## 1 Introduction  
Epoxy resins are widely used in adhesives, coatings, electronics, sporting goods, and aerospace applications, owing to their excellent properties of being a polymeric material with high strength, stiffness, temperature resistance, dimensional stability, and fatigue resistance [1]. Cellulose nanofiber (CNF) is a large aspect ratio, string-like, sustainable material, which is highly crystalline and consists of transversely-filled long cellulose molecules linked by strong hydrogen bonds. It is well-known that the long cellulose molecules are incorporated into the cell walls of higher plants, such as hemicellulose and lignin [2, 3]. In order to fully capitalize on the intensified properties of doped nano-particles, one of the most critical things is that they should have a homogeneous dispersion in the polymeric matrix. Different dispersion methods have been considered, including the use of the dilution method, ultrasonication, high shear mixing, the addition of a chemical surfactant, and so on [4, 5, 6, 7, 8, 9].  
To avoid CNF agglomeration, nanofiber networks are prepared by filtration from a dilute CNF water suspension. The process involves solvent exchange with acetone, and the ultrafiltration of fiber slurries using a Millipore ultrafiltration apparatus, with membranes to preserve the structure of the individual nanofibers. [PERSON] et al. dispersed modified CNF using silane and titanate coupling agents in acetone and reported an increase of storage modulus from 2.59 to 3.45 GPa at 30 \({}^{\circ}\)C, with a nanocellulose content of 5 wt.% [4]. [PERSON] et al. discussed the effects of cellulose on the curing behavior and properties and suggested that a nanocellulose content of 0.5 phr (per hundred resin)is the optimum content [5]. [PERSON] and [PERSON] dispersed cellulose whiskers in dimethylformamide (DMF) by either freeze-drying, or solvent exchange procedures, to avoid using coupling agents [6]. They reported that the Young's modulus of the epoxy resin with 20 vol.% of tunicate whiskers was 5.7 GPa, while that of the neat epoxy resin was 1.6 GPa. [PERSON] and [PERSON] mixed water-soluble components with microfibrillated cellulose, followed by suspension freeze-drying and curing processes at elevated temperature [7]. They reported that the Young's modulus and the tensile strength of the epoxy resin were increased from 1.7 to 2.6 GPa, and from 60 MPa to approximately 80 MPa, respectively. As mentioned above, there are several studies of CNF reinforced polymer composite materials with higher CNF weight fractions (1 wt.% -).  
On the other hand, [PERSON] et al. fabricated CNF and polysulfone (PSF) modified epoxy nanocomposites using a combination of solvent exchange and melt blending [8]. They reported that a CNF addition of 0.2 wt.% increased the impact strength by \(\sim\)49%. [PERSON] et al. also reported that the insertion of epoxy resin with 0.1 wt.% CNF layers increased the flexural strength of glass fiber reinforced plastic (GFRP) composite laminates by 125%, whereas the flexural modulus of the CNF layer inserted GFRP laminates was constant [9]. Therefore, they concluded that a slight CNF addition (\(\sim\)1 vol.%) can increase the mechanical properties of the resin matrix.  
In this study, we prepared extremely-low CNF (\(\sim\)0.44 vol.%) reinforced epoxy resin matrix (epoxy-CNF) composites via high shear mixing. After that, we evaluated and analyzed the flexural properties of the epoxy-CNF composites by the three-point flexural test and finite element method, respectively. Moreover, we discussed the strengthening mechanism of epoxy-CNF composites, based on organic chemistry.