The Finite Element modeling of electrospun nano fiber mesh using ...

Proceedings of the 5 th International Conference on Nanostructures (ICNS5) 6 -9 March 2014, Kish Island, Iran

The Finite Element modeling of electrospun nano fiber mesh using microstructure architecture Analysis 1

M. Gorji* 1 , Ali. A. A. Jeddi2 , A. A. Gharehaghaji2 , M. Haghpanahi3 Department of Textile Engineering, Science and Research Branch, Islamic A zad University, Tehran, Iran 2 Textile Eng ineering Depart ment, A mirkab ir Un iversity of Technology, Tehran, Iran 3 Mechanical Engineering Depart ment, Science and Technology University, Tehran, Iran * [email protected]

Abstract: This research was aimed to reduce the difference between theory and experiment in the study of fibrous networks through investigation of the micro mechanics of electrospun polyurethane (PU). The produced PU web in this research has different morphologies. The structural parameters were obtained through the analysis of SEM images. Three-dimensional network was simulated with the help of software. In this simulat ion, each fiber was modeled as hyperelastic materials and each crosslink was modeled as MPC tie. Also, Finite Element Method (FEM) was used to model stress-strain behavior of PU and ABAQUS software was applied to investigate the effect of major parameters such as fiber diameter, fiber orientation and thickness of web. The stress -strain curves of networks were compared by modeling measurements at three different morphologies. The model by using third order reduced polynominal as fiber hyperelatic potential energy function showed good agreement with experiment that confirm the tensile behavior of PU web can be explained entirely by microstructure of the network.

Keywords (11 Bold): electrospun nanofiber, FEM, micro arch itecture, hyperelastic material Introduction One of the promising methods in producing fibrous structures for membrane application such as protective clothing is electrospinning method[1]. There is limitation in the utility of electrospun fused fiber meshes which is imposed by the lack of a theoretical framework to predict the relationship between the bulk mechanical properties and properties of the individual fibers and the effect of properties of individual fibers on the bulk mechanical properties. This framework is multiscale in nature, with the web dimension being on the centimeter length scale, while the underlying fibrillar architecture on the micrometer scale. One critical factor is the existence of a dependency of native nanofibrous structure response to fiber orientation, diameter, and reorientation in response to strain suggesting that both length scales are necessary, thus regarding this fact, it is concluded that continuum constitutive models often cannot predict the tissue response under every loading condition. The advantage of multiscale, structure-based mathematical models in description of mechanical behavior of nanofibrous structure is their scale separation property[2]. In this study, submicron fiber networks were electrospun selected form a poly urethane elastomer and there is not an absolute value for firber diameter and orientation, they were varied systematically. The dependency of the tensile and elongation on the network microstructure were determined using mechanical testing. A structure model was developed in which homogenization techniques is used to study mechanical behavior of polyurethane. In this model, three dimentionality and interaction between the PU fibers was considered. The three-dimensional finite element method was employed for the analysis. Finally, the model was compared with experimental.

Materials and method An electrospining solution was used that is obtained from 13,14and 15 percent wt./vol of commercial PU and then it was dissolved in tetrahydrofuran and N,Ndimethylformamide mixture (60:40, 55/45 ,50/50, v/v). In the electrospinning process , the prepared solution was electrospun simultaneously on the rotating drum from two opposite nozzles. Figure 1 shows a typical SEM of electrospun PU web. A program which was encoded in MATLAB Software was used to calculate nanofibers orientation (version 7.0.0.1920) with the same direction explained in the previous work [3]. The dumbbell-shaped specimens were prepared and tested with a crosshead speed of 50 mm/min based on ASTM D-638in order to determine tensile properties of the mats. To create a 3 dimensional model in Abaquse, the average of diameter, fiber length in different interval (between 0180 degree) and orientation of fiber in different parts of electrospun nanofiber mesh the same as the real sample. fibre has a wire shape in the produced model by software. A wire is depicted as a line in Abaqus/CAE and used to idealize a solid in which its diameter is considered smaller than its length. This feature is more affordable than other features like solid.

