The Constitutive Relation Of High Polymers Modeled By Fractional Order Derivative And Its Application

High polymers has a series of good properties in physics. So it is widely used in industry, agriculture, advanced science and our daily life. And the mechanics is the most important section in those properties, because it is the major element which decide the reasonable application of high polymers. The most advantage of high polymers is its high elasticity and viscoelasticity. It depends greatly on the environmental factors such as temperature, frequency, strain amplitude and so on, which present difficulties for modeling constitutive relation and studying their mechanic properties.From the definition of fractional order derivative, the new idea that replacing the traditional Newton dashpot with Abel dashpot is proposed here. And the damping properties of viscoelastic material described by using both theories of fractional order derivative and classical viscoelasticity. The experiments of creep, stress relaxation and dynamic behavior of high polymers in MTS831.10 Testing System having been carried out. And the date of test has also been simulated by traditional viscoelastic model and fractional model respectively. In the end of this paper, the factional model was well applied into the dynamic behavior of damper and the constitutive relation of soil. The analysis results show that:The damping properties of viscoelastic material described by fractional operator not only depend on the change of frequency, but also on the fractional operator. Comparing with classical model, fractional model could also describe the related mechanic behavior accurately in wider range of frequency.Fractional model could accurately simulate the curves of storage modulus and dissipation modulus of high polymers, moreover, which has a simple and uniform form, only a few of the parameters should be adjusted in the calculation process, and the result is more accurate than Maxwell model, Kelvin model and three elements solid model.In the experiment of dynamic behavior of high polymers, the parameters of fractional model extremely vary with the change of static strain. But the fractional operator has little change. So the choose of static strain is very important, and which must be shown in the experiment. Comparing to static strain , dynamic amplitude has less effect on storage modulus,...