*2.1.2. Macro level analyses*

the behavior of woven composite materials under three-point bending was investigated at a

In each of the aforementioned studies, only a fabric cell was modeled, as a periodic boundary condition was used instead of repeating cells to create the whole specimen geometry. In general, there are two types of periodic boundary conditions known as parallel and series models. In a parallel model, it is assumed that the displacement of all constituents (cells) is the same and the load is shared between them. On the other hand, the stress is presumed to be the same in all cells in a series model, and the general displacement is the sum of that of each cell. In order to avoid such boundary assumptions, some researchers have opted to create the whole specimen meso-model by reproducing a large number of cells adjacent to each other. A good example of such approach is the simulation conducted by Chandekar and Kelkar [8]. Making use of LS-DYNA, they investigated the low velocity impact of glass and carbon woven composite materials [8]. The mosaic pattern was chosen to repeat the unit cells so as to produce the whole plate geometry. Although comparable results were observed between numerical and experimental results, running such simulations normally takes a considerable time,

In order to reduce computational time in meso-level modeling of woven composites, a second RVE methodology has been introduced. In this approach, the RVE is divided into several subcells, instead of a great number of elements. Where one level of homogenization was consid‐ ered in the first RVE modeling approach, two levels of homogenizations are performed in the second approach; the first of which is to find the general mechanical properties of sub-cells and the second is to determine the general mechanical behavior of the whole cell. The first research in this area was performed by Ishikawa and Chou [9]. Employing the classical laminate theory, they studied the elastic behavior of woven fabric materials in three models, including mosaic, undulation, and bridging models [9]. In the mosaic pattern, the fiber continuity and its crimping were not taken into account. However, these factors were consid‐ ered in the undulation model. One of the main limitations of this model was that two UD layers were assumed instead of one interlaced layer. After this work, some researchers attempted to conduct investigations into the failure behavior of woven fabric materials using the subconstituents method [10–12]. In one of the latest papers in this area, Li et al. predicted the stiffness matrix, strength, and damage evolution of woven fabric materials using Abaqus [13]. They used parallel-series assumption for the two-level homogenization. Six failure variables referring to six failure modes, including longitudinal, transverse, and out-plane failures, besides shear failure in 12, 23, and 13 directions, were taken into account. The maximum stress was chosen as the failure criterion of both fibers and matrix. The numerical results were comparable with the experimental data of tensile tests on a glass epoxy woven composite.

Although using RVEs as representatives of woven fabric materials could help designers predict the general behavior of these materials with some accuracy, this method relies on some limiting assumptions. For instance, a common assumption is that fibers and matrix have perfect contact with each other. In other words, the interface between yarns and matrix is assumed to be bonded perfectly under arbitrary deformation conditions. In reality, however, voids which arise during manufacturing processes are inevitable. On top of that, even by assuming perfect

comprising their effectiveness for large scale industrial simulations.

multi-scale (micro-meso-macro) level [7].

238 Non-woven Fabrics

As a general characteristic, macro level analyses do not take into account the micro failures in the composite specimens. Although macro level analysis of damage mechanism in woven fabric materials is not as complex as its micro/meso level counterparts, it is more practical (costeffective) for large scale simulations. The published works in this area can be divided into three categories as follows.
