## 2 Modeling Approach
### Modeling Strategy Based on Mechanical Properties of Single NCF Lamina  
The mesomechanical unit cell of a QNCF is shown in Figure 1a. The models include deviations of the fiber orientations in inner and outer plies, such as cracks and channels. For continuous plies NCF, the disturbance caused by the stitch in fiber direction is different in different plies. In the outer fibrous plies, the stitching pulls fibers aside forming long \"channels\" in the \(0^{\circ}\) lamina and rhomboidal \"cracks\" in \(45^{\circ}\) lamina. In the inner, rhomboidal \"cracks\" are induced in the \(90^{\circ}\) and \(-45^{\circ}\) lamina, and the size of these inner cracks is smaller than that of outer cracks. The direction of the large diagonal of the rhomb and the channel corresponds to the fiber direction in the py.  
The different openings in the individual plies in QNCF composites will lead to a difference in mechanical properties of single NCF lamina. In property testing of NCF composites, different non-crimped UD specimens are requires to test to determinate the mechanical properties of single QNCF lamina. The schematic diagrams of production these different warp-knitted non-crimped UD specimens are shown in Figure 2, and the angle between the fibers and the process direction are \(90^{\circ}\), \(0^{\circ}\) and \(45^{\circ}\), respectively. Remarkably, the fiber distortions of the UD specimens induced by the stitch yarn are different. Geometrical model of unit cells of these different specimens, are shown in Figure 3. These UD specimens also include different gaps and channels. After injection molding, the composite laminates are cut out following in the fiber direction for mechanical testing. In meso-scale analysis, the unit cells of QNCF should also include the meso-scale geometry features of different non-crimped UD specimens as shown in Figure 3.  
Figure 1: The geometrical model of mesomechanical unit cell development for single quadriaxial non-crimp fabric (QNCF) lamina: (**a**) unit cells of a QNCF layer; (**b**) individual fibrous plies in the QNCF layer; and (**c**) geometrical model of unit cells of individual QNCF lamina.  
Figure 2: Schematic diagram of production different warp-knitted unidirectional non-crimp fabric (UD-NCF): (**a**) the production of \(90^{\circ}\) Layers; (**b**) the production of \(0^{\circ}\) layers; and (**c**) the production of \(45^{\circ}\) layers. 1—Process direction; 2—Fiber direction; 3—Thread; 4—Transport system; 5—Wetf carriage system.  
To improve the efficiency of meso-scale analysis, the QNCF layer is decomposed into individualplies as shown in Figure 1b. Considering that the testing method of mechanical properties of single QNCF lamina, the unit cells are select along fiber direction as shown in Figure 1b. Since inter \(-45^{\circ}\) and \(90^{\circ}\) lamina have the same volume fraction and crack size, they are classified as one model. Then three types of unit cells of individual QNCF lamina are formed, which are shown in Figure 1c. Although this modeling strategy decomposes the QNCF layer, the major fiber architecture is still considered in the model, including channel, inter small crack, face large crack, and local fiber contents.