  This paper investigates some physical features that give rise to complexity
within the self-gravitating static cylindrical structure coupled with
anisotropic distribution in the energy-momentum squared gravity. To accomplish
this, we formulate the modified field equations and explore the structure of
the astronomical body. The C-energy and Tolman mass are also calculated to
discuss the matter distribution. We then obtain some structure scalars via
orthogonal splitting of the Riemann tensor. Since, the complexity of the
considered structure is influenced by a variety of variables, including
anisotropic pressure and inhomogeneous energy density, etc. thus, we adopt the
factor $\mathcal{Y}_{TF}$ as the complexity factor. Further, the
complexity-free condition along with the Gokhroo-Mehra model and polytropic
equation of state are taken to generate their corresponding solutions. We
deduce that the inclusion of additional terms of this modified theory leads to
a more complicated system.
