(Dr. Christopher Lynch, advisor)
"Constitutive Models for Ferroelectric Materials"
As more and more design is done and testing is modeled using numerical simulations, it is essential that the calculated behavior closely simulates observed material behavior. The work on the constitutive law of the material helps the models to simulate as much as possible the reality. In the case of the ferroelectric material, different constitutive models have been proposed to simulate the hysteresis behavior of the ceramic. Two approaches are considered: the macroscopic approach that seems to be more efficient and is used in many commercial codes and the microscopic approach that is more accurate but requires more calculation. The goal of this thesis is to improve the simulation of the behavior of the ceramics by working on the constitutive laws and then implementation in the finite element codes.
The first step of this thesis was a macroscopic approach. The aim was to implement one of these models (the ferroelastic behavior) in the commercial finite element code ABAQUS. This was done by programming a UMAT fortran code which acts like a correction of the calculation made by the main code. The results gave good hysteresis loops and produced remanent strains in response to mechanical loadings. In order to proceed with the study, the piezoelectric should have been modeled, but problems with implementing the electrical loading stopped the progression. An alternate approach, the microscopic approach, became the focus for simulation of the electro-mechanical behavior.
Wei Chen (1999) wrote his own micromechanics code and finite element
code for the simulation of the behavior of the ceramic. Using this micromechanics
code, the second step of this thesis was to find more accurate constitutive
laws. Taking into account the anisotropy of the ceramic improved the simulation.
Experiments were done to determine the effect of mechanical and electric
loadings on the anisotropy. At the same time new constitutive laws were
written. These were tested and programmed in the micromechanics code. A
comparison between the experimental and simulated results was done. Once
the laws are well defined, a further step would be to implement these new
constitutive laws in the finite element code.