Large deformation analysis of functionally graded cylinder under extension-torsion: analytical closed form and finite element solutions.

In this study, an analytical solution has been developed to examine the mechanical behavior of an incompressible functionally graded hyperelastic cylinder subjected to simultaneous extension and torsion. The recently proposed exp-exp strain energy density is employed to predict the behavior of hyperelastic material, and its related material parameters are assumed to vary along the radial direction in an exponential fashion. Finite element analysis is conducted by preparing a userdefined UHYPER subroutine in ABAQUS to evaluate the proposed analytical solutions. FEM results and those of the analytical solution are in good agreement for various stretches and twists and reveal that the form of stress distributions and the maximum stress depend on the exponential power in the material variation function. In contrast to axial stretch, the effect of twist on the distribution of longitudinal stress is more complicated, and for large twists, two extrema in the stress distribution plot are observed, which move toward the center and outer surface of the cylinder on further twisting. Moreover, the longitudinal stress controls the variation of von-Mises and strain energy density throughout the radial direction. Additionally, considering an axial stretch, a point is identified where the axial force arising from torsion is compressive for stretches below this value, and it brings about the cylinder to elongate under twisting. However, this part of the total axial force varies from a tension state to a compression one for larger stretches, i.e., by increasing the twist, the cylinder first tends to shorten and then elongates on further twisting. [ABSTRACT FROM AUTHOR]