Finite Bending and Straightening of Hyperelastic Materials: Analytical Solution and FEM

Abstract

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.

Kinematic modeling and solution of rigid-flexible and variable-diameter underwater continuous manipulator with load

“…Therefore, the minimum elastic strain energy of WHAMs in the process of pressurization and loading is set as the optimization function to obtain the solution of the length of the WHAMs. According to the strain energy function of silicon rubber material described by the neo-Hookean model, the strain energy function of WHAMs can be expressed as [27] U The original length of WHAMs before pressurized is specified as the rated maximum working length. The optimization algorithm can be expressed as X = l 11 , l 12 , l 13 , l 21 , ..., l ij…”

“…Therefore, the minimum elastic strain energy of WHAMs in the process of pressurization and loading is set as the optimization function to obtain the solution of the length of the WHAMs. According to the strain energy function of silicon rubber material described by the neo-Hookean model, the strain energy function of WHAMs can be expressed as [27]…”

PH-sensitive hydrogel-based valves: A transient fully-coupled fluid-solid interaction study

“…Soft materials, recently drew researcher's attention due to their vast applications (Attaran et al, 2018;Ehrenhofer and Wallmersperger, 2018;Sheikhi et al, 2019;Shojaeifard and Baghani, 2019;Shojaeifard et al, 2019a;Valiollahi et al, 2019aValiollahi et al, , 2019b. Thus far, fabricating a wide variety of microfluidic devices, including micro-pumps, micro-valves, micro-mixers, and microsensors has been evolved regarding their vast applications in different formats.…”

Coupled thermo-mechanical swelling of a thermo-responsive hydrogel hollow cylinder under extension-torsion: Analytical Solution and FEM

“…Due to the vast application of soft material such as rubber-like and hydrogel, recently, numerous studies have been conducted on these materials application in diverse problems (Sheikhi et al, 2019;Shojaeifard and Baghani, 2019;Shojaeifard et al, 2019aShojaeifard et al, , 2019bValiollahi et al, 2019aValiollahi et al, , 2019b. In this vein, the problem of combined extension and torsion of a cylinder drew great attention from researchers regarding its application in engineering and biomechanics of soft tissues, for example, passive papillary muscles of the heart (Criscione et al, 1999;Humphrey, 2013;Humphrey et al, 1992;Taber, 2004).…”