Some 50 years ago, Zener considered transverse vibrations of a homogeneous, isotropic, and thermoelastic beam. Invoking the Thomson effect, he observed that the tensile side cools while the compressional side heats up resulting in irreversible heat transfer across the neutral axis. This led him to postulate the existence of thermoelastic damping that he modeled in terms of standard anelastic solids. With the advent of metal-matrix composites, there is a need for a theory of thermoelastic damping in engineering materials that are inherently anisotropic and heterogeneous. Unfortunately, Zener's simple model cannot be easily extended to composite materials; this defines the objective of this paper.
Taking the Second Law of Thermodynamics as our starting point, we calculate the thermoelastic damping from the entropy created due to irreversible heat transfer. The thermal currents can be set up either as a result of an inhomogeneous stress field in a homogeneous medium, or a homogeneous stress field in an inhomogeneous medium, or both. The exact theory is equally applicable to monolithic or composite materials. As illustrative examples, we solve three boundary value problems: 1. The damping of an isotropic and homogeneous beam undergoing flexural vibration. 2. The interface damping resulting from the longitudinal vibrations of two rods in thermomechanical contact. 3. The damping in a thermoelastic inclusion in a rod subjected to uniaxial stress.