Analytical studies on the LAOS behaviors of some popularly used viscoelastic constitutive equations with a new insight on stress decomposition of normal stresses

Shear stress of Large Amplitude Oscillatory Shear (LAOS) is known to be decomposed to elastic and viscous stresses. According to the parity of normal stress with respect to shear strain and shear rate, it also can be mathematically decomposed into two parts: N_EE (even symmetry part for both strain and strain rate) and N_OO (odd symmetry part for both shear strain and shear rate). However, the physical meaning of the decomposed normal stress is questionable. This paper is to prove the conjecture that N_EE is elastic and N_OO is viscous under the condition of time-strain separability. For the purpose of the proof, we developed mathematical tools for the analytical solutions of LAOS. We applied the mathematical methods to some popularly used constitutive equations such as the convected Maxwell models, the separable Kaye-Bernstein-Kearsley-Zepas (K-BKZ) model, the Giesekus model, and the Phan-Thien and Tanner model.