  Many thixo-viscoelastic materials have been reported to undergo enhancement
in elastic modulus with time and decrease in the same under application of
deformation field. Incorporation of this feature in a viscoelastic structural
kinetic model has an apparent possibility of violating the second law of
thermodynamics. Furthermore, in a related experimental observation, stress has
been reported to undergo a non-monotonic change as a function of time under the
application of constant strain. We analyze both these scenarios through a
structural kinetic model that shows viscoelastic aging but undergoes
rejuvenation only due to the viscous rate of strain. We observe that such
formalism does not violate the second law. Interestingly, the proposed simple
formalism predicts the experimental observation of the non-monotonic stress
relaxation very well.
