A thermodynamic framework to model thixotropic materials

• A Thermodynamic framework is developed to develop models for Thixotropic materials.
• The framework appeals to the maximization of entropy production.
• The model includes those developed earlier for describing Thixotropic materials.

Thixotropic materials are widely used in a variety of industrial applications. The constitutive relations to describe these materials are based on one-dimensional experiments in which the material is subjected to a shear motion and there is no unique methodology to obtain proper three-dimensional models. The path towards generalization to a three-dimensional framework is invariably carried out in a ad hoc manner. Here we propose a three-dimensional model that stems from a general thermodynamic framework that has proved to be quite robust in the development of constitutive relations, namely the application of the second law of thermodynamics together with the maximization of the entropy production. This leads to a constitutive equation that has the same form of a generalized Upper Convected Maxwell equation, if we require that changes of microstructure due to the deformation of each Maxwell element that comprises the model are reversible. Changes in microstructure are governed by a potential that is a measure of the difference between the current structure and the equilibrium structure associated with it. The equilibrium structure associated with the current structure is determined by the current value of stress, considered the main break up agent. We assume that the state of equilibrium would be achieved in a Motion With Constant Stress History, starting from the current stress state, until a steady state where the kinematics is not changing.