During the process of damping of a structure, the mechanical energy is converted to thermal energy. Yet, the most commonly used model for material damping is the linear viscous damping. There are many attempts to develop thermodynamic models for damping. To adequately describe damping, we need more variables than the classical state variables. A simple thermodynamic model that is based on the framework of extended non-equilibrium thermodynamics is presented. Heat flux, non-equilibrium stress field and the associated non-equilibrium internal energy are used as additional variables. Longitudinal vibrations of a uniform rod are studied to present the flexibility of thermodynamic modeling for material damping.

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