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Magnetic shape memory alloys (MSMAs) are materials with strong nonlinearity, which will show hysteresis when it works. In the current paper, a differential model is proposed to describe the hysteresis in MSMAs caused by magnetic field induced martensite reorientation based on Landau theory of phase transitions. First, the three-dimensional model is simplified into a one-dimensional case, and the hysteresis in MSMAs is described by three martensite variant orientations. Then, a traditional Landau free energy is introduced, and the traditional Landau model is obtained by using the Euler–Lagrange equation. However, it is found that the prediction accuracy of the model is not ideal compared with the experimental data. Thus, an improved model is proposed, and the traditional Landau free energy is replaced by a function that can be determined by the easily measured physical quantities in the experimental curve. Numerical experiments show that the prediction effect of the improved model is much better than the traditional Landau model, and the stress dependence is also demonstrated. Moreover, the proposed improved model has the advantages for dynamic analysis and control with its differential form. Therefore, the frequency dependence of the improved model is demonstrated and a feedback linearization control methodology is proposed to make the system develops in the desired trajectory.

Shape memory alloy (SMA) is a very important smart material, which has been widely used in many fields, especially in vibration. Phase transformation can be induced by changing temperature and its stiffness changes accordingly. In this paper, the primary resonance vibration of a one-dimensional SMA oscillator is analyzed using the harmonic balance (HB) method. The amplitude-frequency curves of the SMA oscillator with different temperatures are drawn, and the effect of temperature and frequency on the amplitude is discussed. Then, the energy flow of SMA in the vibration process is researched by the power flow analysis (PFA) approach. The time-averaged input power (TAIP) is calculated using the analytical and numerical method, respectively, and the calculation time is compared. It is found that the difference between the analytical and numerical solutions is not significant in most cases, but the calculation time of analytical solution is only about one-tenth of that of the numerical solution, which is very important in saving computational cost, real-time control and so on. Finally, some other characteristics of energy flow in the SMA oscillator are identified.

In the current paper, energy dissipation via stress-induced polarization switching in ferroelectric material is investigated, and the feasibility of its application in sound wave absorption is analysed. For the system design and analysis, a phenomenological model based on the modified Landau phase transition theory is constructed to describe the polarization switching. A simple and robust energy dissipation prototype is introduced. The hysteretic dynamics associated with the polarization switching process and the energy dissipation process are investigated. The dependence of the energy dissipation on the bias voltage, frequency, and resistance is analysed in detail. The energy dissipation density in one cycle is calculated. It is shown that the resistance has a strong influence on the energy dissipation. Meanwhile, a better energy dissipation effect could be obtained by setting an appropriate resistance for the low-frequency excitation. The feasibility of using ferroelectric materials for low-frequency sound wave absorption is validated. For a specific acoustic energy dissipation device, corresponding design and analysis will be discussed in our future papers.

This paper is an extended study on the model of the hysteretic dynamics of magnetorheological dampers based on a phenomenological phase transition theory (Wang and Kamath in Smart Mater. Struct. 15(6):1725–1733, 2006). It is demonstrated that, by appropriately choosing model parameters, the frequency dependence of the hysteretic dynamics can be captured very well by the model based on phase transition theory. Whilst by introducing an appropriate rescaling coefficient to account for the strength of the magnetized particle chains with various magnetic field strengths, the field strength dependence of the hysteretic dynamics can also be captured very well by the same differential equation with the same set of model parameters. There are in total eight model parameters introduced for capturing the hysteretic dynamics, including its dependence on the loading rate and field strength.

Whiskers, designated as W, were prepared from hemp fibers. Both fibers and whiskers were characterized by Fourier transform infrared spectroscopy, thermogravimetric analysis. Scanning electron microscopy and transmission electron microscopy were used to evaluate the dimensions of the fibers and whiskers, respectively. By incorporating different weight fraction of the fibers and whiskers into soy protein isolate, we prepared two different composites designated as SC and SC-W, respectively. Thiodiglycol was used as a plasticizer for the preparation of composites. The SC and SC-W composites were characterized and compared in terms of mechanical properties, volume fraction of porosity, and water uptake. The results indicated that there was not much significant difference in the properties of the composites. In fact, mechanical properties of fiber-reinforced composites were higher than whisker-reinforced composites at optimum weight fractions. This study can give us the idea about the judicious use of fibers or whiskers as reinforcement materials.

