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2016 Vol. 37, No. 1
Published: 2016-02-24
1
Phase Field Simulations of Microstructure Evolution
The macroscopic properties of materials are highly dependent on microscopic structures. The enhancement of material performance by microstructures has drawn much attention in both industry and academia. Due to the discontinuity of field variables at the interface, the sharp interface model based on the local theory has the difficulty in predicting the microstructure evolution of materials. The phase field method based on the nonlocal theory employs a diffusive interface concept to model the interface, which exhibits several advantages over sharp interface model in predicting the arbitrary and complex microstructures of materials. In this paper, we firstly introduce the fundamental theory of phase field method, which includes the free boundary problem, diffusive interface model, nonlocal free energy function, the phase field governing equation and its numerical solution. Secondly, we present some research work on the phase field simulations of ferroelectric, ferromagnetic and multiferroic materials, with a brief introduction to phase field simulations of the microstructure evolution of softer mater and Li-ion battery. Finally, we give a summary and propose a few research topics of phase field simulations worthy to be investigated.
2016 Vol. 37 (1): 1-33 [
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697
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34
The Key Mechanical Problems on Hydraulic Fracture in Shale
Zhuo Zhuang
Shale gas is unconventional natural gas stored in shale in free or absorbed form, and sometimes in free fluid phase. The exploitation of shale gas has become a promising field of green energy development in China. Although great success has been achieved in shale gas revolution in North America with the technique of hydraulic fracturing, only 5~15% of the stored oil and gas could be exploited. In order to improve the production of shale oil and gas, a huge challenge accompanied with great opportunities is presented to the mechanics researchers. Based on the recent study results of our research group, this paper introduces and summarizes the key mechanical problems of shale hydraulic fracturing from the aspects of theory, numerical simulation and experiment. The main contents include developing a large-object experiment, establishing the shale constitutive model and fracture mechanics theory, and developing the numerical simulation method for coupling fracture mechanics and fluid mechanics of fracture network. The investigation on hydraulic fracture is of great significance and innovation and will lay a solid foundation for the physical experiment model, fracture mechanics theory and numerical simulation techniques of effective exploitation of shale gas in China.
2016 Vol. 37 (1): 34-49 [
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429
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50
Mechanical Properties and Depoling of Porous Poled PZT95/5 Ferroelectric Ceramics under Uniaxial Compression
Four kinds of poled lead zirconate titanate (PZT95/5) ferroelectric ceramics were fabricated with a range of different porosity levels by systematic additions of added pore formers. The mechanical behavior, domian switching, phase transformation and depoling behavior of porous poled PZT95/5 ferroelectric ceramics were investigated as a function of porosity. The unlinear deformation mechanism of porous poled PZT95/5 ferroelectric ceramics is attributed to the domian switching and phase transformation processes and not related to the deformation and collapse of voids. The depolarization mechanism of porous poled PZT95/5 ferroelectric ceramics is caused by both domian-reorientation and phase transformation. The elastic modulus and fracture strength the porous poled PZT95/5 ferroelectric ceramics are decreased with the porosities, but the fracture strain is independent on the porosities.Critical stresses of the domian switching and phase transformation and the peak of polarization released of poled PZT95/5 ferroelectric ceramics linearly decrease with increasing porosities, but the critical volumetric strain needed for phase transformation and the rate of polarization released are independent on the porosities.
2016 Vol. 37 (1): 50-58 [
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238
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59
The p-Version Finite Element Method for Modeling Weak Discontinuties Problems
There exist many weak discontinuity problems such as inclusion problems in the practical engineering computations. For the commonly used finite element (FEM) methods, mesh refinement or the increase of element order throughout the domain is usually used in order to ensure that each point on the interface can satisfy the given high degree of accuracy. But this will lead to rapid growth of the computer’s physical memory and the CPU time. The p-version adaptive FEM method is an efficient numerical method which can greatly improve the accuracy of calculation through adaptively increasing the order of elements used in the FEM analysis. In this paper, we have designed the corresponding p-version adaptive FEM method for modeling the weak discontinuity problems and emphatically discussed the influence of different error control standards on the computational results of each point on the interface. Moreover, we have made the numerical computation and simulation for some typical weak discontinuity problems. The numerical results are shown that the p-version adaptive FEM method is very efficient for the solution of the weak discontinuity problems, and the efficiency can be greatly improved by obtaining the reliable numerical results with fewer elements.
