AbstractMaterial damping in a continuum, which inherently involves multiple coupled irreversible thermodynamic processes, is associated with irreversible interchanges of various forms of energy. In this paper, a hybrid framework of internal state variables and extended state variables is proposed to formulate a material damping model for complex materials. For a typical simple material, damping model is developed in the framework of extended irreversible thermodynamics. Nonequilibrium quantities, i.e. thermodynamic fluxes, are introduced as extended state variables to supplement for the description of a local nonequilibrium state. The relaxation characteristics of these thermodynamic fluxes, which are a symbol of nonequilibrium characteristics, are modeled by first-order relaxation equations. For a typical system, we introduced heat flux and nonequilibrium (viscous) stresses as thermodynamic fluxes corresponding to irreversible heat transport and viscous processes. Coupling between equilibrium and nonequilibrium mechanical and thermal fields are modeled. Explicit expressions for specific free energy, specific entropy, and specific internal energy are derived. The energy balance equation that governs interchanges of various forms of energy is then obtained to complete the formulation. We have investigated various limiting cases of the developed model and related these limiting cases to typical thermodynamic damping models. We have applied the model to study the dissipation characteristics of longitudinal vibrations of a rod and then compared with other damping models.