Introduction

In the last decade, electrospun scaffolds have attracted attention due to their high porosity and controllable morphology, as well as the use of simple and low cost equipment during their production (Neisiany et al. 2017a; Persano et al. 2013). Tissue engineering is one of the areas in which electrospun scaffolds are being widely studied because their well-connected structures resemble the extracellular matrix in body tissues (Costa-Júnior et al. 2009). The mechanical properties of scaffolds are extremely important for biomedical applications; however, most of the publications are limited only to experimental measurements (Abdalkarim et al. 2017; Khalf et al. 2015; Linh and Lee 2012; Neisiany et al. 2017b). Analyzing the mechanical behavior of nonwoven fibers and verifying them with the available mechanical models can open the door for prediction of mechanical properties of electrospun scaffolds (Kumar and Rawal 2017). Consequently, the required amount of reinforcements in polymeric matrix can be estimated before scaffold fabrication.

In order to simulate the mechanical behavior of an element, its geometrical structure must be initially considered. In the case of an electrospun scaffold (Fig. 1a); its architecture resembles an interconnected structure of fibers, which have a random alignment. From another point of view, an electrospun scaffold consists of a series of connected pores (highly porous structure), even to the depth of scaffold, similar to open-celled foam (Fig. 1b). According to the definition, polymeric foams can be considered as a composite of polymer matrix and dispersed gas bubbles or cells. Open-celled foam is defined as a structure in which cells are interconnected throughout its bulk (Lee and Ramesh 2004). Several models have been used to predict the modulus of open-celled foams basing on the porosity of the foams (Shulmeister 1998). Therefore, these models are a reliable approach to analyze the mechanical behavior of electrospun scaffolds.

Fig. 1
figure 1

Two different views of an electrospun fibrous network (a), open-celled structure (b), and a series of single fibrous nanocomposites (c)

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Taking a deeper look into an electrospun scaffold, it is a network of many submicron- or nano-fibers. Hence, in the case of using a reinforcing agent, a single fiber can be considered as a nanocomposite named as a single fibrous nanocomposite (Fig. 1c). Based on the type of filler, e.g. particles or short fibers, related models can be applied to predict mechanical properties of a fiber. Direct measurement of single fiber mechanical properties is challenging, since isolating and controlling the experimental conditions of nanosized electrospun fibers are difficult. Several techniques including nanoindentation (Baji et al. 2010; Wang and Barber 2012), AFM nanoindentation (Tan et al. 2005), AFM three-point bend test (Stachewicz et al. 2012; Tan and Lim 2004), and nano-tensile test (Bazbouz and Stylios 2010; Inai et al. 2005) have been used to measure the mechanical properties of single electrospun fibers. In the present study, AFM nanoindentation was used to directly measure Young’s modulus of nanofibers.

Some advantages such as biocompatibility, water solubility, hydrophilicity, and nontoxicity of electrospun poly(vinyl alcohol) (PVA) fibers resulted in a great deal of attention directed towards their applications in new areas, such as biomedical and membrane (Adibzadeh et al. 2014; Agrawal and Pramanik 2016; Yang et al. 2008). However, low stiffness of PVA limits its applications, particularly in hard tissue engineering. Because electrospun fibers have submicron diameters, it necessitates the incorporation of nano-scale fillers to produce electrospun PVA nanocomposites. Various nano-sized fillers such as nanohydroxy apatite (nHAp) (Degirmenbasi et al. 2006; Kim et al. 2008; Sheikh et al. 2010), nanosilver (Dong et al. 2010), calcium carbonate (Sambudi et al. 2015), biphasic calcium phosphate (Linh et al. 2013), bioactive glass (Pon-On et al. 2014), zeolite and silica nanoparticles (Mehrasa et al. 2016), nanoclays (Islam et al. 2015; Koosha et al. 2015; Liu et al. 2014), titanium dioxide (Shokrollahi et al. 2014), graphene oxide (Barzegar et al. 2015; Wang et al. 2013), γ-Fe2O3 (Fallahiarezoudar et al. 2015), and cellulose nanomaterials (Lee and Deng 2013; Ma et al. 2014; Xiao et al. 2016) have been successfully incorporated into electrospun PVA fibers. Electrospun nanocomposites of PVA with two different nanofillers i.e. nanohydroxy apatite and cellulose nanofibers were successfully developed in our previous studies (Enayati et al. 2016a, b).

