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Flexor tendon repair has conventionally been done by suturing techniques. However, in recent times, there have been attempts of using fibrous braided structures for the repair of ruptured tendons. In this regard, the numerical analysis of the flexural stiffness of a braided structure under bending moments is vital for understanding its capabilities in the repair of flexor tendons. In this paper, the bending deflection, curvature, contact stresses and flexural bending stiffness in the braided structure due to bending moments are simulated using Finite Element (FE) techniques. Three dimensional geometry and FE models of five sets of biaxial braided structures were developed using a python programming script. The FE models of the hybrid biaxial braids were imported into ABAQUS (v17) for post-processing and analysis. It was established that the braided fabric with largest braid angle,
*θ* = 52.5
° had the highest flexural deflection while the lowest deflection was seen in the results of the braided structure with the least braid angle,
*θ* = 38.5
°. The results in this study also portrayed that the curvature in biaxial braids will increase with a decrease in the angle between the braided yarns. This was also consistent with the change of bending angle of the biaxial structures under a bending moment. The deformation of the structures increased with increase in the braid angles. This implies that the flexural bending stiffness decreased with increase in braid angle. The stress limits during bending of the braided structures were established to be within the range that could be handled by flexor tendons during finger bending.

Flexor tendons are found in the fingers of the human hand (

Braided structures have been used in diverse fields and for myriad applications [1-3]. In the medical fields, stents are mainly used for support in annular structures and their potential in flexor tendon repair has been explored, [4,5]. In order to develop a braided structure suitable for possible application in tendon repair, flexural bending is a crucial deformation parameter that could be considered.

The analysis of the mechanical deformation of braided structures has been performed using mathematical models [

The aim of this study was to investigate the bending of biaxial braided structures in their potential use in tendon repair. In this context therefore, the flexural bending and stress distribution under a moment which may occur due to finger flexion were investigated based on finite element methods. 3D models of hybrid biaxial configurations of braided structures were developed and analyzed. Stress distributions at the yarn-yarn interface are obtained based on the numerical and analytical results.

The geometrical model of the biaxial braided structures were developed using a pre-processor (pFormex 0.9.0), [

Parameter | Description | Value |
---|---|---|

D (mm) | initial nominal diameter | 2 |

d (mm) | yarn diameter | 0.06 |

n (-) | total number of yarns | 16 |

L (mm) | initial nominal length | 10 |

E (mpa) | Young’s modulus | 206,000 |

μ (-) | friction | 0.2 |

Y (N) | yield strength | 2450 |

The finite element model of the biaxial braided structure (hybrid) created in pyFormex was imported into ABAQUS (v17). The flexural bending moment was induced by a moment of 1.5 N∙mm using a smooth step amplitude at 0.01 s at one end of the braided structure while the proximal end of the structure was fixed by constraining all displacements and rotations. This was done using the following steps:

· symmetrical boundary conditions applied to all nodes at one of of the braided structure to constrain the displacement and rotation;

u 1 = 0 , u 2 = 0 , u 3 = 0 , u r 1 = 0 , u r 2 = 0 , u r 3 = 0

· the nodes at the opposite end of the braided structure are constrained to a reference point (RP) using an MPC constraint and a moment load applied to the RP.

These boundary conditions mimic the actual flexor tendon bending behaviour during finger movement during flexion as illustrated in

The numerical analysis of the flexural bending stiffness was performed using beam theory, which implies that a braided structure can be regarded as a beam [

E I = m L 2 α (1)

The flexural bending deformation of the braided structure can also be computed at different curvatures [

E I = m ρ (2)

where the curvature of the braided structure under the bending moment, m can be evaluated as:

1 ρ = m E I (3)

The mathematically evaluated flexural stiffness was used to verify the FEA data from the bending simulations by computing root mean square error (RMSE) (Equation (4)) and mean absolute percentage error (MAPE) (Equation (5)) between analytical data and the FE data.

RMSE = 1 N ∑ n = 0 N − 1 ( y a ( n ) − y i ( n ) ) 2 (4)

MAPE = 1 n ∑ | y a − y i y a | (5)

where y a = analytical data, y i = FE data.

In order to investigate the effects of bending moment on flexural deflection of the braided structure, 5 numerical models of the biaxial braided structure were developed by varying the braid angle. The results of the evolution of the bending moment with deflection are illustrated by the curves in

The deflection in the braided structure with θ = 38.5 ∘ as observed to decrease after bending moment of 1 N∙mm. This was probably due to the cover factor in the structure which caused more yarn-yarn displacement within the structure. This is also illustrated by the drop in the contact stress at this point within the structure as shown in

The analysis results of the change in the bending moment with curvature are illustrated by the curves in

The results for the bending angle of the braided structure with change in the bending moment are shown in

The analysis results of the change in the bending moment with contact stress at the yarb-yarn interface is illustrated by the curves in

The numerical results of the bending stiffness with increasing bending moment are shown in

The verification of the FE models used in this study was performed by evaluating the bending stiffness of the biaxial braided structure at θ = 52.5 ∘ using the beam theory approach proposed in previous research [

Numerical models for a biaxial braided structure were developed in this study. Five sets of the structure were developed by varying the braided angle in terms of θ = 38.5 ∘ , θ = 42.5 ∘ , θ = 45 ∘ , θ = 48.5 ∘ and θ = 52.5 ∘ . A bending moment was applied on each of the models to mimic the flexing of a human finger and an FEA method used to investigate the flexural bending properties of the biaxial braids. It can be seen that when the braided fabric with largest braid angle ( θ = 52.5 ∘ ) had the highest flexural deflection while the lowest deflection was seen in the results of the braided structure with the least braid angle ( θ = 38.5 ∘ ). The results in this study portrayed the curvature in biaxial braids will increase when the decrease in the angle between the braided yarns. This was also consistent with the bending angle of the biaxial structures under a bending moment which suggested that the deformation was as a result of the applied

bending moment. Therefore, the deformation of the structures increased with increase in the braid angles. In this regard, the numerical results of the bending stiffness with increasing bending moment decreased with increase in braid angle.

The authors declare no conflicts of interest regarding the publication of this paper.