Modeling of materials with internal variables using a thermomechanical approach

In this thesis, the thermomechanical approach with internal variables has been thoroughly analyzed. This approach is based on the combination of thermodynamic principles and continuum mechanics. Therefore it reflects the physical essence of constitutive behavior of materials. Based on this approach, a one-dimensional constitutive model for the two-way shape memory effect and a one-dimensional constitutive model for piezoceramics have been developed, respectively.

In modeling the two-way shape memory effect, a residual stress σ_re is introduced as a controlling parameter for the two-way shape memory effect. A further refinement of the transformation kinetics expression for two-way shape memory is derived. It is demonstrated that the material parameters required by this model can be calculated or measured using a standard materials testing apparatus. A numerical study is conducted and the effectiveness of this model is verified.

In the constitutive modeling of piezoceramics, a new internal state variable is introduced to relate the macroscopic behavior of a piezoceramic with its micro-properties. A phenomenological formulation of polarization reversal is proposed, and then a fully-coupled thermo-electro-mechanical model is developed. It is shown that the theory developed can describe the electromechanical behavior of piezoceramics well.