Hysteresis and precondition of viscoelastic solid models

We first study the hysteresis and precondition of Kelvin models under the condition of loading and unloading of saw-tooth wave, whereafter we prove out a series of sufficient conditions of models and inputted strains for producing hysteresis and precondition in this paper. We discuss the monotonic and limit property of hysteresis and precondition.We prove that the hysteresis loop's width decreases with increase of period and is greater or equal to zero. At the same time we prove that for the fractional-order Kelvin model and under the condition of quasi-linear theory the above conclusions also hold.