Single chain stochastic polymer modeling at high strain rates.

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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 ... continued below

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39 p.

Creation Information

Harstad, E. N. (Eric N.); Harlow, Francis Harvey, & Schreyer, H. L. January 1, 2001.

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Description

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 nonuniform 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.

Physical Description

39 p.

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  • Submitted to: 2002 ASME Pressure Vessels&Piping Conference, August 4-8, 2002, Vancouver, British Columbia, Canada

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  • Report No.: LA-UR-01-6877
  • Grant Number: none
  • Office of Scientific & Technical Information Report Number: 975917
  • Archival Resource Key: ark:/67531/metadc927565

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  • January 1, 2001

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 4:49 p.m.

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Harstad, E. N. (Eric N.); Harlow, Francis Harvey, & Schreyer, H. L. Single chain stochastic polymer modeling at high strain rates., article, January 1, 2001; United States. (digital.library.unt.edu/ark:/67531/metadc927565/: accessed September 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.