Statistical Mechanics of Viscoelasticity

Abstract

The theory of viscoelasticity is developed from the point of view of statistical mechanics. The general transport relations (for linear processes) are treated with a modified form of the Chapman-Enskog method, the modification being such as to take into account the existence of large internal relaxation times. The stress is then found to depend on the past history of the strain or strain rate, with relaxation functions which are time-dependent correlation functions. Certain basic properties of the relaxation functions then follow almost immediately. In particular the shear and volume relaxation functions are shown to be positive-definite functions of the time. The theory is linear, but no assumptions are made regarding the reference state, which may be an arbitrary state of strain. The thermodynamics of a stressed medium, which is necessary for application of the Chapman-Enskog method, is discussed in an appendix.