Thermo-hyper-viscoelastic analysis of a rubber cylinder under cyclic deformation

In the present work, analysis of the thermal behavior of a rubber cylinder under the repeated deformation is studied. This problem is divided into two correlated parts including transient thermal heat conduction and cyclic mechanical loading. To find the best approach-numerical method, the problem is modeled and analyzed by three approaches including coupled approach-FEM, uncoupled approach-FEM as well as Green’s function. To evaluate the dissipating energy due to hysteresis, the Prony–Mooney–Rivlin constitutive hyper-viscoelastic mathematical model is considered. To model the thermal effects and heat buildup due to dissipating energy, this energy is accounted for as a heat source inside the part in three different forms including pointwise, planar, and volumetric. It is shown that the FEM-based coupled approach presents the most accurate estimation. However, for steady-state estimation of mid-point and wall-point temperatures, the best method is Green’s function with the planar and the volumetric heat source assumptions. Moreover, a study on the effect of frequency of loading cycles in temperature distribution shows that the more the frequency, the larger the difference between the temperature of the mid-point and wall-point, and the higher maximum temperature inside the rubber.