A Second-Law Analysis of Thermoelastic Damping

In accordance with the Thomson effect (Thomson, 1853), when a thermoelastic solid is subjected to a tensile stress, it cools. Similarly, when a homogeneous material is subjected to an inhomogeneous stress field or when an heterogeneous material is subjected to any stress field (homogeneous or inhomogeneous), different parts of the material undergo different temperature changes. As a result irreversible heat conduction occurs and entropy is produced. In this paper we take the second law of thermodynamics as our starting point and develop a general theory for calculating the thermoelastic damping from the entropy produced.