Creep Curves Generated by a Nonlinear Flow Model of Tixotropic Viscoelastoplastic Media Taking into Account Structure Evolution

Abstract

We continue the systematic analytical study of the nonlinear Maxwell-type constitutive equation for shear flow of tixotropic viscoelastoplastic media formulated in the previous article. It accounts for interaction of deformation process and structure evolution, namely, the influence of the kinetics of formation and breakage of chain cross-links, agglomerations of molecules, and crystallites on viscosity and shear modulus and deformation influence on the kinetics. The constitutive equation is governed by an increasing material function and six positive parameters. Assuming that the stress is constant (in order to simulate creep conditions), we formulate the set of two nonlinear differential equations for two unknown functions (namely, strain and cross-links density) and obtain its exact general solution in explicit form. We examine the properties of creep curves generated by the model for arbitrary material function and material parameters and analyze dependence of creep curves and cross-links density on time, stress level, initial cross-links density, and material parameters governing the model. Thus, we prove that the model not only describes basic phenomena observed for simple shear flow of shear thinning fluids, but can simulate creep, relaxation, and other phenomena observed for solid bodies.