2016 Vol. 37 (1): 59-73 [
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348
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74
Experimental Research on Damping Behavior of Rock Subjected to Cyclic Loading
In order to discuss damping behaviors of rock under the stepped axial cyclic loading, WDT–1500 material testing machine is used to carry out sandstone, conglomerate and glutenite cycle loading tests in different stress levels and different stress amplitudes. The response properties of dynamic shear modulus and damping parameters about stress amplitude, strain amplitude and stress level under cyclic loading are realized. Also, the comparative analysis is made of damping behaviors under different loading conditions, whereby revealing that the dynamic shear modulus and damping parameters have their their varying laws with stress levels, stress amplitudes and moisture. Hyperbolic model is capable of describing the stress-strain relationship of rock under stepped axial cyclic loading. The interrelation of rock between dynamic shear modulus and strain and stress amplitude are obtained under stepped axial cyclic loading. A model of interrelation between dynamic shear modulus and damping ratio is proposed for rock in different stress levels and different stress amplitudes. The results show that the model is capable of describing the damping behavior of rock under stepped axial cyclic loading.
2016 Vol. 37 (1): 74-82 [
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246
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83
Frictionless Contact Problem of Dodecagonal System in Two-dimensional Quasicrystals
Frictionless contact problem of dodecagonal system in two-dimensional quasicrystals is researched by using integral transform method. By introducing displacement functions, the complicated partial differential equations of the plane elastic problems of dodecagonal system in two-dimensional quasicrystals are turned into two independent biharmonic equations. A contact problem with action of a rigid flat die in the dodecagonal system in two-dimensional quasicrystalline material was solved by using Fourier analysis and dual integral equations theory. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has -1/2order singularity in the edge of the contact zone, which provide the important mechanics parameter for contact deformation of quasicrystalline material.
2016 Vol. 37 (1): 83-89 [
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263
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90
The Anti-control of the Hopf Bifurcation of the Cable-stayed Beam
In recent year, there has been increasing interest in bifurcation control. Anti-control of bifurcation, as opposed to the bifurcation control, which refers to design a controller to reduce some existing bifurcation dynamics of a given nonlinear system, means to create a needed bifurcation at a needed location with preferred properties by appropriate control. In this paper, we investigate the anti-control of Hopf bifurcations. The washout-filter-aided controller has great application value in the application. In this study, we want to introduce a Hopf bifurcation at an designed stable equilibrium point. Following, a washout-filter-aided controller is employed together to deal with the problem. At last, according to the Poincare map and expansion method of power series, we can prove the advantage of using washout-filter-aided controller to obtain a certain Hopf bifurcation at the needed location. By defining a mapping, we can make the system to increase to (2+1)-dimensional system. In this case, the Poincare section can be chosen suitably. Following, the numbers of the fixed points can be determined by using the second derivative of the function. In addition, the fixed point can be solved by using the Poincare map. There are some conclusions can be obtained. In order to unchange the location of the equilibrium points, we can modify the parameters of the feedback controller. Then, by using washout-filter-aided dynamic feedback controller, a Hopf bifurcation is created with needed location and preferable properties. According to the calculation of the Poincare map, there is one fixed point of the system at most. Moreover, the equilibrium is the same one at which the system is designed to operate with the use of washout-filter-aided dynamic feedback controller. In addition, the period solution near the bifurcation point can be obtained with Poincare map. According to the proof of the Poincare map in theory, a Hopf bifurcation can be created at a needed location with preferred properties by the dynamic feedback control indeed. In the future, a greater action may be induced in more applications by the work on anti-control of bifurcations.
2016 Vol. 37 (1): 90-94 [
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213
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