# Determination of the Elasticity Modulus of Additively Manufactured Wrist Hand Orthoses

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Plan

- Production of samples: standard three-point bending samples, samples in the shape of the central part of the orthosis without openwork and with an openwork, samples in the shape of the entire orthosis;
- Determination of the density of sample materials;
- Bending tests;
- Modeling and simulation of sample load (FEM); and
- Comparison of the experimentally and simulated displacement values, determination of real value of elastic modulus on the basis of simulation results.

_{s}) is equal to the force obtained during the experiment (P

_{e}) and that the mass and geometric values are the same in the simulation and experiment, the real value of the elastic modulus (E

_{e}) can be determined according to Equation (1), derived directly from Hooke’s law.

_{e}= (U

_{is}× E

_{s})/U

_{ie},

- E
_{e}—real value of elastic modulus (MPa); - E
_{s}—simulated value of elastic modulus (MPa); - U
_{ie}—experimentally obtained displacement value (mm); and - U
_{is}—simulated displacement value (mm).

#### 2.2. Manufacturing of Samples

#### 2.3. Methodology of Bending Tests

#### 2.4. Methodology of Finite Element Analysis

_{i}) results obtained during the experimental tests. Tetrahedral elements with 10 nodes on the element (C3D10) [29] were used to apply the mesh.

_{s}= 1000 MPa and Poisson number = 0.38. The entered value of E, due to the adopted method of calculating the actual values of the modulus with the assumed homogenization of the material, is an indicative value used in accordance with Equation (1).

## 3. Results

#### 3.1. Bending Test Results

_{i}) graphs for individual samples in the series. An exemplary diagram for a series of basic samples P.1 is shown in Figure 8.

_{i}) diagrams.

#### 3.2. Finite Element Analysis Results

_{i}= U

_{2}= U

_{y}) is presented in Table 5.

_{i}values presented in Table 6 are only of a reference nature and were used to determine the actual value of the elastic modulus.

#### 3.3. Result Comparison

_{is}was 0.595 mm, which was a 0.1% difference from the experimental results (U

_{ie}= 0.596).

## 4. Discussion

^{3}] into the solid model and comparing the mass obtained from the model with the mass of the real object.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Dimensions of the test samples:(

**a**) basic sample, iso view with the marked spacing of the supports of the testing machine: Lc = 100 mm, L = 64 mm, h = 4 mm, b = 10 mm.Samples in the shape of the central part of the orthosis: (

**b**) full sample—orthosis fragment, (

**c**) openwork sample—orthosis fragment, (

**d**) orthosis-shaped sample (wall thickness of 4 mm).

**Figure 4.**Three-point bending of the sample: view of the working tooling of the testing machine, bending of the sample: (

**a**) basic, (

**b**) in the shape of the central part of the orthosis, (

**c**) in the shape of an orthosis.

**Figure 5.**Simulation model of P series samples: (1) pressing element, (2) tested sample, (3) base, (4) place of application, (5) place of receiving force.

**Figure 6.**Boundary conditions and method of loading the sample in the shape of: the middle part of the orthosis: (

**a**) full (series F), (

**b**) with openwork (series O), (

**c**) whole orthosis (WHO series).

**Figure 7.**Finite element mesh superimposed on the test specimen in the shape of the entire orthosis of high geometric complexity (partial view).

**Figure 10.**Force (P)–displacement (U

_{i}) dependence from average values for samples in the shape of the middle part of the orthosis and the entire orthosis.

**Figure 11.**The obtained von Mises stress map on the WHO.1 orthosis model, visible local stress concentration of 40.8 MPa.

**Figure 12.**Force (P)–displacement (U

_{i}) dependence for the O.3 sample: juxtaposition of experimental and simulation results.

Machine | Extrusion Temperature | Extrusion Speed | Layer Thickness | Material |
---|---|---|---|---|

FlashForge Creator Pro | 240 °C | 30 mm/s | 0.25 mm | ABS |

Series Designation | Sample No. | Weight of Samples [g] | Std. Deviation | Avg. Weight [g] |
---|---|---|---|---|

