Nonlinear Dynamic Modeling of Elastomer With Langevin-Chain Spring

This paper developed a simple material model in which the classical Kelvin-Voigt model is modified by the Langevin-chain spring and the Newtonian dashpot. The full range of the force-deformation relationship of elastomer chains is described by the Langevin chain and the inter- and intra-molecular interaction is characterized by the viscosity coefficient of the Newtonian dashpot.  This model has extremely simple mathematical structure and has very clear physical meaning.  It can capture the features of dynamics of elastomer in wide range, from linear to nonlinear.  This model has been used to analyze and explain the nonlinear dynamic behavior of an unfilled cured rubber under simple shear. The effects of temperature and filler particles are also discussed conceptually.