Thermodynamically modeling of nonlinear rheological materials and a new energy-based approach to determine the corresponding material parameters

A thermodynamical system can be described by the field equations that are governed by the balance equations and the appropriate constitutive equations. For polymer melts or adhesives under thermal loading nonlinear constitutive equations are necessary. The development of nonlinear constitutive relations compatible with the thermodynamical principles will be presented in detail according to ordinary and extended irreversible thermodynamics. This engineering approach results in a straight forward way of adding complexity to the material or constitutive equations. The necessary material constants in these constitutive equations can be obtained by exploiting an energy-based method. This method will be presented in detail. By utilizing the energy-based method we measured the material parameters of an epoxy (non-cured) adhesive in a standard cone-plate rheometer. The usual output data of the reometer was coded in python for the proposed inverse method. Such a computation lasts less than a minute in a standard laptop since there is a unique solution.
The research leading to these results has been published under [1] and all computational codes are published in [2], they can be used under GNU General Public License [3]. Dr. B. E. Abali is working as a lecturer in the Chair of Continuum Mechanics and Materials Theory, Institute of Mechanics at the Berlin Institute of Technology (Technische Universitaet Berlin) for more details see [4].
[1] http://opus4.kobv.de/opus4-tuberlin/frontdoor/index/index/docId/4892.
[2] http://www.lkm.tu-berlin.de/ComputationalReality.
[3] http://www.gnu.org/licenses/.
[4] http://www.lkm.tu-berlin.de/bea.