Dynamic relaxation approach with periodic boundary conditions in determining the 3-D woven textile micro-geometry

A dynamic digital element approach, utilizing a dynamic relaxation procedure, is developed to determine 3-D woven textile micro-geometries. Three yarn/tow structures, including plain yarn, twisted yarn, and twisted tow, are generated by the digital element mesh. An explicit algorithm with a periodic boundary condition is employed to calculate nodal forces, accelerations, velocities, and displacements within the unit cell. Because the majority of the computing time is consumed to detect contacts between fibers, an efficient contact search algorithm is proposed. In addition, a multi-level dynamic relaxation procedure is implemented to further reduce computer time. The yarn-level fabric micro-geometry is also generated in a format that can be read by commercial finite element software. The micro-geometries derived from numerical simulations are compared to the microscopic images of actual fabrics. Good agreement is found between numerical results and experimental results.