Multi-chain digital element analysis in textile mechanics

The concept of multi-chain digital element analysis is established. This new approach is a general numerical tool for textile mechanics. It can be used for textile process design and for fabric deformation, strength and failure analyses. In multi-chain digital analysis, fabric is considered as an assembly of yarns; furthermore, a yarn is considered as an assembly of fibers. Each fiber is modeled as a frictionless pin-connected rod element chain, defined as “digital chain”. Once the length of these rod elements approaches zero, the digital chain becomes a fully flexible one-dimensional entity with a circular cross section. It imitates the physicality of the fiber. Since a yarn is composed of many fibers, it is modeled as an assembly of digital chains. Contact between digital chains is modeled by contact elements. A procedure, similar to finite element analysis, is adopted. Displacement of fiber inside a fabric is derived based upon the global stiffness matrix and the boundary conditions. As a result, both detailed yarn paths and cross-section shape can be traced during the textile forming process or fabric deformation. In order to describe the new concept, two numerical examples are presented. The multi-chain digital element approach is used for the simulation of the two-dimensional weaving and three-dimensional braiding processes. One can observe, section-by-section, the yarn cross-section shape inside the woven and braided fabric.