• Diffusion;
  • polyamides;
  • constitutive modelling;
  • humidity;
  • internal variables;
  • Gibbs free energy.


In this work a model to describe the behaviour of polymers close to glass transition depending on environmental influences will be presented. The focus lies here – besides modelling influences of mechanical or thermal loads – on the moisture-depended properties of polymers. To this end an ansatz based on thermodynamics with internal state variables will be used and enhanced. Adding a second phase – here water – to the balance equations allows under certain circumstances to achieve one single entropy inequality. Based on the Coleman & Noll type of evaluation of the Clausius-Duhem inequality formulated for the Gibbs free energy, a thermomechanically consistent material model is derived, which is based on a series expansion of the Gibbs free energy around thermodynamic equilibrium. Now, besides constraints emanating from the second law of thermodynamics, it is possible to obtain three relations between the stress, the temperature, the internal variables and the water content on the one side and the strain, the entropy and the chemical potential of the water content on the other. Adjusting the free parameters in these relations – taking into account the remaining entropy inequality – enables inter alia sufficiently accurate reproduction of measuring data from dynamic tension tests with PA 6.