Large Strain Viscoelastic Constitutive Models for Rubber, Part I: Formulations

Abstract

Constitutive models for large strain isothermal viscoelastic deformations of rubber are reviewed. The models discussed are for materials which have separable long and short term stresses, and for which the short term stresses have separable time and strain effects. They include the history integral model, an internal stress variable model, an internal stretch variable model, and an internal solid model. The internal stretch variable model and the internal solid model were motivated by molecular descriptions of rubber viscoelasticity. The material tests required to determine the constants for these large strain models are discussed. The classical problem of determining a rubber energy density function, used to describe both the long term and short term energy in these models, is reviewed. A method to assure Drucker stability, a commonly overlooked issue, is presented for experimentally determined Rivlin energy density function expansions. Also, an improved method for determining the coefficients of a Prony series, which defines a material's relaxation time spectrum, from experimental relaxation data is presented.

Domain of validity and fit of Gent-Thomas and Flory-Erman rubber models to data

“…This is at variance with the regression analysis of the constrained energy function by Johnson et al [16]. From Figure 2a, we see that the single process is irrelevant.…”

Nonlinear reptation in molecular based hysteresis models for polymers

“…Tube reptation models for deformations of viscoelastic polymers were introduced by Doi and Edwards [15] and were further developed by Johnson, et.al., in several papers [19,20]. In this section we give a brief overview of their models and assumptions in the case of tensile deformations since they serve as a starting point for the derivation of our nonlinear reptation model in Sec.…”

Nonlinear Reptation in Molecular Based Hysteresis Models for Polymers

“…Tube reptation models for deformations of viscoelastic polymers were introduced by Doi and Edwards [15], and were further developed by Johnson, et.al., in several papers [19,20]. In this section we give a brief overview of their models and assumptions in the case of tensile deformations since they serve as a starting point for the derivation of our nonlinear reptation model in Section 3.…”