Influence of Structural Evolution and Load Level on the Properties of Creep and Recovery Curves Generated by a Nonlinear Model for Thixotropic Viscoelastoplastic Media

Abstract This paper continues the systematic analytical study of the properties of the previously constructed nonlinear shear deformation model of thixotropic viscoelastoplastic media, which takes into account the mutual influence of deformation and structural evolution. The ability of the model to describe the behavior of liquid and solid media (solidifying/solidified) is analyzed. The focus is on the response properties of the model to step loading, in particular, creep and recovery curves and curves of incremental cyclic loading. The aim is to find out what typical effects of viscoelastoplastic media the model can describe and what unusual effects/properties are generated by changes in the structuredness compared to typical creep and recovery curves of structurally stable materials. A system of two nonlinear differential equations is obtained to describe the response of the system to a given loading (not deformation) program, such as creep under constant load and arbitrary piecewise constant stress. A general solution to the Cauchy problem for this system is constructed in an explicit form for six arbitrary material parameters and an increasing material function governing the model, i.e. expressions are derived as quadratures for the shear strain and structuredness as functions of time, which depend on the initial conditions and all parameters of the model and loading program. An analytical study is performed for the basic properties of the family of creep and recovery curves and the structural evolution in these processes, their dependence on the time (monotonicity and convexity intervals, extrema, asymptotes, etc.), on the material parameters and function of the model, on the stress level and initial structuredness of the material, and on the initial stage of loading to a given stress before creep. It is proven that creep curves always increase with time, do not have inflection points, and have oblique asymptotes (although their initial arcs can differ considerably from straight lines). The structuredness at constant stress (at each incremental loading step, in particular, at zero stress) is always monotonic unlike other loading modes, but can decrease or increase depending on the relationship between the stress level and the initial structuredness at each incremental loading step. The model is shown to describe unusual effects observed in tests on some materials, e.g. the difference in the absolute values of strain jumps during loading and complete unloading and the opposite sign of residual strain with respect to the stress and strain signs at the creep stage. Several applicability indicators of the model are found, which can be conveniently verified using experimental data. Responses of the model to cyclic loading/unloading (creep/recovery), induced oscillations of the structuredness, and their effect on the rate of plastic strain accumulation are studied.