SINGLE CHAIN STOCHASTIC POLYMER MODELING AT HIGH STRAIN RATES

摘要

Our goal is to develop constitutive relations for the behavior of a solid polymer during high-strain-rate deformations. In contrast to the classic thermodynamic techniques for deriving stress-strain response in static (equilibrium) circumstances, we employ a statistical-mechanics approach, in which we evolve a probability distribution function (PDF) for the velocity fluctuations of the repeating units of the chain. We use a Langevin description for the dynamics of a single repeating unit and a Lioville equation to describe the variations of the PDF. Moments of the PDF give the conservation equations for a single polymer chain embedded in other similar chains. To extract single-chain analytical constitutive relations these equations have been solved for representative loading paths. By this process we discover that a measure of non-uniform chain link displacement serves this purpose very well. We then derive an evolution equation for the descriptor function, with the result being a history-dependent constitutive relation.