Refining rheological model for description of linear and nonlinear viscoelasticity of polymer systems

The article reviews the current mesoscopic modeling of flows for polymer solutions and melts of various structures. It also demonstrates the unified structure of the rheological constitutive relation, up to a certain dissipative function. Linear and nonlinear effects are considered for the simple shear and uniaxial tension of polymer melts based on the modified Vinogradov and Pokrovskii rheological model. The model can describe with adequate accuracy the linear viscoelasticity of fluid polymer systems, as well as transient processes at the shear flow and uniaxial elongation. It was compared with other experimental data for the melt of an industrial polyethylene sample. The nonlinear viscoelastic response of a polymer material was modeled at large periodic deformations. The calculation results were obtained via the Runge-Kutta approach with in-line subprograms of MATLAB IT environment. They were later compared with the experimental data for the solution of polyethylene oxide in dimethyl sulfoxide. The nonlinear behavior of the polymer sample manifested itself in the distortion of the viscoelastic response of the material at sinusoidal oscillations. In this case the shear stresses are no longer the correct harmonics and a "step" appears at the leading edge of the response. Besides, their amplitude is not proportional to the amplitude of the shift. The paper also considers the superposition of the oscillating shear flow on the simple shear. The distortion of the viscoelastic response is observed here though, unlike the high-amplitude periodic deformation, the curvatures of the upper and lower half-waves of the response differ. Since there is still no experimental data for this case, this work expects to encourage the researchers working in the field of nonlinear viscoelastic properties of polymer solutions and melts for further endeavors.