The aim of the current work is to investigate the mechanical properties of electrospun PVA and its nanocomposites containing nHAp and CNF individually and simultaneously. Then, the experimental measurements are compared with the predictions obtained using theoretical models to prove the accuracy of these models. Considering the PVA nanocomposite as a single fiber, modified Halpin–Tsai (Halpin 1992; Ramakrishna et al. 2006) and Ouali (Ouali et al. 1991; Pooyan et al. 2012) models are used to predict the Young’s modulus of CNF-reinforced PVA (as a short-fiber reinforced composite). In the case of nanocomposites containing both nHAp and CNF, since there is not any model to predict the stiffness of a three-component composite, PVA and nHAp are assumed as matrix and CNF as short-fiber reinforcement. Since the synthesized nHAps are in particle form, therefore their better dispersion in PVA matrix and also expected interactions between them and PVA either by hydrogen bonding or [OH–]-Ca2+-[–OH] linkages (Degirmenbasi et al. 2006; Kim et al. 2008; Lee and Deng 2013), this assumption can be acceptable. Electrospun scaffold is considered as an open-celled structure of highly porous nonwoven fibrous nanocomposites and therefore some mechanical models are applied to estimate the Young’s modulus of interconnected porous structure. In such models, the modulus of porous structure is proportional to the porosity and modulus of dense (nonporous) material. It is believed that although the presence of high porosity in electrospun scaffolds dramatically reduced the stiffness, the nanofiller reinforcements could compensate for such a reduction.

Experimental

Materials and samples preparation

Polymer

Poly(vinyl alcohol) was supplied by Sigma-Aldrich Company (USA). Its molecular weight and degree of hydrolysis were 124,000 g/mol and 98–98.8% respectively.

Cellulose nanofiber (CNF) extraction

The CNFs were extracted from wheat straw with a chemo-mechanical procedure, as described in our earlier work (Enayati et al. 2016a). Chemicals used during the isolation process including sodium hydroxide (NaOH) granules, hydrochloric acid (HCl) 37 wt%, sodium chlorite (NaClO2) 25 wt%, sulfuric acid (H2SO4) 97 wt%, and potassium permanganate flakes (KMnO4), were supplied by Merck (Germany).

Nanohydroxy apatite (nHAp) synthesis

Nanohydroxy apatite, grain size of 15 ± 1 nm, was supplied by Institute of High Pressure Physics, Polish Academy of Sciences (Poland).

PVA, PVA/nHAp PVA/CNF, and PVA/nHAp/CNF nanofiber preparation

PVA solution and its suspensions i.e. PVA/nHAp, PVA/CNF, and PVA/nHAp/CNF were prepared in 80 °C distilled water for 90 min. Next, prepared samples were electrospun. Applied voltage, collection distance, solution rate and needle inner diameter were 18 kV, 15 cm, 700 μL/h and 0.34 mm, respectively. A detailed description of the nanofiber fabrication procedure was presented earlier (Enayati et al. 2016a). Samples containing different amount of nanofillers were coded such as PVA8/nHAp10/CNF3, which means a suspension containing 10 wt% of nHAp and 3 wt% of CNF in a 8 wt% PVA aqueous solution.

Nanofiber characterization

Scanning electron microscopy (SEM)

The spun nanofibers were coated with a thin layer of gold and their morphology was analyzed with scanning electron microscope (SEM, JEOL, JSM-6390LV, Japan) at an accelerating voltage of 10 kV.

Field emission scanning electron microscopy (FE-SEM)

FE-SEM microscope Zeiss Ultra Plus GEMINI (Germany) was used to measure cellulose nanofibers diameter. Prior to observations, samples were coated with a carbon layer. Observations were conducted at accelerating voltage of 2 and 3 kV with SE detector.

