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 stepwise loading, in particular, creep and recovery curves and curves of incremental cyclic loading. The goal 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 crosslinking degree compared to typical creep and recovery curves of structurally stable materials. A system of two nonlinear differential equations is obtained which describe the response of the system to a given loading program (not deformation program, as before), such as creep under constant load and arbitrary piecewise constant load. A general solution to the Cauchy problem for this system is constructed in 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 crosslinking degree 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 time (monotonicity and convexity intervals, extrema, asymptotes, etc.), on the material parameters and function of the model, on the stress level and initial crosslinking degree of the material, and on the initial stage of loading to a given stress before creep. It was proven that creep curves always increase in time, do not have inflection points and have oblique asymptotes (although their initial portions can differ considerably from straight lines), and the crosslinking degree 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 crosslinking degree at each incremental loading step. The model is shown to describe unusual effects observed in tests of 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 were found, which can be conveniently verified using experimental data. The responses of the model to cyclic loading/unloading (creep/recovery), induced oscillations of the crosslinking degree, and their effect on the rate of plastic strain accumulation were studied.
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