On thermodynamic consistency of strain gradient elasticity

Thermodynamic consistency assures that a description of a phenomenon satisfies the fundamental laws of thermodynamics. Verifying thermodynamic consistency of strain gradient elasticity is not trivial. It involves introducing internal variables. The single internal variable theory provides a framework for justifying the thermodynamic consistency of strain gradient elasticity. The dual internal variables approach, which produces hyperbolic evolution equations, overcomes the restrictions of strain gradient elasticity models.