Porosity measurement

Porosity (φ) of the electrospun samples was calculated by comparing the apparent density (ρ) to the bulk density of the scaffolds. Rectangular samples were cut from the electrospun mats and their length, width and thickness were accurately measured to determine the volume (V). The dry weight of the samples (m) was measured with an analytical balance with the accuracy of 10−4 g. The density of each sample was calculated from its volume and weight according to Eq. (1).

$$\rho = \frac{m}{V}$$
(1)

The porosity, φ, was calculated from the measured average density of the samples, ρ, and the bulk density, ρo, from Eq. (2) (Meng et al. 2010).

$$\varphi = \left( {1 - \frac{\rho }{{\rho_{0} }}} \right) \times 100$$
(2)

AFM nanoindentation

The nanomaterial stiffness was directly measured by AFM nanoindentation analysis. A Ntegra (NT-MDT, Russia) AFM was used to quantify the Young’s modulus of the samples. The microscope was equipped with a single crystal silicon cantilever (NSG01, NT-MDT, Russia) with nominal tip radius of 10 nm during the nanocellulose analysis. The spring constant of the previously calibrated cantilever was 11.16 N/m while the sample deposition was carried out by drop casting of the nanocellulose dispersion onto a freshly cleaved mica surface.

The AFM nanoindentation analysis was also performed to locally measure the Young’s modulus of single electrospun fibers. A NSG01 cantilever with spring constant of 2.13 N/m was mounted on the AFM head to probe the electrospun fibers and the samples were prepared by placing a few electrospun fibers onto a mica slide.

At the beginning, the cantilever sensitivity calibration was required (for both sample types) by indenting a clean area of the mica substrate before stiffness measurements. In addition, the slope of the linear signal was recorded when the cantilever is in contact with the reference surface. Furthermore, the tip of the used cantilever was characterized before the indentations as well as after the analyses by SEM and test silicon grating scanning (TGT1, NT-MDT) in order to test their morphological and structural integrity. The AFM topography of the samples surface was collected before each indentation set of measurements. The images were obtained using the described setup operating in tapping contact mode. The selected nanomaterials were analyzed in several zones by collecting a series of force curves. At least 25 indents were performed on each fiber and five different fibers were analyzed for every sample. All the recorded force curves were exported and analyzed. The raw data (cantilever deflection–piezo movement graphs) were converted into applied load force versus indentation depth curves by using the calculated cantilever spring constants and deflection sensitivities. The Young’s moduli were evaluated analyzing the loading curves slope and finally the average value was calculated by taking into consideration all the recorded measurements for each sample. In this work, the indented single nanomaterials were treated as a cylinder and the AFM tip as a sphere (Pierini et al. 2016). The nanofibers Young’s modulus (E) was calculated by fitting the Hertz model into the loading data using Eq. (3)

$$E = E_{r} \left( {1 - v_{f}^{2} } \right)$$
(3)

where νf is the Poisson’s ratio of the material and Er is the relative elastic modulus. The relative elastic modulus is defined by Eq. (4).

$$E_{r} = \sqrt {\frac{{9P^{2} }}{{16R_{e} \delta^{3} }}}$$
(4)

where P is the force applied, δ is the indentation depth, and Re is the equivalent radius for a spherical indenter evaluated by Eq. (5).

$$R_{e} = \sqrt {\frac{{R_{t}^{2} R_{f} }}{{R_{t} + R_{f} }}}$$
(5)

where Rt is the tip radius of curvature and Rf is the radius of the nanomaterials.

Tensile test

The tensile modulus (E) of electrospun non-woven mats was determined from stress–strain plots obtained from tensile test using uniaxial extension (Instron 4205, USA). The load cell, gauge length, and extension rate were 50 N, 20 mm, and 10 mm/min, respectively. The dimensions of samples were 5 mm (length) × 40 mm (width) × 100 μm (thickness).

Results and discussion

Characterization of extracted cellulose fibers

After chemo-mechanical treatment on wheat straw, observation of final product by FE-SEM confirmed the successful isolation of cellulose nanofibers with average diameter of 30 nm. Detailed results are available in our previous work (Enayati et al. 2016a).

Characterization of electrospun mats

Figure 2 shows the SEM images of electrospun pure PVA (Fig. 2a), and its nanocomposites containing 10 wt% nHAp (Fig. 2b), and 10 wt% nHAp and 3 wt% CNF (Fig. 2c). Smooth fibers of pure PVA change to more irregular after addition of both nanofillers. Moreover, nanofiller incorporation leads to fiber diameter reduction. The complete results and discussion on fiber morphology and diameter can be found in our previous works (Enayati et al. 2016a, b).

