On a model of viscoelasticity with internal state variables

Abstract

In classical theories of viscoelasticity, time-dependent effects are accounted for only with respect to the mechanical properties. However, glass-forming materials such as polymers, for example, also show viscoelastic effects in their thermal properties as can be seen from measurements of the coefficient of thermal expansion or the heat capacity. In this contribution, a model is presented that is able to describe effects associated with the glass transition in the mechanical as well as the thermal properties in one consistent approach. To this end, the state space known from equilibrium thermodynamics is enlarged by internal state variables. These variables are to describe the deviation from equilibrium, hence allowing for a description of viscoelastic effects. Closed form expressions for the complex modulus as well as the compliance, the complex heat capacity at constant stress as well as at constant strain, and the complex coefficient of thermal expansion as well as the thermal modulus are derived and discussed.