# Finite Element Study of a Threaded Fastening: The Case of Surgical Screws in Bone

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## Abstract

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## 1. Introduction

## 2. Axisymmetric Two-Dimensional FE Model

## 3. Comparison with a Three-Dimensional FE Model

^{6}elements, see Figure 7. The materials were steel and bone as previously defined, and the contact definition was a frictional one with friction coefficient values as before, see Table 1. All remaining settings were imposed as in the two-dimensional case to generate a model suitable for comparing with the axisymmetric case.

## 4. Simplified Bolt Thread Modelling

#### 4.1. Comparison of a Symmetric ISO68 Thread

#### 4.2. Comparison of an Asymmetric HA Thread

#### 4.3. Scale Factor Effects

## 5. Model Definition and Computing Time

- Simplified bolt thread modelling. Requires the implementation of a simple geometry (cylinder) to define the thread region, and three input parameters. The mesh needs a simple size control based on the pitch value, and easy to define.
- Detailed two-dimensional FE model. The geometry for the contact teeth must be fully defined as a CAD format. The contact regions depend on the number of threads, in this case eight individual contacts. The mesh requires attention: first, a simple size control by pitch, but also customized size controls in the thread edges and the fillets, which implies higher time effort for the definition of the mesh. Indeed, the two-dimensional analysis may not be at all adequate for the overall problem definition.
- Detailed three-dimensional FE models. Again, the geometry must be fully input in CAD format. The contact regions depend on the number of threads, and the individual thread-to-thread contacts. The mesh must be fully customized to obtain smooth transitions at the tiny features. Small element sizes and growing control are needed to have uniform elements, and to avoid deformed elements, which produce inaccurate results.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Drawing of the threads according to (

**a**), ISO5835-HA; (

**b**), metric ISO68; (

**c**), Withworth BS84.

**Figure 2.**Drawing of the geometry and mesh defined for the two-dimensional axisymmetric Finite Element (FE) models. Upper panels: general view of threads ISO68 (

**a**) and ISO5845-HA (

**b**). Note that the number of inserted threads is the same in both cases. Lower panels: detailed view of threads ISO68 (

**c**) and ISO5845-HA (

**d**). The scale is now the same and the different size is given by the thread pitch definition.

**Figure 3.**Boundary conditions (BC) application over two-dimensional model (

**a**) and three-dimensional model (

**b**). The same BC are used in all models and geometries.

**Figure 5.**Force measured on each thread relative to the applied force. This load is defined as the contact reaction on the thread. The results are for threads ISO68 for steel-steel and steel-bone contacts, and for HA thread with steel-bone contact, according to the legend.

**Figure 6.**Von Mises stress along a path in the bone defined parallel to the screw axis and separated 0.25p from the outermost diameter of the internal thread. The lines correspond to the calculations done with a two-dimensional axisymmetric FE model of ISO68 M2 thread with steel-steel and steel-bone contact, and 2mm HA thread with steel-bone contact.

**Figure 7.**Drawing and detail of the screw and plate used for the three-dimensional FE model, showing the complex mesh defined, with a large density at the thread contact region: (

**a**), global mesh view; (

**b**), detailed view near the contact region.

**Figure 8.**Von Mises stress along a path in the bone defined parallel to the screw axis and separated 0.25 p from the outermost diameter of the internal thread. The lines correspond to two-dimensional and three-dimensional FE models for a HA 2 mm thread in steel-bone contact.

**Figure 9.**Stress state (von Mises) along a path in the bone defined parallel to the screw axis and separated 0.25 p from the outermost diameter of the internal thread. The lines correspond to the two-dimensional FE model and the simplified model, for an ISO68 M2 thread in steel-bone contact. Thread pitch is 0.4 mm.

**Figure 10.**Von Mises stress along a path in the bone defined parallel to the screw axis and separated 0.25 p from the outermost diameter of the internal thread. The lines correspond to the two-dimensional FE model and the simplified model, for an HA 2 mm thread in steel-bone contact. Thread pitch is 0.6 mm.

**Figure 11.**Von Mises stress along a path in the bone defined parallel to the screw axis and separated 0.25 p from the outermost diameter of the internal thread. The lines correspond to the two-dimensional FE model and the simplified model, for values corresponding to a HA thread of 5 mm in steel-bone contact. Thread pitch is 1.75 mm.

Steel AISI-316L | Bone | |

Young’s Modulus (GPa) | 193 | 16 |

Poisson’s ratio | 0.3 | 0.3 |

Density (g/cm^{3}) | 7850 | 1900 |

Yield Stress (MPa] | 290 | 102 |

Steel-Steel | Steel-Bone | |

Friction coefficient | 0.1 | 0.37 |

**Table 2.**CPU (Central Processing Unit) solving time of the models (Intel Core i7-4820K 3.70 GHz, 64 GB RAM).

Model | Elapsed Time |
---|---|

ISO58 M2 steel-steel contact 2-dim FE | 5 s |

ISO58 M2 steel-bone contact 2-dim FE | 5 s |

ISO5835 HA steel-bone contact 2-dim FE | 27 s |

ISO5835 HA steel-bone contact 3-dim FE | 3187 s |

ISO58 M2 steel-bone 2-dim simplified | 7 s |

ISO5835 HA steel-bone 2-dim simplified | 9 s |

ISO5835 HA steel-bone 3-dim simplified | 76 s |

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**MDPI and ACS Style**

López-Campos, J.A.; Segade, A.; Casarejos, E.; Fernández, J.R.; Vilán, J.A.; Izquierdo, P. Finite Element Study of a Threaded Fastening: The Case of Surgical Screws in Bone. *Symmetry* **2018**, *10*, 335.
https://doi.org/10.3390/sym10080335

**AMA Style**

López-Campos JA, Segade A, Casarejos E, Fernández JR, Vilán JA, Izquierdo P. Finite Element Study of a Threaded Fastening: The Case of Surgical Screws in Bone. *Symmetry*. 2018; 10(8):335.
https://doi.org/10.3390/sym10080335

**Chicago/Turabian Style**

López-Campos, J. A., A. Segade, E. Casarejos, J. R. Fernández, J. A. Vilán, and P. Izquierdo. 2018. "Finite Element Study of a Threaded Fastening: The Case of Surgical Screws in Bone" *Symmetry* 10, no. 8: 335.
https://doi.org/10.3390/sym10080335