Fig. 2
figure 2

SEM images of electrospun: a PVA8, b nHAp8/nHAp10, c PVA8/nHAp10/CNF3

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Table 1 lists the average fiber diameter and porosity of electrospun mats. According to the Table 1, all samples show high porosity, more than 70%, which is an important parameter for tissue engineering applications. Although the highest porosity content belongs to pure PVA fiber mat, addition of fillers slightly reduced the porosity which is in accordance with fiber diameter reduction (Meng et al. 2010).

Table 1 Fiber diameter and porosity of electrospun PVA and its nanocomposites
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Mechanical behavior

In the previous work, it was shown that PVA/nHAp nanocomposites that incorporated with 1 and 10 wt% of nanoparticles had higher stiffness (Enayati et al. 2016a), therefore these samples were selected for adding different amounts of CNF. Figure 3 displays the effect of CNF content on elastic modulus of nanocomposites with two different nHAp contents.

Fig. 3
figure 3

Effect of CNF loading on elastic modulus of PVA8/nHAp1 and PVA8/nHAp10

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As it can be observed, PVA8/nHAp1 and PVA8/nHAp10 reinforced with 5 and 3 wt% of CNF, respectively, show the largest modulus in each nanocomposite group. Detailed explanation of such trend has been presented previously (Enayati et al. 2016a). According to the obtained mechanical stiffness, PVA8/nHAp1/CNF5 and PVA8/nHAp10/CNF3 were chosen for more mechanical analysis. In addition, for comparison, samples of PVA8/CNF3 and PVA8/CNF5 were electrospun and mechanically characterized.

In order to study the reinforcement effect of nanofillers, the moduli of the CNF and electrospun single fibers were measured using a nanoindenter (Table 2). Cellulose nanofibers have modulus 40 ± 4.05 GPa, which is in agreement with results reported by Usov et al. (2015). Low modulus of pure electrospun PVA (1.7 GPa for PVA8) was increased by 44 and 90% after incorporation of 3 and 5 wt% of CNF, respectively. It was reported by Lee (Lee and Deng 2013) that stiffness of PVA/cellulose nanowhisker electrospun fibers was linearly increased by increasing cellulose nanowhisker contents. The same trend was also observed in this study. Nanoindentation of PVA nanocomposites containing nHAp shows much higher stiffness as 12.73 GPa for 1 wt% nHAp and 15.74 GPa for 10 wt% nHAp. The addition of CNF to nHAp/PVA nanocomposites also raised the stiffness by approximately 10%.

Table 2 Modulus of nanocomposites determined by nanoindentation method
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Analysis of single-fiber nanocomposite: comparison with theoretical models

Two theoretical models were applied to predict the stiffness of CNF-loaded nanocomposites and their outcomes were compared with the experimental results to verify the accuracy of models.

Halpin–Tsai model (Halpin 1992) has been widely used to predict modulus of short-discontinuous fiber filled composites. The main assumption of this model is that there is no filler–filler interaction Similar to any other micromechanical model, Halpin–Tsai model attempts to estimate the composite modulus based on the modulus of the reinforcement and matrix materials, as well as the shape and volume fraction of the aligned inclusion phase. Based on the orientation of the fibers toward the tensile test direction, longitudinal, transverse, and isotropic Halpin–Tsai models can be applied.

According to these models, longitudinal modulus (EL) is calculated from Eq. (6).

$$E_{L} = E_{m} \frac{{1 + \zeta \eta_{L} v_{f} }}{{1 - \eta_{L} v_{f} }}$$
(6)

where Em and Ef are modulus of matrix and fibers, vf is fiber volume fraction, and ηL and ζ (aspect ratio) are defined from Eqs. (7) and (8), respectively.

$$\eta_{L} = \frac{{\frac{{E_{f} }}{{E_{m} }} - 1}}{{\frac{{E_{f} }}{{E_{m} }} - \zeta }}$$
(7)
$$\zeta = 2\frac{l}{d}$$
(8)

where l and d are length and diameter of CNF, respectively.

