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.