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.

在目前的工作中，研究了橡胶筒在反复变形下的热行为分析。该问题分为两个相关部分，包括瞬态热传导和循环机械载荷。为了找到最佳的方法-数值方法，通过耦合方法-FEM，非耦合方法-FEM以及格林函数三种方法对问题进行建模和分析。为了评估由于磁滞引起的耗散能量，考虑了Prony–Mooney–Rivlin本构超粘弹性数学模型。为了模拟由于耗散能量而产生的热效应和热量，该能量以三种不同形式（包括点向，平面和体积）作为零件内部的热源。结果表明，基于FEM的耦合方法可提供最准确的估计。但是，对于中点和壁点温度的稳态估计，最好的方法是在平面和体积热源假设的前提下采用格林函数。此外，对加载循环频率对温度分布的影响的研究表明，频率越多，中点和壁点的温度差就越大，橡胶内部的最高温度越高。