P.1 | 1 | 2.404 | 0.005 | 2.405 |

2 | 2.405 | |||

3 | 2.396 | |||

4 | 2.407 | |||

5 | 2.413 | |||

P.2 | 1 | 2.540 | 0.074 | 2.482 |

2 | 2.396 | |||

3 | 2.549 | |||

4 | 2.386 | |||

5 | 2.539 | |||

P.3. | 1 | 2.187 | 0.009 | 2.191 |

2 | 2.184 | |||

3 | 2.183 | |||

4 | 2.192 | |||

5 | 2.208 | |||

F.1 | 1 | 11.288 | 0.078 | 11.210 |

2 | 11.104 | |||

3 | 11.238 | |||

F.2 | 1 | 11.468 | 0.061 | 11.403 |

2 | 11.419 | |||

3 | 11.321 | |||

F.3 | 1 | 11.107 | 0.021 | 11.120 |

2 | 11.150 | |||

3 | 11.103 | |||

F.4 | 1 | 11.416 | 0.048 | 11.484 |

2 | 11.523 | |||

3 | 11.514 | |||

O.1 | 1 | 10.741 | 0.155 | 10.641 |

2 | 10.423 | |||

3 | 10.760 | |||

O.2 | 1 | 10.591 | 0.010 | 10.606 |

2 | 10.612 | |||

3 | 10.614 | |||

O.3 | 1 | 11.218 | 0.016 | 11.235 |

2 | 11.231 | |||

3 | 11.257 | |||

O.4 | 1 | 11.251 | 0.062 | 11.180 |

2 | 11.189 | |||

3 | 11.099 | |||

WHO.1 | 1 | 49.272 | 0.045 | 49.332 |

2 | 49.342 | |||

3 | 49.382 |

Sample, Series | Shape of Element | Type | Global Size | Amount of Nodes | Amount of Elements |
---|---|---|---|---|---|

Basic, P | Tetrahedral | C3D10 | 1 mm | 42,567 | 27,478 |

Fragment, F | Tetrahedral | C3D10 | 1.25 mm | 110,629 | 72,696 |

Fragment, O | Tetrahedral | C3D10 | 1.25 mm | 104,163 | 66,515 |

Entire orthosis, WHO | Tetrahedral | C3D10 | 1.00 mm | 1,219,383 | 807,520 |

Series Designation | Obtained Average Value U_{i} [mm] | Std. Deviation | Loading Force [N] | Qty of Samples |
---|---|---|---|---|

P.1 | 0.728 | 0.012 | 10 | 5 |

P.2 | 0.837 | 0.030 | ||

P.3 | 0.933 | 0.045 | ||

F.1 | 0.424 | 0.029 | 100 | 3 |

F.2 | 0.742 | 0.044 | ||

F.3 | 0.777 | 0.019 | ||

F.4 | 0.744 | 0.008 | ||

O.1 | 0.547 | 0.029 | ||

O.2 | 0.759 | 0.028 | ||

O.3 | 0.596 | 0.008 | ||

O.4 | 0.638 | 0.045 | ||

WHO.1 | 1.747 | 0.083 |

Series Designation | P Force Value [N] | Obtained U_{i} Displacement [mm] | Result as a Colorful Map | Approx. Computing Time [s] |
---|---|---|---|---|

P | 10 | 1.028 | 60 | |

F | 100 | 0.192 | 150 | |

O | 100 | 0.346 | 150 | |

WHO | 100 | 0.937 | 600 |

Designation | Average Density ρs [g/cm^{3}] | Deviation from Series WHO.1 [%] | Obtained E Modulus [MPa] | Deviation from Series WHO.1 [%] |
---|---|---|---|---|

P.1 | 0.601 | 11 | 1423 | 165 |

P.2 | 0.621 | 15 | 1238 | 131 |

P.3 | 0.548 | 1 | 1110 | 107 |

F.1 | 0.479 | 12 | 453 | 16 |

F.2 | 0.488 | 10 | 259 | 52 |

F.3 | 0.475 | 12 | 247 | 54 |

F.4 | 0.491 | 9 | 258 | 52 |

O.1 | 0.554 | 2 | 633 | 18 |

O.2 | 0.552 | 2 | 456 | 15 |

O.3 | 0.585 | 8 | 581 | 8 |

O.4 | 0.582 | 7 | 543 | 1 |

WHO.1 | 0.542 | 0 | 536 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Łukaszewski, K.; Wichniarek, R.; Górski, F.
Determination of the Elasticity Modulus of Additively Manufactured Wrist Hand Orthoses. *Materials* **2020**, *13*, 4379.
https://doi.org/10.3390/ma13194379

**AMA Style**

Łukaszewski K, Wichniarek R, Górski F.
Determination of the Elasticity Modulus of Additively Manufactured Wrist Hand Orthoses. *Materials*. 2020; 13(19):4379.
https://doi.org/10.3390/ma13194379

**Chicago/Turabian Style**

Łukaszewski, Krzysztof, Radosław Wichniarek, and Filip Górski.
2020. "Determination of the Elasticity Modulus of Additively Manufactured Wrist Hand Orthoses" *Materials* 13, no. 19: 4379.
https://doi.org/10.3390/ma13194379