Abstract: In order to better solve the long-term stability problem of concrete structure and study the stress relaxation characteristics of concrete structure, an unsteady fractional order stress relaxation time-dependent model was established. The model used fractional order theory to fractionalize the traditional integer-order stress relaxation model. By constructing the relationship between damage variables, time and model parameters, and considering the effect of time on the fractional order number of model, a new unsteady fractional order stress relaxation time-dependent constitutive model was established. Finally, the correctness and rationality of the model were verified by experimental data. The results show that the model curve is highly consistent with the experimental curve, which indicates that the unsteady fractional order model is suitable for reflecting the deformation process of rock stress relaxation. It can better describe the whole process of stress relaxation change. In general, the fitting degree of the model is much higher than that of the J-body model. In the latter case, the model curve has a large deviation from the test curve under the action of large strain.

Key words: stress relaxation, unsteady fractional order, time-dependent constitutive model, damage variable, time