Reversible large electric-field-induced strain caused by reversible orientation switchings in BaTiO3 is modeled using the Landau’s theory of phase transition. A triple well free energy function is constructed. Each of its minima is associated with one of the polarization orientations involved. Nonlinear constitutive laws accounting for reversible orientation switchings and electrostriction effects are obtained by using thermodynamic equilibrium conditions. Hysteretic dynamics of one-dimensional structures is described by coupled nonlinear differential equations. Double hysteretic loops in the electric and mechanic fields are both successfully modeled. Giant reversible electrostriction is modeled as a consequence of reversible orientation switchings via electro-mechanical couplings. Comparisons with experimental results reported in literatures are presented.

In this paper, a macroscopic differential model for the nonlinear dynamics of the electric field in ferroelectric ceramics is developed on the basis of polarization switching theory. In a one-dimensional description, dynamics with hysteresis caused by polarization switching is modelled by using the Landau theory of phase transitions for single-crystal cases. For ferroelectric ceramics, the orientation of the principal axis of grains is assumed to have a certain distribution. The overall dynamics is determined by making a weighted combination of the dynamics of each grain. The weight function for the combination is taken phenomenologically based on experimental observations. It is shown that experimental hysteresis can be reproduced by the macroscopic differential model precisely.

The morphology and structure of the regenerated cellulose membranes prepared from its NaOH–urea aqueous solution by coagulating with 5 wt% H2SO4–10 wt% Na2SO4 aqueous solution with different temperatures and times were investigated. The pore size, water permeability and physical properties of the membranes were measured with scanning electron micrograph (SEM), wide X-ray diffraction (WXRD), Fourier transfer infrared spectroscopy (FTIR), flow rate method, and tensile testing. The SEM observation revealed that the structure and pore size of the membranes changed drastically as a function of the coagulation temperature. The membranes coagulated at lower temperatures tended to form the relatively small pore size than those at higher temperatures. On the contrary, the membranes coagulated at different times exhibited similar pore size. Interestingly, the mean pore size and water permeability of the membranes increased from 110 nm with standard deviation (SD) of 25 nm and 12 ml h−1 m−2 mmHg−1 respectively to 1,230 nm with SD of 180 nm and 43 ml h−1 m−2 mmHg−1 with an increase in coagulation temperature from 10 to 60°C. However, the membranes regenerated below 20°C exhibited the dense structure as well as good tensile strength and elongation at break. The result from FTIR and ultraviolet-visible (UV-vis) spectroscopy indicated that the relatively strong intermolecular hydrogen bonds exist in the cellulose membranes prepared at lower coagulation temperatures. This work provided a promising way to prepare cellulose materials with different pore sizes and physical properties by controlling the coagulation temperature.

In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modeling of shape memory alloys (SMA). Computational experiments are carried out to study the thermo-mechanical wave interactions in a SMA rod, and a patch. Both mechanically and thermally induced phase transformations, as well as hysteresis effects, in a 1D structure are successfully simulated with the developed methodology. In the 2D case, the main focus is given to square-to-rectangular transformations and examples of martensitic combinations under different mechanical loadings are provided.

Nonlinear kinetic parameter estimation plays an essential role in kinetic study in reaction engineering. In the present study, the feasibility and reliability of the simultaneous parameter estimation problem is investigated for a multi-component photocatalytic process. The kinetic model is given by the L-H equation, and the estimation problem is solved by a hybrid genetic-simplex optimization method. Here, the genetic algorithm is applied to find out, roughly, the location of the global optimal point, and the simplex algorithm is subsequently adopted for accurate convergence. In applying this technique to a real system and analyzing its reliability, it is shown that this approach results in a reliable estimation for a rather wide range of parameter value, and that all parameters can be estimated simultaneously. Using this approach, one can estimate kinetic parameters for all components from data measured in only one time experiment.