STATISTICAL DESCRIPTION OF HISTORY-DEPENDENT CREEP CONSTITUTIVE-EQUATIONS FOR VISCOELASTIC MEDIA

Abstract

In this paper a nonequilibrium statistical ensemble theory is used to describe viscoelastic creep behaviors. By using the history-dependent distribution function and taking stress as a controllable kinetics argument, a stress ensemble is introduced for obtaining the corresponding thermodynamics functionals such as entropy, enthalpy and the Gibbs free energy, etc. With consideration of the dissipation constraint to materials with memory, the creep stress-strain relation can be automatically obtained through the compatible conditions among thermodynamic functionals. Moreover, when higher-order Fourier transform components of stress are further considered as controllable arguments, the wavelength-dependent stress-strain relations characterized by the Fourier components of strain can also be obtained within the framework of the thermodynamics theory with memory. Discussion of linearly dissipative systems in which a dissipation-fluctuation mechanism is involved gives an explicit physical interpretation to the viscoelastic creep function by the time correlation function of the Hamiltonian and other relevant quantities. Besides, all the results obtained are shown to be self-consistent when simplified to an equilibrium or a local equilibrium state.