Studies of the propagation of stress waves in solid bodies demonstrate that the transmission of elastic energy is accompanied by a dissipation of energy even when the waves have small amplitudes. This dissipation results from imperfections of elasticity within the body and cannot be attributed to loss by radiation, geometrical spreading, or other effects. In a perfectly elastic, homogeneous solid the strain at any point is directly proportional to the instantaneous stress; a pulse or sine wave of infinitesimal amplitude traveling through such a material would have constant energy, and the medium once set into vibration would continue to vibrate indefinitely. Actual materials do not exhibit such ideal behavior; elastic vibrations subside even when the material is isolated from its surroundings.
The study of attenuation of stress waves in solids has demonstrated that Hooke's law does not hold even for extremely small strains. Fortunately, the deviations from perfectly elastic behavior are small, and the usual approximations of elastic wave theory are sufficiently accurate for most materials if the pressure, temperature, and frequency are not varied too widely.
The term “internal friction” has been frequently used for the nonelastic mechanisms that convert strain-energy into heat, thereby damping or attenuating the stress waves in a solid. The accumulation of experimental results seems to indicate that the damping of solids does not satisfy any simple general formula. There have been a number of mechanisms suggested to explain the dissipation of energy in a vibrating solid. These can be grouped into four main types: