On the thermodynamics of pseudo-elastic material models to reproduce the   Mullins effect
  This work focuses on the thermodynamics of pseudo-elastic models which represent the Mullins effect. Two established models are analyzed theoretically, their thermomechanical properties are derived, and certain critical points are identified. These findings are used to deduce an alternative approach to deviate pseudo-elasticity. This is achieved by defining a suitable free energy which imposes conditions on the stress tensor and the dissipation using the Clausius-Duhem inequality. The concept of pseudo-elasticity is then generalized to extend arbitrary thermomechanical, even inelastic, material models to allow for softening effects. Under weak assumptions on the softening function the thermomechanical consistency is shown. 
Christoph Naumann, J\"orn Ihlemann
cond-mat.mtrl-sci