LAUSR

A semi-empirical constitutive equation is suggested for the model comb polymer with the purpose to simultaneously describe the intrinsic medium amplitude oscillatory shear (MAOS) behaviors and transient behaviors in start-up elongational experiments. The molecular stress and hierarchical relaxation of comb polymers are discussed on the basis of the orientation-stretch coupled conformation tensor of both backbone and arm, which are governed by the same evolution equation with different relaxation times. The discrete Baumgaertel–Schausberger–Winter spectrum is adopted for the backbone relaxation. The model has four parameters that are fully determined from the linear spectrum. The equation set is solved analytically by the perturbation method under MAOS and solved numerically under start-up extensional flows. The predictions on the nonlinear rheological behaviors are well consistent with the experiments.