Analytical Description of Stress Waves in Viscoelastic Bars

Majid Aleyaasin, John J Harrigan, J C F Millett

Research output: Contribution to journalArticlepeer-review


Strain-gauged circular rods are used for Split Hopkinson Pressure Bar (SHPB) testing. Strain measurements along the bar are used to determine the stress and displacement histories at the end of the bar. A new wave equation is derived for long polymeric rods. The material properties are modelled as a Maxwell viscoelastic material acting in parallel with an elastic material. Lateral motions of the rod that result from the Poisson effect are accounted for using a new concept called the "effective density". The effects of both the material properties and the diameter of the bar on dispersion and attenuation coefficients are highlighted. The new wave theory simplifies to Wang et. al.'s formula (1994) for one-dimensional waves in polymer rods if the Poisson ratio is set to zero. The predictions simplify to Love's equation for stress waves in elastic bars when rate dependency is removed from the material model.

Original languageEnglish
Pages (from-to)707-710
Number of pages4
JournalShock Compression of Condensed Matter
Issue number1
Publication statusPublished - 2009
EventConference of the American Physical Society Topical Group on Shock Compression of Condensed Matter - Nashville, United States
Duration: 28 Jun 20093 Jul 2009


  • stress Wave propagation
  • viscoelasticity
  • Split Hopkinson Pressure Bar (SHPB)
  • Hopkinson Bar
  • propagation


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