Path-dependent work and energy in large amplitude oscillatory shear flow

Two methods are widely used to quantitatively analyze the nonlinear stress in large amplitude oscillatory shear (LAOS) flow; one is to analyze the stress in time domain and the other in strain or strain rate domain. Distinguished from these two methods, this paper exploits the concept of work and energy to analyze the oscillatory shear stress. The inner area in the strain-stress Lissajous curve after one cycle is known to be related with work, and that of the strain rate-stress Lissajous with energy. To precisely analyze the nonlinear stress, it helps to consider work and energy not only after a complete cycle but also during the cycle. In this paper, we trace the work and energy during the oscillation, together with their derivatives. We apply this concept to perfectly elastic solid, purely viscous liquid, and viscoelastic fluid. By this approach, it is shown that a rheological behavior such as strain thinning can be originated by various origin in the perspective of work and energy, which means that the rheological behavior can be subclassified in terms of work and energy. This approach is useful because it can analyze nonlinear stress without mathematically intriguing higher harmonics and it can be easily applied to any type of material with different stress shape.