Low-dimensional intrinsic material functions for nonlinear viscoelasticity

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 lowdimensional measures for describing leading-order nonlinear responses in large-amplitude oscillatory shear (LAOS). 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 measure experimentally the four intrinsic shear nonlinearities of LAOStrain for a polymeric hydrogel (PVA-Borax) and 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 molecularand micro-scale features of the material. Ewoldt & Bharadwaj Intrinsic LAOS 2