The behaviour of a dislocation pileup with a finite-strength source is investigated in the presence of various stress gradients within a continuum model where a free-dislocation region exists around the source. Expressions for dislocation density and stress field within the pileup are derived for the situation where there are first and second spatial gradients in applied stress. For a pileup configuration under an applied stress, yielding occurs when the force acting on the leading dislocations at the pileup tips reaches the obstacle strength, and at the same time, it is required that the source be at the threshold stress for dislocation production. A numerical methodology is presented to solve the underlying equations that represent the yielding conditions. The yield stress calculated for a pileup configuration is found to depend on stress gradients, obstacle spacing and source/obstacle strengths. It increases with increasing the first stress gradient, yet dependent on the second stress gradient. Furthermore, while the dependency of yield stress on the obstacle spacing intensifies with increasing the first stress gradient, it diminishes with an increase of second stress gradient. Therefore, the second stress gradient, as a newly introduced parameter, can provide a new physical insight into the size-dependent plasticity phenomena at small length scales. 相似文献
Understanding the factors that affect self-diffusion in isoreticular and multivariate (MTV) MOFs is key to their application in drug delivery, separations, and heterogeneous catalysis. Here, we measure the apparent self-diffusion of solvents saturated within the pores of large single crystals of MOF-5, IRMOF-3 (amino-functionalized MOF-5), and 17 MTV-MOF-5/IRMOF-3 materials at various mole fractions. We find that the apparent self-diffusion coefficient of N,N-dimethylformamide (DMF) may be tuned linearly between the diffusion coefficients of MOF-5 and IRMOF-3 as a function of the linker mole fraction. We compare a series of solvents at saturation in MOF-5 and IRMOF-3 to elucidate the mechanism by which the linker amino groups tune molecular diffusion. The ratio of the self-diffusion coefficients for solvents in MOF-5 to those in IRMOF-3 is similar across all solvents tested, regardless of solvent polarity. We conclude that average pore aperture, not solvent-linker chemical interactions, is the primary factor responsible for the different diffusion dynamics upon introduction of an amino group to the linker. 相似文献
The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.
In this study, the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects (SEs). The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers. Utilizing the modified Halpin-Tsai model, the material parameters of composite layers are obtained. The displacement field is determined by the sinusoidal shear deformation theory (SSDT). The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs. Subsequently, the nonlocal strain gradient theory (NSGT) is used to obtain the equations of motion. Next, the effects of scale parameters, graphene distribution, orthotropic viscoelastic foundation, and SEs on the propagation behavior are numerically examined. The results reveal that the wave frequency is a periodic function of the orthotropic angle. Furthermore, the wave frequency increases with the increase in the SEs.
Applied Mathematics and Mechanics - The stress and the strain should be defined as statistical variables averaged over the representative volume elements for any real continuum system. It is shown... 相似文献
As an innovative thermal energy technology, the spray-type packed bed has advantages of high efficiency and low cost. A liquid distributor is the key component for the spray-type packed bed for scattering heat-transfer liquid drops evenly. In this study, the distribution performance and pressure drop of the perforated plate distributors of different orifice diameters were studied experimentally. The experimental results indicate that orifice diameter has a greater effect on the distribution performance compared to flow rate. With an increase in flow rate, the flow pattern through the distributor changes from the uncovered drop to the covered drop and then to the jet flow. The covered drop pattern shows the best performance with a good distribution and a small pressure drop simultaneously, which is the design and optimization principle of the distributor for a spray-type packed bed. 相似文献
The slant from horizontal size disparity is geometrically predictable. The apparent slant, however, is usually not equivalent
to the prediction as numerous visual factors affect it. The aim of this study is to examine whether the vertical angular subtense
of a stimulus with horizontal size disparity alters the magnitude of perceived slant for a given horizontal angular subtense.
The results indicate that a smaller angular subtense of display produces a smaller magnitude of slant perception. 相似文献
The duration of the hypercrosslinking reaction has been used to control the extent of small pores formation in polymer‐based monolithic stationary phases. Segments of five columns hypercrosslinked for 30–360 min were coupled via zero‐volume unions to prepare columns with segmented porosity gradients. The steepness of the porosity gradient affected column efficiency, mass transfer resistance, and separation of both small‐molecule alkylbenzenes and high‐molar‐mass polystyrene standards. In addition, the segmented column with the steepest porosity gradient was prepared as a single column with a continuous porosity gradient. The steepness of porosity gradient in this type column was tuned. Compared to a completely hypercrosslinked column, the column with the shallower gradient produced comparable size‐exclusion separation of polystyrene standards but allowed higher column permeability. The completely hypercrosslinked column and the column with porosity gradient were successfully coupled in online two‐dimensional liquid chromatography of polymers. 相似文献