Modeling and Finite Element Analysis of Smart Materials

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Title: Modeling and Finite Element Analysis of Smart Materials
Author: Li, Qifu
Advisors: Ralph Smith, Committee Member
Stefan Seelecke, Committee Chair
Clement Kleinstreuer, Committee Member
Gregory Buckner, Committee Member
Abstract: This dissertation consists of two parts, the modeling of piezoceramic (PZT) actuators and the finite element implementation of a shape memory alloy (SMA) model and the subsequent thermo-mechanically coupled multifield analysis of several devices, such as tensile wire and cantilever beam actuators. Both models are based on similar free energy expressions and allow for a unified treatment of a number of active materials. PZT actuators have been widely used in positioning applications due to their high bandwidth, high resolution, compact and light weight characteristics. However PZT materials also exhibit some inherent undesirable nonlinear effects like hysteresis, creep and frequency dependent response. To improve the performance of PZT actuators, these effects need to be taken into account. In this dissertation, based on a free energy model for perfect single crystal PZT materials and motivated by its extension to homogenized model for polycrystalline materials, a parameterization method is developed to model the hysteresis behaviors of polycrystalline PZT materials. In the parameterization method, the effective barrier is assumed to be a function of the phase fraction. Major loop effective barriers are identified from experimental polarization-electric field diagrams as functions of the phase fraction. Minor loops are constructed by major loops using a linear mapping method and a bookkeeping algorithm. A robust algorithm, which preserves the simple structure and efficiency of the original perfect single crystal model, is implemented to simulate the rate dependent minor loop behavior of the PZT materials and compared to experimental data. Shape memory alloys (SMAs) represent another type of smart materials that have been extensively used in many engineering applications due to their unique material properties, and new devices like SMA microactuators are constantly being developed. To facilitate these new development, an efficient computational tool like the finite element method has to be used in order to simulate the highly nonlinear, load-history and temperature dependent responses of SMA materials. In this dissertation, a 1-D free energy SMA model is implemented into the finite element software package FEMLAB using its general PDE form by treating the evolution equations of phase fractions as degenerated PDEs coupled with the mechanical equilibrium equation and the heat transfer equation. First, without including the latent heat effect and neglecting the heat transfer equation, simulations are conducted for SMA bars to demonstrate that the model can predict the low temperature quasiplastic and high temperature superelastic behaviors as well as shape memory effect. The finite element implementation is then expanded by including the nonlinear transient heat transfer equation with the phase transformation induced latent heat as a coupling term. In contrast to the so-called staggered iteration approach, where the individual fields are solved for in a decoupled way within an iteration, FEMLAB allows for a fully coupled solution. This approach generally provides for a robust and efficient solution even in the case of strong coupling between the fields. A number of different applications are then studied for the first time using such a coupled multi-field approach. The particular focus is on the effects of inhomogeneous fields and the strong coupling between thermal and mechanical fields. Tensile simulations of an SMA wire under different thermal boundary conditions with different loading rates are conducted to demonstrate the inhomogeneity and rate effects of the system responses. By including the Joule heating, the performance of an SMA wire actuator under different thermal boundary conditions is studied. The 1-D free energy model is also implemented into FEMLAB to study the inhomogeneous SMA beam bending problems by using the Euler-Bernoulli beam bending theory. The SMA beam bending problem is modeled as a system of first order PDEs and boundary conditions are implemented as Dirichlet boundary conditions. Detailed analysis is presented for inhomogeneous bending behavior of an SMA cantilever beam under constant temperatures and thermo-mechanical loading, respectively. The rate-dependent responses of an SMA cantilever beam due to strong thermo-mechanical coupling are also studied. Finally, using traditional incremental finite element method, the 1-D free energy model is also implemented into the finite element program ANSYS using its BEAM188 element and the user defined material subroutine USERMAT, which also serves as a validation tool for the FEMLAB implementation. Convergence behavior is studied systematically.
Date: 2006-08-22
Degree: PhD
Discipline: Mechanical Engineering

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