The Influence of the Ramp Deformation Stage and Structure Evolution on the Properties of Stress Relaxation Curves Produced by Nonlinear Models of Viscoelastic-Plastic Media

The systematic analytical study of the previously developed nonlinear constitutive equation (CE) for the shear flow of thixotropic viscoelastic-plastic media, which accounts for the interplay of deformation and structural evolution, is continued. For an arbitrary set of six material parameters and an increasing material function governing the model, the basic properties of families of stress relaxation curves (RCs) generated by the CE at instantaneous loading and under ramp loading (taking into account a rise time to a specified strain level), as well as relaxation modulus, structural evolution features and relaxation time under these loading conditions are analytically studied. The analysis focuses on the ramp RCs dependence on material parameters and function of the CE and on a rise time and strain level. The unusual (but observed in tests) properties of RCs arising as a result of structural changes, compared to typical RCs of structurally stable materials (test RCs and RCs generated by linear or nonlinear CEs), are studied. This includes the dependence of RCs and the relaxation modulus on strain level and rise time, as well as the emergence of new relaxation scenarios compared to those observed under step loading. It is proven that for any material parameters and CE function, all ramp RCs decrease with time and have the common zero asymptote. However, RC convexity and increase in RCs family with strain level may be broken due to sufficiently rapid structural changes. This behavior contrasts with experimental RCs for structurally stable materials and RC families generated by the Boltzmann-Volterra viscoelastic CE. The studied CE can describe both convex downward RCs and RCs with inflection points, as well as the growth of RCs and the relaxation modulus with strain level, including the non-monotonic dependence of relaxation curve families on strain level. The initial deformation stage (loading history) significantly affects expression of these effects and the evolution of the relaxation time of the model. It is shown that a high strain rate at the initial stage may induce too high stress in a material and rapid structure break, which will change the material properties drastically, accelerate stress relaxation phase and make RCs with different strain levels to intersect and intertwine. Conversely, a gradual and lasting strain increase to the target level can distort the expected RC properties if the material is structurally mobile and the initial structuredness is significantly less than the equilibrium value. At the initial stage, the material may have time to increase its structuredness (e.g., during processes like gelation or resin curing in composites or 3D printing of photopolymers), which leads to a slowdown of further stress relaxation. The article demonstrates all these effects, which are related to the influence of the initial loading stage, or nonlinearity, or the structural evolution. It explains the possible reasons for families of RCs with unusual properties observed in some experimental studies. It is shown that ignoring the influence of initial loading stage and the possibility of structural changes in a material during deformation may lead to incorrect interpretations of test data and observed phenomena.