Study On Linear And Nonlinear Fractional Operator Constitutive Relation Of Polymers

Polymer material has a series of excellent physical properties, especially with mechanical properties of high elasticity or viscoelasticity. Since the mechanical properties of viscoelastic material are complex and have a strong dependence on temperature, frequency, strain amplitude and other external factors, which present difficulties for theoretical analysis and establishment of mechanical model. Practice and theory have shown that fractional operator described in the constitutive model can well describe constitutive relation and mechanical properties of some of the solid polymer viscoelastic materials, but also describe the mechanical behavior accurately in wider range of frequency.In this paper, from the general linear constitutive theory, study several linear constitutive model used currently and widely, it focused on common fractional derivative Kelvin model and fractional derivative Maxwell model of the constitutive model described with fractional operator, and improved the processing of mechanical parameters properly. MTS831.10 Testing System is used to conduct the experiment of dynamic mechanical behavior of polymer materials, the experimental results is stimulated presented by the linear model or nonlinear model, and study the mechanical behavior expressed by them.In the fractional derivative linear constitutive theory, in the past the model parameters were obtained through the method of fitting the storage modulus and dissipation modulus, or by fitting the relaxation curve, but the model parameters obtained by this two ways have a big difference in the practice. This article find the relation of storage modulus and dissipation modulus of fractional derivative Kelvin model and Maxwell model, the relation of storage compliance and dissipation compliance, which seeks their common parameters by fitting the storage modulus and the dissipation modulus, the storage compliance and the dissipation compliance.The results show that:, for some materials of this test, linear model described by fractional operator can describe the mechanical properties of polymer materials accurately comparing with several other linear models, moreover, which is simpler, fewer parameters. Some viscoelastic material that can not be described by linear fractional derivative constitutive,can be described its nonlinear phenomenon by this paper give an improved to Nasuno and Shimizu proposed nonlinear fractional derivative constitutive basic model.Nonlinear damping coefficient's parameters change with the static pressure shrinkage dramatic changes, while fractional derivative of fractional order r value changed little.Fractional derivative model theory overcomes the serious shortcoming of the classic model that the results cannot fit the experimental dada very well, for the mechanical properties of some viscoelastic material, which bring more accurate and reasonable description. Fractional derivative model is more attractive s in the constitutive study of high polymers, structural vibration control and rock theology.