Fiberwalk: a random walk approach to fiber representative volume element creation

Attaining accurate representative geometry for a finite element analysis at various scales can be a challenging research task. Added complications arise when the geometry is representing a manufactured or biological composite. In this study, a representative geometry of linear fibrous composites was created at the microscale and is employed to reproduce crystalline microfibril stacking of Kevlar to form a single fibril joined by a non-ordered crystal structure. The structure can have ellipsoidal or rectangular microfibrils stacked in ellipsoidal or rectangular fibrils and may have any desired packing ratio within the 1-100% range. In order to build a fibrous structure along a path, a Random Walk methodology was used. Since the directionality of the fibers is random, but always stepping from one side of the path toward the other, the fibers can wind around each other and tangle or terminate if needed. Another key concept of this method is the addition of a rotation matrix operation for the path of the fibers. This allows the path around the three local coordinates to be in a linear or sinusoidal direction. The resultant geometry produced can represent the tortuous path nanofibrils undergo. Moreover, rotation about the path axis allows for the twisted geometry of ring spun yarn, and metal cable to be reproduced. Inclusion of spherical objects to the path of the fibers has been accommodated to reproduce fiber projection around, or end at, an obstruction in their path. This approach allows representing impurities at the fibril, fiber, or yarn level of composite fabric manufacturing.