In transverse Halpin–Tsai model ζ = 2 so the model is explained by Eq. (9).

$$E_{T} = E_{m} \frac{{1 + 2\eta_{T} v_{f} }}{{1 - \eta_{T} v_{f} }}$$
(9)
$$\eta_{T} = \frac{{\frac{{E_{f} }}{{E_{m} }} - 1}}{{\frac{{E_{f} }}{{E_{m} }} - 2}}$$
(10)

Isotropic Halpin–Tsai model is fractional summation of both EL and ET (Eq. 11).

$$E = \frac{3}{8}E_{L} + \frac{5}{8}E_{T}$$
(11)

To predict the elastic modulus of composites, another model was derived by Ouali (Ouali et al. 1991). This model considers the behavior of an incomplete set of interconnected elements and allows the transition from a local to an infinite communication state where the critical volume fraction or percolation threshold separates the two phases. This model assumed formation of rigid structure when interconnections between series of elements (here, cellulose nanofibers) reach the percolation threshold. Pooyan et al. (2012) applied this model to predict the modulus of nanocomposites of cellulose acetate propionate (CAP) reinforced by cellulose nanowhiskers. According to this model, the effective elastic modulus (Ec) of the composite is defined as Eq. (12).

$$E_{c} = \frac{{\left( {1 - 2\psi + \psi v_{f} } \right)E_{m} E_{f} + \left( {1 - v_{f} } \right)\psi E_{f}^{2} }}{{\left( {1 - v_{f} } \right)E_{f} + \left( {v_{f} - \psi } \right)E_{m} }}$$
(12)

In which vf, Ef, and Em are fiber volume fraction, filler and matrix modulus, respectively. Ψ is an adjustable parameter according to Eq. (13).

$$\left\{ {\begin{array}{*{20}l} {\psi = 0, } \hfill & { \quad v_{f} \le v_{{f_{c} }} } \hfill \\ {\psi = v_{f} \left( {\frac{{v_{f} - v_{{f_{c} }} }}{{1 - v_{{f_{c} }} }}} \right)^{b} ,} \hfill & {\quad v_{f} > v_{{f_{c} }} } \hfill \\ \end{array} } \right.$$
(13)

The parameter b describes the network density with a universal value of 0.4 for a three-dimensional fiber system (Pooyan et al. 2012). Term of v fc corresponds to the critical volume fraction or percolation threshold that depends on the aspect ratio of reinforcing agent and its distribution within the matrix (Eq. 14).

$$v_{{f_{c} }} = \frac{0.7}{{\frac{l}{d}}}$$
(14)

where l and d are fiber length and diameter, respectively.

In above mentioned two models, modulus of CNF and PVA obtained by nanoindentation method is found to be 40 and 1.78 GPa (Table 2), respectively. As described earlier, in three-component nanocomposites, matrix is considered to be PVA/nHAp and CNF is as reinforcement. The aspect ratio of CNF is taken to be 100 (Fernandes et al. 2013). Since the density of CNF is 1.5 g/cm3 (Pooyan et al. 2012), the fiber volume fraction is considered to be as fiber weight fraction.

The moduli of nanocomposites calculated by both models are presented in Table 3.

Table 3 Comparison of nanocomposites modulus from models and experiments
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It can be noticed from Table 3 that the longitudinal modulus calculated using Halpin–Tsai model is in good agreement with the experimental value for PVA8/CNF3 nanocomposite, which suggests partial orientation of 3 wt% CNF within the electrospun fiber. Two other models provide a slightly lower agreement with experiments. By increasing filler content, the experimental values are closer to isotropic Halpin–Tsai modulus which can be due to random arrangement of fibers. This is more evident when nHAp is present in the matrix, even in the presence of a high shear field. Comparing the Halpin–Tsai modulus (E) with experimental data, it can be concluded that nanocomposites loaded by only 3 and 5 wt% CNF and also the one including 5 wt% CNF and small content of nHAp (1 wt%) have a better coincidence with this theoretical model. However, at high filler content (10 wt% nHAp and 3 wt%), there is more discrepancy. This effect can be attributed to the no filler–filler assumption in this model leading to better agreement at smaller filler content with less pronounced filler interactions. On the other hand, the predicted moduli by Ouali model matches better with experiment (6–7% difference) for three-component nanocomposites, while for PVA/CNF composites the discrepancy is 19–30%. As mentioned, Ouali model assumes that when interactions between fillers reach the percolation threshold, a rigid structure is formed. Therefore, better prediction of this model at higher contents of fillers and for three-component composites could be related to this assumption. In general, both models, particularly Ouali model, underestimate the experimental results. Furthermore, Halpin–Tsai has better prediction at lower filler content and Ouali model at higher filler content and three-component composites.

