Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials

Abstract

Three simple constitutive relationships are studied for application to viscoelastic materials. Experimental results for both a rubbery and a glassy viscoelastic material are fit by the three schemes. The Kelvin-Voigt scheme is shown to be adequate in only limited frequency ranges. A three-parameter fractional order constitutive relationship provides a substantially better model over a much larger bandwidth. A four-parameter fractional model improves on the accuracy in materials with significant glassy regions