## 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.