# Bio-Inspired Sutures: Using Finite Element Analysis to Parameterize the Mechanical Response of Dovetail Sutures in Simulated Bending of a Curved Structure

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Suture Variation

#### 2.2. Total Suture Length

#### 2.3. Model Setup

#### 2.4. Model Outputs

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Three suture geometry parameters were varied: tab radius (r), contact angle (θ), and tangent length (L).

**Figure 3.**Suture shapes produced as the contact angle (

**a**,

**b**,

**e**,

**f**vs.

**c**,

**d**,

**g**,

**h**), tangent length (

**a**,

**c**,

**e**,

**g**vs.

**b**,

**d**,

**f**,

**h**), and tab radius (

**a**–

**d**vs.

**e**–

**h**) are changed.

**Figure 4.**Representative example of the relationship between total suture length (global variable) and suture tab radius and tangent length, for a contact angle of 20° (the three local variables). While the three local variables are interchangeable (i.e., the same data can be graphed using different variables on the x-axis), plotting tangent length on the x-axis is the easiest to interpret, since L has the largest range of variation.

**Figure 5.**FEM setup: indenter displaces 6.5 mm, the bottom archway faces are fixed, and the three contacting surface pairs are modeled with frictionless contact.

**Figure 6.**Mesh near the contacting surfaces of the suture for an archway with a contact angle of 20°, tab radius of 3 mm, and tangent length of 2 mm with (

**a**) the initial fine contact mesh sizing of 0.5 mm, and (

**b**) the updated extra-fine contact mesh sizing of 0.2 mm.

**Figure 8.**Total deformation (in mm) of the two base cases: (

**a**) solid archway with no suture; (

**b**) archway with a straight-line suture; and (

**c**) one representative case with a dovetail suture. A scale factor of 3 was used to exaggerate the deformed shape. The maximum deformation in (

**b**,

**c**) exceeded the applied indenter displacement of 6.5 mm.

**Figure 9.**(

**a**) Final contact force and (

**b**) total strain energy plotted as a function of the total suture length in each archway pair.

**Figure 10.**Final contact force and total strain energy for archways with a suture tab radius of 1 mm (

**a**,

**b**) and 2 mm (

**c**,

**d**) as a function of the total suture length.

**Table 1.**Mesh convergence results obtained from a representative archway structure (θ = 20°, r = 3 mm, and L = 4 mm). Quadratic elements were used in all three cases. The percent change indicates the percent change in the model output compared with the previous mesh (i.e., from coarse to medium and from medium to fine).

Mesh Parameters | Nodes (Qty) | Elements (Qty) | Final Contact Force (N) | % Change | Total Strain Energy (mJ) | % Change | |
---|---|---|---|---|---|---|---|

Coarse | Global element size 3 mm | 53,114 | 11,133 | 18,878.2 | N/A | 59,355 | N/A |

Medium | Global element size 3 mm, contact sizing 1 mm | 177,144 | 39,784 | 19,388.0 | 2.70% | 61,695 | 3.94% |

Fine | Global element size 3 mm, contact sizing 0.5 mm | 508,028 | 118,875 | 19,423.4 | 0.18% | 62,171 | 0.77% |

Parameter | Optimal Case | Least Optimal Case |
---|---|---|

Contact angle | 20° | 0° |

Tab radius | 1 mm | 1 mm |

Tangent length | 2 mm | 17.5 mm |

Number of suture repeats | 8 repeats | 6 repeats |

Total suture length | 99.7 mm | 249.1 mm |

Final contact force | 23,124 N | 16,295 N |

Total strain energy | 74,331 mJ | 51,494 mJ |

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**MDPI and ACS Style**

Gibbons, M.M.; Chen, D.A.
Bio-Inspired Sutures: Using Finite Element Analysis to Parameterize the Mechanical Response of Dovetail Sutures in Simulated Bending of a Curved Structure. *Biomimetics* **2022**, *7*, 82.
https://doi.org/10.3390/biomimetics7020082

**AMA Style**

Gibbons MM, Chen DA.
Bio-Inspired Sutures: Using Finite Element Analysis to Parameterize the Mechanical Response of Dovetail Sutures in Simulated Bending of a Curved Structure. *Biomimetics*. 2022; 7(2):82.
https://doi.org/10.3390/biomimetics7020082

**Chicago/Turabian Style**

Gibbons, Melissa M., and Diana A. Chen.
2022. "Bio-Inspired Sutures: Using Finite Element Analysis to Parameterize the Mechanical Response of Dovetail Sutures in Simulated Bending of a Curved Structure" *Biomimetics* 7, no. 2: 82.
https://doi.org/10.3390/biomimetics7020082