Linear Dissipation in Solids

Abstract

In solid materials the properties of transient creep, internal friction and dispersion can be correlated on the basis of a linear theory, if the strains are small throughout. The theory, first given by Boltzmann, is developed in some detail. Dissipative properties of the material are shown to depend on a function of time called the ``creep function'' φ(t). The general condition 1/Q≅constant is examined. This condition is compatible with a creep function of logarithmic type. Velocity dispersion of plane or spherical waves is very small in such a medium. Graphs of 1/Q, phase and group velocities vs frequency are given, and a quantitative relationship between creep and internal friction constants is derived. The results are substantially applicable to the problem of losses in dielectrics, by carrying out the electromechanical analogy.