Implementing Stretch-Based Strain Energy Functions in Large Coupled Axial and Torsional Deformations of Functionally Graded Cylinder

Abstract

In this paper, coupled axial and torsional large deformation of an incompressible isotropic functionally graded nonlinearly elastic solid cylinder is investigated. Utilizing stretch-based constitutive models, where the deformation tensor is non-diagonal is complex. Hence, an analytical approach is presented for combined extension and torsion of functionally graded hyperelastic cylinder. Also, finite element analysis is carried out to verify the proposed analytical solutions. The Ogden model is employed to predict the mechanical behavior of hyperelastic materials whose material parameters are function of radius in an exponential fashion. Both finite element and analytical results are in good agreement and reveal that for positive values of exponential power in material variation function, stress decreases and the rate of stress variation intensifies near the outer surface. A transition point for the hoop stress is identified, where the distribution plots regardless of the value of stretch or twist, intersect and the hoop stress alters from compressive to tensile. For the Ogden model, the torsion induced force is always compressive which means the total axial force starts from being tensile and then eventually becomes compressive i.e., the cylinder always tends to elongate on twisting.

Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading

“…According to this principle, the actual dissipation rate corresponding to a given plastic deformation rate is greater than the fictive dissipation rate , which is expressed from the actual plastic deformation rate and a certain stress on or within the surface ( Figure 4 ). Thus, the principle of maximum dissipation rate implies [ 46 , 47 , 48 , 49 ]: …”

“…Numerical analyses included monitoring of differences or, on the contrary, the degree of conformity of relevant simulation results, which included information on the distribution and magnitude of the maximum equivalent stresses and deformations, the course of mutual dependence of stresses and deformations for the individual hardening models used. The plasticity condition—shear stress intensity constancy (von Mises)—was chosen according to the conclusions of the analyses described in articles [ 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 ].…”

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

“…They compared the analytical results with finite element modeling which illustrates the precision of the presented solutions. They also conducted a study on functionally graded elastomers considering a stretch-based free energy (Valiollahi et al, 2019b).…”

“…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).…”

Swelling response of functionally graded temperature-sensitive hydrogel valves: Analytic solution and finite element method

“…Recently, stretchable materials considering the functionality, viability, and biocompatibility have been vastly utilized in biological and industrial applications. In this regard, finite deformation of high stretchable materials, for example, elastomers and hydrogels, are examined in numerous studies under various loadings including bending (Sheikhi et al, 2019;Shojaeifard et al, 2019b), extension-torsion (Valiollahi et al, 2019a(Valiollahi et al, , 2019b, rotating (Anani and Rahimi, 2016), and pressure-vessel (Almasi et al, 2017) to study their capability. In particular, the temperature-responsive hydrogels are being sensitive to a wide range of environmental temperature and undergoing exceedingly large deformation subjected to a slight temperature variation.…”