New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear

Ewoldt, R.H., McKinley, G.H. and Hosoi, A.E.

Characterizing purely viscous or purely elastic rheological nonlinearities is straightforward using
rheometric tests such as steady shear or step strains. However, a definitive framework does not exist
to characterize materials which exhibit both viscous and elastic nonlinearities simultaneously. We
define a robust and physically meaningful scheme to quantify such behavior, using an imposed large
amplitude oscillatory shear (LAOS) strain. Our new framework includes new material measures and
clearly defined terminology such as intra-/inter-cycle nonlinearities, strain-stiffening/softening, and
shear-thinning/thickening. The method naturally lends a physical interpretation to the higher
Fourier coefficients that are commonly reported to describe the nonlinear stress response. These
nonlinear viscoelastic properties can be used to provide a “rheological fingerprint” in a Pipkin
diagram that characterizes the material response as a function of both imposed frequency and strain
amplitude. We illustrate our new framework by first examining prototypical nonlinear constitutive
models (including purely elastic and purely viscous models, and the nonlinear viscoelastic
constitutive equation proposed by Giesekus). In addition, we use this new framework to study
experimentally two representative nonlinear soft materials, a biopolymer hydrogel and a wormlike
micelle solution. These new material measures can be used to characterize the rheology of any
complex fluid or soft solid and clearly reveal important nonlinear material properties which are
typically obscured by conventional test protocols.