Effect of dentin tubules on the mechanical properties of dentin - part III: Numerical, analysis

Imitating a real tooth and the periodontal supporting tissues, we have established a 2D finite element model and carried out a numerical analysis based on the inhomogeneous and anisotropic (IA) stress-strain relation and strength model of dentin proposed in the preceding Parts I and II, and the conventional homogeneous and isotropic (III) model, respectively. Quite a few cases of loadings for a non-defected and a defected tooth are considered. The numerical results show that the stress level predicted by the IA model is remarkably higher than that by the III model, revealing that the effect of the dentin tubules should be taken into a serious consideration from the viewpoint of biomechanics.

Dynamic analysis of arrest of buckle propagation on a beam on a nonlinear elastic foundation by FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.

Micromechanics analysis of particulate-reinforced composites and their failure mechanisms

Stress fields and failure mechanisms have been investigated in composites with particles either surface treated or untreated under uniaxial tension. Previous experimental observation of failure mechanisms in a composite with untreated particles showed that tensile cracks occurred mostly at the polar region of the particle and grew into interfacial debonding. In a composite with surface-treated particles, however, shear yielding and shear cracking proceeded along the interphase-matrix interface at the polar area of the matrix and thus may improve the mechanical behaviour of the material. The finite element calculations showed that octahedral shear stress at the polar and longitudinal areas of the particle treated by coupling agents is much larger than that of materials with untreated particles, and the shear stress distribution around the interface is sensitive to the interphase property. The results suggest that a th ree-phase model can describe the composites with surface-treated fillers.

An analysis of the effects of symmetrical tilt grain boundaries on the plastic deformation

A numerical investigation on the simple polycrystals containing three symmetrical tilt grain boundaries (GBs) is carried out within the framework of crystal plasticity which precisely considers the finite deformation and finite lattice rotation as well as elastic anisotropy. The calculated results show that the slip geometry and the redistribution of stresses arising from the anisotropy and boundary constraint play an important role in the plastic deformation in the simple polycrystals. The stress level along GB is sensitive to the load level and misorientation, and the stresses along QB are distributed nonuniformly. The GB may exhibit a softening or strengthening feature, which depends on the misorientation angle. The localized deformation bands usually develop accompanying the GB plastic deformation, the impingement of the localized band on the GB may result in another localized deformation band. The yield stresses with different misorientation angles are favorably compared with the experimental results.

Higher-order analysis of crack tip fields in elastic power-law hardening materials

A HIGHER-ORDER asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode 1. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K1, K2 and K5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K1, K2 and K4. It is found that appropriate choices of K2 and K4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.

An asymptotic analysis for one dimensional stress wave propagation in damaged viscoelastic media

A regular perturbation technique is suggested to deal with the problem of one dimensional stress wave propagation in viscoelastic media with damage. Based upon the first order asymptotic solution obtained, the characteristics of wave attenuation are studied. In fact, there exist three different time-dependent phenomena featuring the dynamic response of the materials, the first expressing the characteristics of wave propagation, the second indicating the innate effect of visco-elastic matrix and the third coming from the time dependent damage. The comparision of first order asymptotic solution with the numerical results calculated by a finite difference procedure shows that the perturbation expansion technique may offer a useful approach to the problem concerned.

Some theorems in asymptotic analysis

Basing ourselves on the analysis of magnitude of order, we strictly prove fundamental lemmas for asymptotic integral, including the cases of infinite region. Then a general formula for asymptotic expansion of integrals is given. Finally, we derive a sufficient condition for an ordinary differential equation to possess a solution of the Frobenius series type at finite irregular singularities or branching points.

A surface energy model and application to mechanical behavior analysis of single crystals at sub-micron scale

Size effects of mechanical behaviors of materials are referred to the variation of the mechanical behavior due to the sample sizes changing from macroscale to micro-/nanoscales. At the micro-/nanoscale, since sample has a relatively high specific surface area (SSA) (ratio of surface area to volume), the surface although it is often neglected at the macroscale, becomes prominent in governing the energy effect, although it is often neglected at the macroscale, becomes prominent in governing the mechanical behavior. In the present research, a continuum model considering the surface energy effect is developed through introducing the surface energy to total potential energy. Simultaneously, a corresponding finite element method is developed. The model is used to analyze the axial equilibrium strain problem for a Cu nanowire at the external loading-free state. As another application of the model, from dimensional analysis, the size effects of uniform compression tests on the microscale cylinder specimens for Ni and Au single crystals are analyzed and compared with experiments in literatures. (C) 2009 Elsevier B.V. All rights reserved.

