Linxiang Wang

Thermo-Mechanical Wave Propagations in Shape Memory Alloy Rod with Phase Transformations

In the present study, a mathematical model is developed to analyze the wave propagation processes in shape memory alloy rods. The first order phase transformations and associated thermo-mechanical coupling effects are accounted for by employing the modified Ginzburg-Landau-Devonshire theory. The effect of internal friction is considered by using a Rayleigh dissipation term. Chebyshev collocation method is employed together with the backward differentiation methods for numerical analysis. Numerical experiments are performed. Wave propagations caused by impact loadings are analyzed for different initial temperatures. It is demonstrated that thermal waves will be induced. Phase transformations in the material will complicate their propagation patterns. Dissipation effects are enhanced by internal friction, while dispersion during wave propagations is induced by interfacial energy term.

Control of coupled hysteretic dynamics of ferroelectric materials with a Landau-type differential model and feedback linearization

In the current paper, the hysteretic dynamics and butterfly-shaped behavior of ferroelectric materials are modeled and controlled with a macroscopic differential model inspired by the Landau theory of first-order phase transformations. Hysteretic dynamic behavior of the materials is analyzed as a consequence of orientation switching and the governing equations of the dynamics are formulated as coupled differential equations describing system states switching from one equilibrium state to another. The rate dependence of hysteresis is included in the analysis. A nonlinear feedback strategy is introduced for the linearization and a simple and efficient control strategy is proposed. Comparison of the results obtained with the developed model and their experimental counterparts is presented.

Thermomechanical Waves in SMA Patches under Small Mechanical Loadings

2D thermo-mechanical waves in SMA (Shape Memory Alloys) patches are simulated with a model derived for a special case of material transformations. The mathematical model includes the coupling effect between thermal and mechanical fields. It is shown that the classical 1D Falk dynamical model of SMA is a special case of the formulated 2D model. The differential algebraic approach is adopted for the numerical analysis. Computational experiments are carried out with small distributed mechanical loadings to analyze thermo-mechanical waves and coupling effects. Numerical results from 2D structures are compared with its 1D analog which is already been verified.

Simulation of nonlinear thermomechanical waves with an empirical low dimensional model

In this paper we analyse the performance of a low dimensional model for the nonlinear thermo-mechanical waves. The model has been obtained by using proper orthogonal decomposition methods combined with a Galerkin projection. First, we analyse the original PDE model in order to obtain the system states at many time instances. Then, by using an empirical orthogonal basis extracted from our numerical results, we construct an empirical low dimensional model. Finally, we compare the results obtained with the original PDE model and those obtained with our low-dimensional model. These comparisons are carried out for mechanically induced phase transformations in a shape-memory alloy rod.

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling. We present numerical results for the reciprocal-transducer system and identify the influence of nonlinearities on the system dynamics at high and low frequency as well as electrical impedance effects due to tuning by a series inductance. It is found that nonlinear effects are not important at high frequencies (1 MHz) subject to high-input voltages, but they become important under high-voltage and off-resonance conditions

Computational aspects of conservative difference schemes for shape memory alloys applications

In this paper we describe a new conservative difference scheme and apply it to the description of the dynamics of a shape memory alloy rod. The scheme preserves the conservation of the total energy on the grid. A major emphasis is given to the description of hysteresis effects in almost-elastic, pseudoelastic and quasiplastic regimes. Stress-strain dependencies are analysed and computational experiments are presented for main thermomechanical characteristics of the material, including displacement and temperature fields.

Nonlinear Coupled Thermomechanical Waves: Modelling Shear Type Phase Transformation in Shape Memory Alloys

Starting from a two-dimensional model approximating the dynamics of cubic-to-tetragonal and tetragonal-to-orthorhombic phase transformations in shape memory materials, it is shown that the Falk model in the one dimensional case is a special case of the formulated model. Computational experiments based on a conservative difference scheme are carried out to analyse thermomechanical wave interactions in a rod with shape memory effect.

Macroscopic Differential Model for Hysteresis and Butterfly-Shaped Behavior in Ferroelectric Materials

In the current paper, a macroscopic differential model is constructed on the basis of the Landau theory of the first order phase transformation. Hysteresis loops and butterfly-shaped behaviors are modeled as a consequence of polarizations and orientation switchings. A non-convex free energy function is constructed to characterize different polarization orientations in the materials. Polarizations and orientation switchings are modeled by formulating the system state switching from one equilibrium state to another, as differential equations. The hysteresis loops and butterfly-shaped behaviors are successfully modeled. Comparison of the model results with the experimental counterpart is also presented.

Feedback Linearization of Hysteretic Thermoelastic Dynamics of Shape Memory Alloy Actuators with Phase Transformations

In the current paper, a macroscopic differential model for the hysteretic dynamics in shape memory alloy actuators is constructed by using the modified Landau theory of the first order phase transformation. An intrinsic thermo-mechanical coupling is achieved by constructing the free energy as a function depends on both mechanical deformation and the material temperature. Both shape memory and pseudoelastic effects are modeled. The hysteretic dynamics is linearized by introducing another hysteresis loop via nonlinear feedback strategy, which cancels the original one.

Nonlinearities and hysteresis phenomena in reciprocal ultrasound systems

Nonlinearities and hysteresis effects in a re- ciprocal ultrasound system is examined by a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic where the polarization process in the material can be modeled by minimizing the Helmholtz free energy function, i.e., each polarization state is associated with a minimum of the free energy function. Based on the free-energy function, nonlinear constitutive laws can be obtained accounting for effects such as hysteresis. The elastic field is assumed to be coupled linearly with other fields while the electric field is nonlinearly coupled to the electric displacement. We present step-response results for the transmitter and receiver of a reciprocal-transducer system and identify the influence of nonlinearities on the system dynamics. components) is modelled with nonlinear constitutive laws capable of capturing the hysteresis features in the E-D relations. The proposed model is based on polarization switching theory employing the Landau - Ginzburg theory so as to characterize different polarization directions. Ther- modynamical equilibrium conditions allow the constitutive laws to be obtained. We finally present the dynamical behaviour of a one-dimensional reciprocal system using the proposed model.