A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading

In this paper, we attempted to construct a constitutive model to deal with the phenomenon of cavitation and cavity growth in a rubber-like material subjected to an arbitrary tri-axial loading. To this end, we considered a spherical elementary representative volume in a general Rivlin's incompressible material containing a central spherical cavity. The kinematics proposed by [Hou, H.S., Abeyaratne, R., 1992. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571-722] was adopted in order to construct an approximate but optimal field. In order to establish a suitable constitutive law for this class of materials, we utilized the homogenisation technique that permits us to calculate the average strain energy density of the volume. The cavity growth was considered through a physically realistic failure criterion. Combination of the constitutive law and the failure criterion enables us to describe correctly the global behaviour and the damage evolution of the material under tri-axial loading. It was shown that the present models can efficiently reproduce different stress states, varying from uniaxial to tri-axial tensions, observed in experimentations. Comparison between predicted results and experimental data proves that the proposed model is accurate and physically reasonable. Another advantage is that the proposed model does not need special identification work, the initial Rivlin's law for the corresponding incompressible material is sufficient to form the new law for the compressible material resulted from cavitation procedure. (C) 2007 Elsevier Ltd. All rights reserved.

Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model

The beam lattice-type models, such as the Euler-Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr-Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.

A geometrical model of GaN morphology in initial growth stage

Based on morphology observed by atomic force microscopy, a geometrical model was proposed in order to explain the statistical results obtained from morphology observation on GaN in initial growth stage. Four parameters were introduced to describe the morphology characteristics in this model. Least-square fitting of height distribution was performed. The height distribution derived from the model agreed well with that obtained from experimental records. It was also found that the model should be further advanced to understand the growth of GaN in initial growth stage. (C) 2002 Elsevier Science BY. All rights reserved.

A surface kinetics model for the growth of Si1-xGex by UHV/CVD using SiH4/CeH4

The surface reaction mechanism of Si1-xGex/Si growth using SiH4 and GeH4 in UHV/CVD system was studied. The saturated adsorption and desorption of SiH4 from Si(1 0 0) surface was investigated with the help of TPD and RHEED, and it was found that all the 4 hydrogen atoms of one SiH4 molecule were adsorbed to the Si surface, which meant that the dissociated adsorption ratio was proportional to 4 power of surface vacancies. The analysis of the reaction of GeH4 was also done. A new surface reaction kinetic model on Si1-xGex/Si epitaxial growth under UHV conditions by SiH4/GeH4 was proposed based on these studies. The predictions of the model were verified by the experimental results. (C) 2000 Elsevier Science B.V. All rights reserved.

Dynamics of nonlinear error growth and season-dependent predictability of El Nino events in the Zebiak-Cane model

With the intermediate-complexity Zebiak-Cane model, we investigate the 'spring predictability barrier' (SPB) problem for El Nino events by tracing the evolution of conditional nonlinear optimal perturbation (CNOP), where CNOP is superimposed on the El Nino events and acts as the initial error with the biggest negative effect on the El Nino prediction. We show that the evolution of CNOP-type errors has obvious seasonal dependence and yields a significant SPB, with the most severe occurring in predictions made before the boreal spring in the growth phase of El Nino. The CNOP-type errors can be classified into two types: one possessing a sea-surface-temperature anomaly pattern with negative anomalies in the equatorial central-western Pacific, positive anomalies in the equatorial eastern Pacific, and a thermocline depth anomaly pattern with positive anomalies along the Equator, and another with patterns almost opposite to those of the former type. In predictions through the spring in the growth phase of El Nino, the initial error with the worst effect on the prediction tends to be the latter type of CNOP error, whereas in predictions through the spring in the decaying phase, the initial error with the biggest negative effect on the prediction is inclined to be the former type of CNOP error. Although the linear singular vector (LSV)-type errors also have patterns similar to the CNOP-type errors, they cover a more localized area than the CNOP-type errors and cause a much smaller prediction error, yielding a less significant SPB. Random errors in the initial conditions are also superimposed on El Nino events to investigate the SPB. We find that, whenever the predictions start, the random errors neither exhibit an obvious season-dependent evolution nor yield a large prediction error, and thus may not be responsible for the SPB phenomenon for El Nino events. These results suggest that the occurrence of the SPB is closely related to particular initial error patterns. The two kinds of CNOP-type error are most likely to cause a significant SPB. They have opposite signs and, consequently, opposite growth behaviours, a result which may demonstrate two dynamical mechanisms of error growth related to SPB: in one case, the errors grow in a manner similar to El Nino; in the other, the errors develop with a tendency opposite to El Nino. The two types of CNOP error may be most likely to provide the information regarding the 'sensitive area' of El Nino-Southern Oscillation (ENSO) predictions. If these types of initial error exist in realistic ENSO predictions and if a target method or a data assimilation approach can filter them, the ENSO forecast skill may be improved. Copyright (C) 2009 Royal Meteorological Society

