Low-dimensional intrinsic material functions for nonlinear viscoelasticity

Randy H. Ewoldt, N. Ashwin Bharadwaj

Research output: Contribution to journalArticlepeer-review


Rheological material functions are used to form our conceptual understanding of a material response. For a nonlinear rheological response, the possible deformation protocols and material measures span a high-dimensional space. Here, we use asymptotic expansions to outline low-dimensional measures for describing leading-order nonlinear responses in large amplitude oscillatory shear (LAOS). This amplitude-intrinsic regime is sometimes called medium amplitude oscillatory shear (MAOS). These intrinsic nonlinear material functions are only a function of oscillatory frequency, and not amplitude. Such measures have been suggested in the past, but here, we clarify what measures exist and give physically meaningful interpretations. Both shear strain control (LAOStrain) and shear stress control (LAOStress) protocols are considered, and nomenclature is introduced to encode the physical interpretations. We report the first experimental measurement of all four intrinsic shear nonlinearities of LAOStrain. For the polymeric hydrogel (polyvinyl alcohol - Borax) we observe typical integer power function asymptotics. The magnitudes and signs of the intrinsic nonlinear fingerprints are used to conceptually model the mechanical response and to infer molecular and microscale features of the material.

Original languageEnglish (US)
Pages (from-to)201-219
Number of pages19
JournalRheologica Acta
Issue number3
StatePublished - Mar 26 2013


  • Large amplitude oscillatory shear
  • Material functions
  • Nonlinear viscoelasticity
  • Polyvinyl alcohol
  • Rheometer
  • Transient polymer network

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics


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