Yarn Constitutive Equations and Elastic Constants
One of the fundamental tasks in studying the
mechanical behavior of a medium is to derive its
stress–strain or constitutive relationships. In the
case of the ideal yarn model defined above, the
fibers can be assumed to be arranged in the transverse
plane in such a manner that there is no
preferential packing geometry in the plane, thus
making the plane mechanically isotropic and allowing
the yarn structure to be treated as a transversely
isotropic material. Consequently, its
stress–strain relationships can be expressed by
the following equation8: