental and numerical modelling of mechanical properties of 3D printed honeycomb structures. Measurement
**2018**, 116, 495–506. [Google Scholar] [CrossRef] - Sood, A.K.; Ohdar, R.K.; Mahapatra, S.S. Experimental investigation and empirical modeling of FDM process for compressive strength improvement. J. Adv. Res.
**2012**, 3, 81–90. [Google Scholar] [CrossRef] [Green Version] - Wu, W.; Geng, P.; Li, G.; Zhao, D.; Zhang, H.; Zhao, J. Influence of layer thickness and raster angle on the mechanical study between PEEK and ABS. Materials
**2015**, 8, 5834–5846. [Google Scholar] [CrossRef] - Hernandez, R.; Slaughter, D.; Whaley, D.; Tate, J.; Asiabanpuor, B. Analyzing the tensile, compressive, and flexural properties of 3D printed ABS parts. In Proceedings of the 27th Annual International Solid Freeform Fabrication Symposium, San Marcos, TX, USA, 8–10 August 2016; pp. 939–950. [Google Scholar]
- Motaparti, K.P. Effect of Build Parameters on Mechanical Properties of Ultem 9085 Parts by Fused Deposition Modeling. Masters’ Thesis, Missouri University of Science and Technology, Rolla, MO, USA, 2016. [Google Scholar]
- Vega, V.; Clements, J.; Lam, T.; Abad, A.; Fritz, B.; Ula, N.; Es-Said, O.S. The effect of layer orientation on the mechanical properties and microstructure of a polymer. J. Mater. Eng. Perform.
**2011**, 20, 978–988. [Google Scholar] [CrossRef] - Mohaed, O.A.; Masood, S.H.; Bhowmik, J.L. Optimization of FDM process parameters: A review of current research and future prospects. Adv. Manuf.
**2015**, 3, 42–52. [Google Scholar] [CrossRef] - Torrado, A.R.; Shemelya, C.M.; English, J.D.; Lin, Y.; Wicker, R.B.; Roberson, D.A. Characterizing the effect of additives to ABS on the echanical property anisotropy of specimens fabricated by material extrusion 3D printing. Add. Manuf.
**2015**, 6, 16–29. [Google Scholar] - Dawoud, M.; Taha, I.; Ebeid, S.J. Mechanical behaviour of ABS: An experimental study using FDM and injection moulding techniques. J. Manuf. Process.
**2016**, 21, 39–45. [Google Scholar] [CrossRef] - Hmeidat, N.S.; Pack, R.C.; Talley, S.J.; Moore, R.B.; Compton, B.G. Mechanical anisotropy in polymer composites produced by material extrusion additive manufacturing. Add. Manuf.
**2020**, 34, 101385. [Google Scholar] [CrossRef] - Rybachuk, M.; Mauger, C.A.; Fiedler, T.; Öchsner, A. Ochsner, Anisotropic mechanical properties of fused deposition modeled parts fabricated by using acrylonitrile butadiene styrene polymer. J. Polym. Eng.
**2017**, 37, 699–706. [Google Scholar] [CrossRef] - Anitha, R.; Arunachalam, S.; Radhakrishnan, P. Critical parameters influencing the quality of prototypes in fused deposition modelling. J. Mater. Proc. Technol.
**2001**, 118, 385–388. [Google Scholar] [CrossRef] - Rodríguez-Panes, A.; Claver, J.; Camacho, A.M. The influence of Manufacturing parameters on the mechanical behaviour of PLA and ABS pieces manufactured by FDM: A comparative analysis. Materials
**2018**, 11, 1333. [Google Scholar] [CrossRef] [Green Version] - Lee, B.; Abdullah, J.; Khan, Z. Optimization of rapid prototyping parameters for production of flexible ABS object. J. Mater. Proc. Technol.
**2005**, 169, 54–61. [Google Scholar] [CrossRef] - Popescu, D.; Zapciu, A.; Amza, C.; Baciu, F.; Marinescu, R. FDM process parameters influence over the mechanical properties of polymer specimens: A. review. Polym. Test.
**2018**, 69, 157–166. [Google Scholar] [CrossRef] - Qi, H.; Boyce, M. Stress-strain behavior of thermoplastic polyurethanes. Mech. Mater.
**2005**, 37, 817–839. [Google Scholar] [CrossRef] - Bergström, J.; Boyce, M. Constitutive modeling of the time-dependent and cyclic loading of elastomers and application to soft biological tissues. Mech. Mater.
**2001**, 33, 523–530. [Google Scholar] [CrossRef] - Hohimer, C.; Christ, J.; Aliheidari, N.; Mo, C.; Ameli, A. 3D printed thermoplastic polyurethane with isotropic material properties. In Behavior and Mechanics of Multifunctional Materials and Composites; SPIE: Bellingham, WA, USA, 2017; Article Number 1016511. [Google Scholar]
- Elmrabet, N.; Siegkas, P. Dimensional consideration on the mechanical properties of 3D printed polymer parts. Polym. Test.
**2020**, 90, 106656. [Google Scholar] [CrossRef] - Kumar, A.; Collini, L.; Daurel, A.; Jeng, J.-Y. Design and additive manufacturing of closed cells from supportless lattice structure. Add. Manuf.
**2020**, 33, 101168. [Google Scholar] [CrossRef] - Collini, L.; Ursini, C.; Kumar, A. Design and optimization of 3D fast printed cellular structures. Mater. Des. Proc. Commun.
**2021**, e227. [Google Scholar] [CrossRef] - Cantrell, J.T.; Rohde, S.; Damiani, D.; Gurmani, R.; DiSandro, L.; Anton, J.; Young, A.; Jerez, A.; Steinbach, D.; Kroese, C.; et al. Experimental characterization of the mechanical properties of 3D-printed ABS and polycarbonate parts. In Advancement of Optical Methods in Experimental Mechanics; Yoshida, S., Lamberti, L., Sciammarella, C., Eds.; Conference Proceedings of the Society for Experimental Mechanics Series; Springer: Cham, Switzerland, 2016; Volume 3. [Google Scholar]
- Zou, R.; Xia, Y.; Liu, S.; Hu, P.; Hou, W.; Hu, Q.; Shan, C. Isotropic and anisotropic elasticity and yielding of 3D printed material. Comp. Part B Eng.
**2016**, 99, 506–513. [Google Scholar] [CrossRef] - Abbot, D.; Kallon, D.; Anghel, C.; Dube, P. Finite Element analysis of 3D printed model via compression tests. Procedia Manuf.
**2019**, 35, 164–173. [Google Scholar] [CrossRef] - Kumar, A.; Collini, L.; Ursini, C.; Jeng, J.-Y. Analyzing the functional properties of closed cell cellular lattice structure designed with thin and thick wall for additive manufacturing. Mater. Des.
**2021**, submitted. [Google Scholar]

