Self-equilibrium configurations of composite strands

We consider the problem of determining the equilibrium of composite strands consisting of a single core yarn surrounded by n-helical side yarns with pre-twists in the absence of any external load: the self-equilibrium configuration (SEC). We formulate the self-equilibrium problem on the basis of the Kirchhoff rod model in which the contact between yarns in three-dimensional space is taken into account in order to include large helical angles and geometrical constraints. We numerically determine the SECs and elucidate the effect of the following factors on them: the pre-twist of each yarn, the ratio of Young's modulus of the core yarn to that of the side yarn, and the number of side yarns. The present results allow us to characterize the initial unloaded state of composite strands.