Modeling nonlinear viscoelastic behavior of elastomers using a micromechanically motivated rate-dependent approach for relaxation times involved in integral-based models

Finite viscoelasticity models are mostly formulated by two different approaches; the hereditary integral approach and multiplicative decomposition of the deformation gradient tensor (F). The first approach utilizes fading-memory functions to reflect the effects of strain history on the current stress state (Drozdov, 1997, Kaliske & Rothert, 1997). This method is mainly motivated by linear viscoelastic models and is a very useful scheme to describe finite viscoelastic behavior of materials. The second approach was originally proposed by Green and Tobolsky (1946) and further explored by several researchers (Reese, 2003, Bergström & Boyce, 2001). Similar to the hereditary integralbased models, most multiplicative decomposition based models have been experimentally validated for a narrow range of strain rates.