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 positivedefinite 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.
A method is described for formulating an exact solution to any problem involving an elastic cylindrical bar with a free lateral surface and mixed time-dependent end conditions. To illustrate the method and to test the practicality of simulating pure end conditions by conditions given in mixed form, a solution is obtained for a particular problem involving both longitudinal and flexural strain. Asymptotic expressions valid at large distances from the end of the bar or for long times after the load is applied are developed for the integrals of the exact solution to the particular problem and predictions based on these expressions are compared with results of an experimental test in which pure end conditions were used. In this case and for large distances or long times, all of the main features of the observed behavior were correctly predicted.
The lowest-order nonvanishing contribution to the viscosity of a crystal lattice is considered. This contribution depends on the cubic anharmonic momentum-flux operator previously derived by the author. An inhomogeneous transport equation, which describes both anharmonic and imperfection phonon scattering and whose solution determines the viscosity, is presented. The scattering operator is then replaced by a singlerelaxation-time approximation where the effective relaxation time is found from lattice-thermal-conductivity experiments. With the aid of a Debye-like model, solutions are obtained for the coefficients of viscosity. From these solutions the attenuations of longitudinal and transverse sound waves are calculated and compared with experiment for Ge and Si, where qualitative agreement is found.
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