Today, tunable soft elastomeric actuators due to their remotely-controllability, fast-response and stiffening have gained great attention. This article aims to develop analytical and numerical tools for thermo-mechanical analysis of an incompressible isotropic thermally-soft actuator subjected to finite bending deformation. To model the finite bending of soft actuator, amongst all existing energy density functions of hyperelastic models, exp-exp, Mooney-Rivlin, and Neo-Hookean models are selected. Under different temperature distributions, the radial and hoop stress components and the bending moment versus mean radius of curvature are presented. The results show the radial stress is more sensitive to the variation of the temperature gradient than the hoop stress. In addition, the variation of the mean radius of curvature has the most significant effect on stress components. It could be concluded, in a constant mean radius of curvature, positive and negative temperature gradient have direct and inverse effect on the stress components magnitude, respectively. As state of the art, the results show that in some mean radius of curvatures and temperature differences (e.g., temperature difference of 70 °C at mean radius of curvatures of 5 m), self-bending phenomenon is observed which means the actuator could be used as a purely thermal actuator. Furthermore, to verify the proposed solution, as a proof-of-concept study, Finite Element Method (FEM) using a user-defined subroutine, UHYPER was used. The results of FEM and analytical solutions are shown to be in a good fit.

This study presents an analytical solution to examine the mechanical behavior of an incompressible, functionally graded hyperelastic cylinder under combined extension and torsion. The exp-exp strain energy density function characterizes the hyperelastic material, with parameters varying exponentially along the radial direction. To validate the solution, finite element simulations using a custom UHYPER in ABAQUS are performed. The analytical and numerical results show strong agreement across different stretch and twist levels. The stress distribution and maximum stress are significantly influenced by the exponential parameter governing material gradients. Unlike axial stretch, torsion induces a more intricate longitudinal stress distribution, with large twisting producing two extrema that shift toward the cylinder’s center and outer surface. Longitudinal stress primarily governs von Mises stress and strain energy density variations across the radial direction. A critical axial stretch is identified, below which torsion-induced axial force transitions to compression, elongating the cylinder during twisting. Beyond this stretch, the axial force shifts from tensile to compressive with increasing twist, causing initial shortening before further elongation.