In this research, an incompressible, isotropic, nonlinear elastic rectangular block and a circular cylindrical sector are studied under bending and straightening moments, respectively. Analytical approaches are presented on implementing of the left Cauchy–Green tensor and Cauchy stresses. In addition, finite element analysis of both problems is carried out using UHYPER user-defined subroutine in ABAQUS to verify the analytical methods. Four different invariant-based strain energy functions, including neo-Hookean, Mooney–Rivlin, Arruda–Boyce, and recently proposed polynomial Exp-Exp models, are examined, and the results are compared. Material parameters of silicon rubber for the strain energy functions are identified by applying an optimization procedure. Finite element method results confirmed the analytical approach with great compatibility. Results showed that the length of the unbent beam does not affect the stress. Likewise, the initial angle of curved structure does not affect the unbending moment and stresses. Moreover, the Exp-Exp model had a slightly different result rather than other strain energies, which means that this model is more conservative than its counterparts. Furthermore, the Exp-Exp strain energy function is calibrated for tissue-like phantom and is compared with experimental data.

In this article, the mechanical swelling behavior of poly-(N-isopropylacrylamide) hydrogel is scrutinized considering a hollow circular cylinder subjected to temperature variation-extension-torsion. Accordingly, an analytical solution is presented to consider the general combined loading on temperature-sensitive hydrogel cylinder for two approaches, considering same temperature for whole structure and solving heat equation to compute internal temperature of structure. Additionally, to evaluate the proposed solution, finite element analysis has been conducted for same problem which revealed excellent conformity for various case studies. Therefore, a user-material subroutine, UHYPER, is implemented to be employed in finite element analysis in order to define swelling of PNIPAM hydrogels. This subroutine was validated using free swelling and constraint swelling with previous and their analytical solutions. Regarding the complexity of material and loading namely, nonlinear finite behavior of hydrogel as well as combined cooling-extension-torsional loading, various factors, cross-linked density, axial stretch, torsional twist and temperature variation, were investigated to clarify the swelling behavior of hydrogel. Solving heat equation, in the second approach, enables us to apply various thermal conditions on this structure, while in previous studies, the temperature of whole structure is considered to vary simultaneously with the same function. This approach can help researchers to examine diverse thermo-mechanicals problem for temperature-sensitive hydrogels.

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