FDTD analysis of Talbot effect of a high density grating

Talbot effect of a grating with different flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging would also be distorted. Furthermore, we can evaluate high density gratings by detecting the near-field distribution.

Rigorous transmittance analysis of a sub-wavelength Sb thin film lens

We quantitatively analysed the factors contributing to the optical transmission enhancement of a sub-wavelength Sb thin film lens, using the finite-difference time-domain (FDTD) method. The results show that the transmission enhancement of the dielectric with a Gaussian distributed refractive index loaded in a sub-wavelength circular hole is not only due to the high refractive index dielectric, but also due to the specific distributions of refractive index. It is the first study about the effects of the refractive index distribution on the transmission of a sub-wavelength aperture. This kind of lens has practical applications in the very small aperture lasers and for near-field optical storage and lithography.

Numerical and experimental analysis on green laser crystallization of amorphous silicon thin films

The effect of laser fluence on the crystallization of amorphous silicon irradiated by a frequency-doubled Nd:YAG laser is studied both theoretically and experimentally. An effective numerical model is set up to predict the melting threshold and the optimized laser fluence for the crystallization of 200-nm-thick amorphous silicon. The variation of the temperature distribution with time and the melt depth is analyzed. Besides the model, the Raman spectra of thin films treated with different fluences are measured to confirm the phase transition and to determine the optimized fluence. The calculating results accord well with those obtained from the experimental data in this research. (C) 2008 Elsevier Ltd. All rights reserved.

Analysis of coupled microcircular resonators coupled to a bus waveguide with high output efficiency

Coupled microcircular resonators tangentially coupled to a bus waveguide, which is between the resonators, are numerically investigated by the finite-difference time-domain technique. For symmetrically coupled microcircular resonators with refractive index of 3.2, radius of 2 mu m, and width of the bus waveguide of 0.4 mu m, a mode Q factor of the order of 105 is obtained for a mode at the frequency of 243 THz. An output coupling efficiency of as high as 0.99 is calculated for a mode with a Q factor ranging from 10(3) to 10(4). The mode Q factor is 2 orders larger than that of the modes confined in a single circular resonator tangentially coupled to the same bus waveguide. Furthermore, the high Q traveling modes in the coupled microcircular resonators are suitable for optical single processing.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 mu m and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 mu m. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 mu m. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor. (C) 2009 Optical Society of America

Mode Analysis for Equilateral-Triangle-Resonator Microlasers with Metal Confinement Layers

Mode characteristics are analyzed for electrically injected equilateral-triangle-resonator (ETR) semiconductor microlasers, which are laterally confined by insulating barrier SiO2 and electrode metals Ti-Au. For the ETR without metal layers, the totally confined mode field patterns are derived based on the reflection phase shifts, and the Q-factors are calculated from the far-field emission of the analytical near field distribution, which are agreement very well with the numerical results of the finite-difference time-domain (FDTD) simulation. The polarization dependence reflections for light rays incident on semiconductor-SiO2 -Ti-Au multi-layer structures are accounted in considering the confinement of TE and TM modes in the ETR with the metal layers. The reflectivity will greatly reduce with a Ti layer between SiO2 and Au for light rays with incident angle less than 30 especially for the TE mode, even the thickness of the Ti layer is only 10 nm. If the ETR is laterally confined by SiO2-Au layers without the Ti layer, the Fabry-Perot type modes with an incident angle of zero on one side of the ETR can also have high Q-factor. The FDTD simulation for the ETR confined by metal layers verifies the above analysis based on multi-layer reflections. The output spectra with mode intervals of whispering-gallery modes and Fabry-Perot type modes are observed from different ETR lasers with side length of 10 m, respectively.

Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries

The influence of imperfect boundaries on the mode quality factor is investigated for equilateral-triangle-resonator (ETR) semiconductor microlasers by the finite difference time domain technique and the Pade approximation with Baker's algorithm. For 2-D ETR with a refractive index of 3.2 and side length of 5 mum, the confined modes can still have a quality factor of about 1000 as small triangles with side length of 1 mum are cut from the vertices of the ETR. For a deformed 5 mum ETR with round vertices and curve sides, the simulated mode quality factors are comparable to the measured results.