Abstract
Transient analyses of vibration phenomena in engine and suspension require high accuracy calculations of load and displacement in rubber parts of such systems. For those calculations, FE analyses are implemented with using constitutive models which are developed by commercial software. However, there are few of constitutive models which can perform all mechanical dynamic behaviours of rubber such as pre-strain dependency, frequency dependency and amplitude dependency when the material subjected to tensile or harmonic vibration loadings. In this paper, a nonlinear viscoelastic constitutive model is developed to be capable of capturing such behaviours observed experimentally under different loading conditions. The proposed constitutive model is an extension of the finite linear viscoelastic model (J.C.Simo, 1987. Computer Methods Appl. Mech. Eng. 60, 153–173) in which based on viscous property of non-Newtonian fluid, the relaxation times of its viscoelastic networks are described as power functions of strain rate to improve prediction results of amplitude dependency (Payne effect) in rubber material. A calculation algorithm with using complex step derivative approximation method to improve convergence of calculation and a determination method of material parameters based on experiments such as relaxation test, constant strain rate test, and harmonic vibration test are introduced for the model to make finite element implementation possible. A very good agreement of prediction results from FE analyses in comparison with experimental data of a rubber material (e.g. the average of the differences of dynamic modulus results between calculations and experiments in material level and component level are less than 10%, 20%, respectively) shows the capability of the model to perform dynamic behaviours of rubber material in wide range of dynamic loading conditions (e.g. in frequency range of 0Hz to several hundred Hz).
KEYWORDS – Constitutive model, Nonlinear viscoelasticity, Finite element analysis (FE analysis), Rubber material