Influence of Local Magnetic Fields on P-Doped Si Floating Zone Melting Crystal Growth in Microgravity

A two-dimensional axisymmetric numerical model is presented to study the influence of local magnetic fields on P-doped Si floating zone melting crystal growth in microgravity. The model is developed based on the finite difference method in a boundary-fitted curvilinear coordinate system. Extensive numerical simulations are carried out, and parameters studied include the curved growth interface shape and the magnetic field configurations. Computed results show that the local magnetic field is more effective in reducing the impurity concentration nonuniformity at the growth interface in comparison with the longitudinal magnetic field. Moreover, the curved growth interface causes more serious impurity concentration nonuniformity at the growth interface than the case with a planar growth interface.

Optical Diagnostic and Modeling Solution Growth Process of Sodium Chlorate Crystals

Both a real time optical interferometric experiment and a numerical simulation of two-dimension non-steady state model were employed to study the growth process of aqueous sodium chlorate crystals. The parameters such as solution concentration distribution, crystal dimensions, growth rate and velocity field were obtained by both experiment and numerical simulation. The influence of earth gravity during crystal growth process was analyzed. A reasonable theory model corresponding to the present experiment is advanced. The thickness of concentration boundary layer was investigated especially. The results from the experiment and numerical simulation match well.

A Numerical Model of Rapid Solidification Processing of Ni-Al Alloy in Planar Flow Casting

A numerical model has been developed for simulating the rapid solidification processing (RSP) of Ni-Al alloy in order to predict the resultant phase composition semi-quantitatively during RSP. The present model couples the initial nucleation temperature evaluating method based on the time dependent nucleation theory, and solidified volume fraction calculation model based on the kinetics model of dendrite growth in undercooled melt. This model has been applied to predict the cooling curve and the volume fraction of solidified phases of Ni-Al alloy in planar flow casting. The numerical results agree with the experimental results semi-quantitatively.

Electromechanical Model of RF MEMS Switches

With the recent rapid growth of Radio Frequency Micro-Electro-Mechanical Systems (RF MEMS) switches, there has developed an emergent requirement for more accurate theoretical models to predict their electromechanical behaviors. Many parameters exist in the analysis of the behavior of the switch, and it is inconvenient for further study. In this paper, an improved model is introduced, considering simultaneously axial stress, residual stress, and fringing-field effect of the fixed-fixed bridge structure. To avoid any unnecessary repetitive model tests and numerical simulation for RF MEMS switches, some dimensionless numbers are derived by making governing equation dimensionless. The electromechanical behavior of the fixed-fixed bridge structure of RF MEMS switches is totally determined by these dimensionless numbers.

The Heterogeneous Growth of P(3MeTh)--An Ellipsometric Study

Successive thicker P(3MeTh) layers are analysed by ex situ conventional and imaging ellipsometry. Thin films display a smooth surface, are compact and homogeneous while for a growth charge above 20 mC cm(-2) the polymer structure modifies to a still uniform but less dense layer. A two-layer model is used and a mathematical procedure is developed to obtain, simultaneously, from the experimental ellipsometric parameters, Delta and Psi, the thickness and the complex refractive index of P(3MeTh) films grown up to 80 mC cm(-2). Thicker polymer layers are disordered and present a high degree of surface roughness. 

Modeling of Ammonothermal Growth of Nitrides

Bulk single crystals of GaN and AlN can be grown from supercritical fluids using the ammonothermal method, which utilizes ammonia as fluid rather than water as in the hydrothermal process. In this process, a mineralizer such as amide, imide or nitride is used to attack a bulk nitride feedstock at temperatures from 200°C to 500°C and pressures from 1 to 4 kbar. Ammonothermal systems have been modeled here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the fluid flow is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. The effects of particle size on flow pattern and temperature distribution in an autoclave are analyzed.

The effect of straining mode on void growth

Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality: loading,while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results.

Study of Growth Mechanism of Lysozyme Crystal by Batch Crystallization Method

The lysozyme crystals were made by batch crystallization method and the distribution of aggregate in solution were measured by dynamic light scattering. The results showed that the dimension of aggregate increased with the increase of the concentration of lysozyme and NaCl, lysozyme molecules aggregated gradually in solution and finally arrived at balance each other. The higher the concentrations of lysozyme and NaCl were, the faster the growth rate of (I 10) face was. The growth rates of lysozyme crystal were obtained by a Zeiss microscope, and the effective surface energy (a) of growing steps were calculated about 4.01 X 10(-8) J.cm(-2) according to the model of multiple two-dimensional nucleation mechanism.