Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 1. The model, Its Basic Properties, Integral Curves, and Phase Portraits

Abstract

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model of the shear flow of thixotropic viscoelastic-plastic media, which takes into account the mutual influence of the deformation process and structure evolution, is carried out. A set of two nonlinear differential equations describing shear at a constant rate and stress relaxation was obtained. Assuming six material parameters and an (increasing) material function that control the model are arbitrary, the basic properties of the families of stress-strain curves at constant strain rates, stress relaxation curves (Part 2) and creep curves (Part 3) generated by the model, and the features of the evolution of the structuredness under these types of loading were analytically studied. The dependences of these curves on time, shear rate, stress level, initial strain and initial structuredness of material (for example, degree of physical crosslinking), as well as on material parameters and function governing the model, were studied. Several indicators of the model applicability are found, which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (properties) are generated by structuredness changes in comparison to typical stress-strain, relaxation and creep curves of structurally stable materials. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: the effects of creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves at a constant rate, strain rate and strain hardening, flow under constant stress, etc. The first part of the article is devoted to formulation of the model and preparation of basis for the second part: the proof of the uniqueness and stability of the equilibrium point of the nonlinear equations set, analytical study of the equilibrium point dependence on all material parameters, possible types of phase portraits and the properties of integral and phase curves of the model.