A geometric average interpretation on the nonlinear oscillatory shear

Abstract

Nonlinear oscillation shear has become an important method to study the complex fluids. However, choosing the suitable material functions is not as simple as that in linear viscoelasticity. A framework is suggested in this work to account for the stress–strain and stress–strain rate relationship based on the concept of mean stress and mean strain (rate) in the Lissajous curves. The applications of such framework in an imposed oscillatory shear strain and an imposed oscillatory shear stress are clearly demonstrated. The intracycle nonlinear modulus and viscosity are defined from the slope of the stress–strain curve and the stress–strain rate curve, respectively. The intercycle nonlinear behaviors are obtained from the strain (rate) amplitude dependence of the zero mean strain (rate) modulus or viscosity. We justify the strain-hardening/softening and shear-thickening/thinning behaviors of nonlinear moduli and viscosities by using typical constitutive models like Bingham model and the Maxwell model. It is found that the modulus (viscosity) defined from the stress–mean strain (rate) curves is the most physical reasonable quantity. In addition, we apply the new analysis method to two yield stress fluids, which reveals critical balance between aging and shear rejuvenation.