**Figure 1.**Unit cells and, respectively, lattice structures with their appropriate geometries and sizes [mm]: (

**a**) open cell; (

**b**) closed thin-walled cell; (

**c**) closed thick-walled cell.

Printing Phase: FDM Parameters | |
---|---|

Nozzle diameter [mm] | 0.4 |

Layer height [mm] | 0.2 |

Printing speed [mm/min] | 1100 |

Print infill [%] | 100 |

Printing temperature [°C] | 230 |

Bed temperature [°C] | 70 |

FDM Machine Parameters | |

Minimum thickness [mm] | 0.6 |

Maximum overhang angle [°] | 50 |

Material Parameter | ${\mathbf{\mu}}_{\mathbf{i}}$ | ${\mathbf{D}}_{\mathbf{i}}$ | ${\mathbf{\alpha}}_{\mathbf{i}}$ |
---|---|---|---|

i = 2, order | 6.1298 | 0.0000 | −1.9004 |

Parameter | S | m | C | A | E |
---|---|---|---|---|---|

value | 2.2 | 4 | 0 | 12 × 10^{−3} | 0.01 |

**Table 4.**Engineering constants: Young’s modulus, Poisson ratio, and shear modulus in the three principal directions.

Material | ${\mathit{E}}_{1*}$ | ${\mathit{E}}_{2*}$ | ${\mathit{E}}_{3*}$ | ${\mathit{v}}_{12}$ | ${\mathit{v}}_{13}$ | ${\mathit{v}}_{23}$ | ${\mathit{G}}_{12}$ | ${\mathit{G}}_{13}$ | ${\mathit{G}}_{23}$ |
---|---|---|---|---|---|---|---|---|---|

Linear elastic | 13 | 26 | 13 | 0.49 | 0.39 | 0.49 | 4.36 | 9.35 | 4.36 |

Topology | Nodes | Elements |
---|---|---|

Open cell | 24,779 | 104,274 |

Closed thin-walled cell | 33,735 | 145,385 |

Closed thick-walled cell | 37,790 | 157,045 |

10% | Stiffness K_{0} [N/mm] | |||
---|---|---|---|---|

EXP | FEM | |||

Ogden | Isotropic LE | Anisotropic LE | ||

Open cell | 331 | 534.6 | 480.8 | 256.4 |

Closed thin walled | 336 | 588.8 | 508.7 | 260.7 |

Closed thick walled | 278.9 | 531.2 | 500.8 | 256.3 |

20% | Stiffness K_{0} [N/mm] | |||

EXP | FEM | |||

Ogden | Isotropic LE | Anisotropic LE | ||

Open | 220.3 | 421.7 | 548.1 | 290.2 |

Closed thin walled | 219.2 | 432.2 | 592 | 294.8 |

Closed thick walled | 181.9 | 403.8 | 524.6 | 266.2 |

30% | Stiffness K_{0} [N/mm] | |||

EXP | FEM | |||

Ogden | Isotropic LE | Anisotropic LE | ||

Open | 165.5 | 389.6 | 568.4 | 307.7 |

Closed thin walled | 161.7 | 380.1 | 609.5 | 306.6 |

Closed thick walled | 137.5 | 366.7 | 521.6 | 253.3 |

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Ursini, C.; Collini, L.
FDM Layering Deposition Effects on Mechanical Response of TPU Lattice Structures. *Materials* **2021**, *14*, 5645.
https://doi.org/10.3390/ma14195645

**AMA Style**

Ursini C, Collini L.
FDM Layering Deposition Effects on Mechanical Response of TPU Lattice Structures. *Materials*. 2021; 14(19):5645.
https://doi.org/10.3390/ma14195645

**Chicago/Turabian Style**

Ursini, Chiara, and Luca Collini.
2021. "FDM Layering Deposition Effects on Mechanical Response of TPU Lattice Structures" *Materials* 14, no. 19: 5645.
https://doi.org/10.3390/ma14195645