DFCA

The concept of DEA is illustrated in Figure 1. Figure 1(a) is a fabric, which is considered as an assembly of unit cells as shown in Figure 1 (b). The unit cell consists of yarns as shown in Figure 1(c). Each yarn is modelled as a bundle of digital filaments as shown in Figure 1 (d). The digital filament is modelled as a chain of rod-elements connected by pins as shown in Figure 1(e). If distance between two filaments is smaller than filament diameter, a contact element is inserted as shown in Figure 1 (f). During simulation, forces applied to each node are computed. Nodal accelerations, nodal velocities and nodal positions are calculated based on an explicit process at each step. As such, fabric deformation under external load is modeled as a non-continuum mechanics problem. DFCA, a computer design and analysis tool based on explicit DEA simulation concepts, was developed at Kansas State University between 2010 and 2020.

The micro-geometry of the textile fabric can be derived by two approaches using DFCA. The most accurate one is to simulate weaving or braiding processes dynamically step-by-step. This method is computer consuming. Further, the composite designer is often unable to obtain detailed weaving and braiding information germane to textile machine kinematics and kinetics. For these reasons, an alternative approach was introduced to generate unit cell micro-geometries as shown in Figure 2. Firstly, a unit cell topology is imported to DFCA based on weaving patterns. Incorporating a tow/yarn structure enables configuration of cell topology with an assigned yarn structure. An initial yarn tension is then applied to each tow/yarn; the tension distributes to each filament and element. The unit cell deforms in concert with the initial yarn tension, which is identified as "targeted yarn tension" in the simulation process. Yarn tension is assessed every 10-100 steps. If it is smaller than the targeted tension, additional tension is applied to maintain a quasi-constant targeted tension throughout the simulation process. This process continues until minimum potential energy is approached. DFCA has been employed to derive micro-geometries of many textile fabric unit cells.

DFCA utilizes an explicit dynamic relaxation solver. The time step applied in explicit simulation must be smaller than the critical time step, which equals the time for a sound wave to travel from the left node to the right node of a digital element. Sound speed relates to the axial modulus of the filament. The higher the modulus, the smaller the critical time step. In fact, the effect of modulus on unit cell geometry is negligible. One can therefore apply a modulus that is much lower than the actual modulus, e.g., one thousandth of the actual modulus, to accelerate the numerical simulation.

DFCA can be employed to produce not only rectangular unit cells, but also sheared unit cells as shown in Figure 3. An angle interlock fabric is generated. The weaving pattern is shown in Figure 3(a). The unit cell is not rectangular, as shown in Figure 3(b), due to weaving kinetics. This unit cell can be assembled into a fabric in a filament level micro-geometry, as shown in Figure 3(c), and then into a yarn level micro-geometry, as shown in Figure 3(d). The surface pattern generated by DFCA is almost identical to the actual surface pattern of the angle interlock of the woven fabric shown in Figure 4.

DFMA has a function to generate conformal FE meshes for textile composites. A conformal FE mesh must satisfy the following three conditions:

1. The element boundary must match the yarn-to-yarn and yarn-to-matrix interface.

2. Nodes must be compatible on the interface between two materials and two elements.

3. Shape functions must be compatible on the interface between two materials and two elements.

Figures 6 and 7 show conformal FE meshes for a 2D plain woven unit cell and for an orthogonal 3D woven unit cell, respectively. The conformal FE mesh can then be input into commercial FE software for composite stress analysis.