Large Strain Viscoelastic Constitutive Models for Rubber, Part II: Determination of Material Constants

Abstract

Abstract A method for determining material constants in large strain viscoelastic materials was demonstrated for a highly saturated nitrile rubber. Material constant selection was based on viscoelastic stress relaxation data at small and large strains, under both tension and compression, and was constrained to assure Drucker stability. Assuming that the viscoelastic strain energy function was both time and strain separable, a Prony series was constructed for the time dependent material constants. For comparison, four different Prony series were developed from collocation methods and a nonlinear regression analysis, each separately based on either large or small tensile strain relaxation data. In addition, a final Prony series was constructed from dynamic data. These Prony series were included in this comparison to judge their ability to predict both large and small strain material behavior. Finite element analyses of large and small step-strain relaxation tests and a single cycle hysteresis loop at large deformations were performed for each set of Prony series. The results were then compared to experimental behavior. The Prony series based on the constrained method accurately predicted step-strain relaxation behavior at all strain levels, for both tension and compression. The finite element results for the other Prony series show that large strain material behavior was best predicted by those Prony series based on large strain material behavior. Similar findings were found for small strain material behavior. The constrained Prony series and the two large strain based Prony series best modeled the experimental hysteresis loop.