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 temperatures of dumbbell-shaped rubber specimens under cyclic deformation. To achieve this, first, a new mathematical equation was developed based on a modified Mooney-Rivlin (MR) strain energy function, the pseudo-elasticity theory, and the inverse analysis method. This equation was used to determine 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 further generated to describe the heat transfer in rubber compounds. Based on 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 seconds 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. Moreover, the RTDS solution characterized an inverse proportional relationship between the rubber temperature increments and the ambient temperatures.