Analysis of electrospun porous scaffolds: comparison with theoretical models

In order to have a prediction of mechanical behavior of electrospun mats and explore its relation to porosity, structural models are used. These models are based on cellular network structures, which were developed for high porosity structures. In such models, the modulus is a function of material porosity. In general, these models are mostly based on regular 2D or 3D packing (Shulmeister 1998; Srivastava and Srivastava 2014) in which the geometry of the considered unit cell plays the main role in model’s equation. In these models, it is assumed that porosity is high (more than 70%), therefore they are suitable for nanofibrous scaffolds. Also, a single unit cell is representative of whole structure.

The simplest structural model is 2D honeycomb in which the unit cell is hexagonal. The effective modulus (E*) according to this model is presented by Eq. (15), where φ is the porosity and E is the modulus of solid (unfoamed) material (Thelen et al. 2004).

$$E^{*} = 1.4939E\left( {1 - \varphi } \right)^{3}$$
(15)

In terms of 3D structures, two of the most widely used unit cells are cubic and tetrakaidecahedron (Fig. 4). The most comprehensive description of cubic model was given by Gibson and Ashby (Eq. 16) (Lee and Ramesh 2004; Srivastava and Srivastava 2014).

$$E^{*} = E\left( {1 - \varphi } \right)^{2}$$
(16)

Another wide-spread model, based on the tetrakaidecahedron (Fig. 4), has been considered by several researchers, among them the most recent and more convenient one is the model developed by Zhu (Zhu et al. 1997) (Eq. 17).

$$E^{*} = \frac{{0.726\,\left( {1 - \varphi } \right)^{2} }}{{1 + 1.09\,\left( {1 - \varphi } \right)}}$$
(17)

The elastic modulus of porous scaffolds were calculated based on the above models and compared with experimental results obtained from tensile test in Table 4. The modulus of solid material is taken from AFM nanoindentation method.

Fig. 4
figure 4

Reproduced with permission from Lee and Ramesh (2004)

Unit cells based on 3D models, Cubic (a) and Tetrakaidecahedron (b) model.

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Table 4 Estimated modulus of electrospun scaffolds calculated from open-celled foam models
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According to Table 4, porosity plays a crucial role in mechanical stiffness of electrospun scaffolds. Due to the presence of high porosity, the tensile modulus decreases dramatically, which is proved by experiment as well as theoretical models. Moreover, all three models have an overestimated prediction of the modulus compared to experimental results. Among them, 2D honeycomb model has the best prediction for all samples. Between 3D models, tetrakaidecahedron model shows the best prediction for scaffolds with lower modulus, while discrepancy is larger for scaffolds with higher modulus. The worst prediction is given by the cubic model. One of the main assumptions in structural models is that single unit cell is representative of whole structure, so predictions of models in Table 4 are directly related to the shape of considered unit cells, which have hexagonal, cubic and tetrakaidecahedronal shapes. We believe that pores or unit cells in an electrospun scaffold are more similar to hexagons and tetrakaidecahedrons, so these models have a better prediction of measured modulus.

Conclusions

Electrospun PVA and its nanocomposites with different content of nHAp and CNF were successfully fabricated. Tensile test and AFM nanoindentaion were applied to measure the tensile modulus of electrospun scaffolds and electrospun single fibers respectively. In addition, theoretical models were used to predict the stiffness of nanocomposites and verify their accuracy by experimental data. For a single nanocomposite fiber, the Halpin–Tsai and Ouali models were used, while for the electrospun scaffolds, structural models related to open-celled structures were used. In general, Halpin–Tsai showed better agreement with the experiment than the Ouali model, especially at lower filler content. By increasing filler content, the Ouali model showed more conformity with experimental data. Due to high porous structure of all electrospun scaffolds (more than 70% porosity), a significant reduction of modulus were observed both from tensile tests and also theoretical predictions using structural models. Among structural models, honeycomb model provided the best prediction, while the cubic model predictions were the worst.