Analytical Description of Stress Waves in Viscoelastic Bars

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.