(553f) Medium Amplitude Parallel Superposition (MAPS) Rheology

A mathematical representation for nonlinear viscoelasticity based on Volterra series expansion of the shear stress as a functional of the shear strain is presented. In this talk, we will develop a theoretical and experimental framework based on this representation, which we call medium amplitude parallel superposition (MAPS) rheology. The framework reveals a new material property, the third order complex modulus, that describes completely the weak, time dependent nonlinearities of the shear stress within a homogeneously sheared viscoelastic material. This nonlinear modulus is a super-set of the response functions measured in medium amplitude oscillatory shear (MAOS) and parallel superposition (PS) experiments. Unlike the MAOS and PS transfer functions, the nonlinear modulus can be used to construct the weakly nonlinear stress response to an arbitrary deformation history. This material function offers a new approach for probing nonlinear viscoelasticity that is data rich. For some simple constitutive models, the third order complex modulus possess startlingly complex and distinctive features. An experimental protocol is presented that allows for direct measurement of the third order complex using existing commercial rheometers and their associated control software. Finally, we demonstrate this experimental protocol through measurement of the nonlinear viscoelasticity in a polymer hydrogel that possesses an ultra-narrow distribution of equilibrium relaxation times.