An Analytical Solution to Predict Temperatures of Dumbbell-Shaped Rubber Specimens Under Cyclic Deformation

Abstract

The objective of this study is to propose an analytical solution that can predict the temperatures of dumbbell-shaped rubber specimens under cyclic deformation. Initially, a new mathematical equation was formulated by modifying the Mooney–Rivlin strain energy function, using the pseudo-elasticity theory and the inverse analysis method. This equation was utilized to calculate the internal heat generation rates of rubber compounds. With heat generation rates, the governing equation of heat conduction and the mathematical expression of boundary conditions were created to describe the heat transfer that occurs within the rubber compounds. By having these equations, a novel analytical solution was developed—the RTDS solution (a solution to predict Rubber Temperatures in Dumbbell-shaped Specimens). This RTDS solution was used to predict rubber temperatures in dumbbell-shaped specimens under cyclic deformation. The results showed that the RTDS solution took 11.9 s to derive the rubber temperature results with an average mean absolute percent error (MAPE) of 9.2% compared with lab recordings. The RTDS solution identified a logarithmic increase in rubber temperatures at rising strain levels, and it also identified an increase in rubber temperatures with the rising strain rates. According to the RTDS solution, there was an inverse correlation between the increases in rubber temperature and the ambient temperatures.