Results and Discussion The experimental results show that fiber diameters increase with increasing electrospinnig duration, polymer content and DMF content in THF/DM F mixture. The results of this study show that thickness and tensile of PU mat increase with increasing electrospinning duration. These results also show that with increasing THF content


tenacity and elongation of layers decrease. The computational model was fit to the stress -strain curve for a PU mesh electrospun from an 14.0 wt% solution (Figure3). The resultant best fit for the fiber potential energy, Uf, was found as below:

modeling results can accurately predict the effect of network thickness on tensile strength.

(1) The obtained results fro m FEM model showed that there is a direct relation between fiber diameter and strength of fibrous network that is the increase in fiber diameter follows an increase in the strength of fibrous network. It is worth noting that these results were obtained by experimental results. The result of experimental and modeling results in two strains (5 and 20 %) with their errors are shown in table 1.

Fig.2: Load versus thickness of fiber network for experimental and computed

As figure 2 shows the modeling results can accurately predict the effect of network thickness on tensile strength. The characteristics that distinguish the presented model from other models are: it incorporates fiber-fiber interaction; it accounts for three-dimensionality of PU fiber meshes, it can predict the mechanical behavior of the PU fiber network at large strain, and it considers PU fiber as hyperelastic material. Fig.1: A typical SEM of electrospun PU web.

Conclusions

Table1: The effect of fiber diameter on strength obtained with experimental and modeling procedure N o.

Fiber

Load(N) in 5% strain

Diamet

Mod

Experi

Error

Load(N) in 5% strain Mod

Experi

Error

er(nm)

eling

mental

(%)

eling

mental

(%)

1

0.61

0.050

0.058

17

0.500

0.582

20

2

0.81

0.060

0.066

9

0.500

0.550

9

3

0.95

0.068

0.076

10

0.670

0.620

8

The pearson correlation test show a 90% correlation between modeling and experimental results. These results are in accordance with the results obtained by other researchers [4]. Statistical analysis shows significant difference between strength of fiber network in different levels of electrospinning duration (2, 4 and 6 hours). With increasing process duration, weight, thickness and strength of layers increase. As figure 5 shows the

The proposed model in this study is based on the finite element method that has been developed for the tensile behavior of electrospun nanofibers. The experimental results indicate that there is a relation between fiber diameter and fiber orientation and the tenacity of electrospun nanofiber mesh so that increasing the fiber diameter and fiber orientation is along with increasing the tenacity of electrospun nanofiber mesh. The results obtained from modeling are in accordance with the experimental results. It is possible to predict the FN mechanical properties and optimization of FNs with strong contact bounds from this proposed model. Since networks with realistic geometries are applicable in this modeling, this analysis can ultimately serve as a tool for understanding the way in which mechanics of fibers and cross links at the microscopic level produce the macroscopic properties of the network.

References [1] R. Bagherzadeh, M. Latifi, S. S. Najar, M. A. Tehran, M. Gorji, L. Kong, “Transport properties of multi-layer fabric based on electrospun nanofiber mats as a


breathable barrier textile material”, Textile Research Journal;82(1): 70–76,2011.

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[2] T.Stylianopoulos, C. A. Bashur, A. S. Goldstein, S.A. Guelcher,V. H. Barocas , "computational prediction of tensile properties of electrospun fiber meshes ", J Mech Behav Biomed Mater. 2008 October; 1(4):326-335 [3] .M. Gorji, Ali. A. A. Jeddi, A. A. Gharehaghaji, “Fabrication and Characterization of Polyurethane Electrospun Nanofiber Membranes for protective

[4] T. Stylianopoulos, V. H. Barocas, “Vo lu me Averaging Theory for the Study of the Mechanics of Collagen Networks”, J. Mech. Behav . Bio med . Mater; 196(31-32): 2981-2990, 2007.