Interface effects on elastic behavior of an edge dislocation in a core–shell nanowire embedded to an infinite matrix

The elastic behavior of an edge dislocation located inside the core of a core–shell nanowire which is embedded in an infinite matrix is studied within the surface/interface elasticity theory. The corresponding boundary value problem is solved exactly by using complex potential functions. An important parameter so-called interface characteristic parameter which has the dimension of length and is a combination of the interface moduli enters the formulations. The stress field of the dislocation, image force acting on the dislocation, and the dislocation strain energy is calculated by considering the interface effect. The introduced characteristic parameter allows the examination of the core–shell size on the image forces acting on the dislocation. The repelling and attracting effects of the interface parameter on the image force are discussed. The equilibrium position of the dislocation is also studied. The dislocation strain energy in the interface elasticity framework is only slightly different from that of traditional elasticity when the dislocation is placed in the central region of the core and reaches its maximum value when it is located near the core–shell interface.     

Interaction between a dislocation and a core–shell nanowire with interface effects

The problem of a screw dislocation interacting with a core–shell nanowire (coated nanowire) containing interface effects (interface stresses) is first investigated. The interaction energy and the interaction force are calculated. The interaction force and the equilibrium position of the dislocation are examined for variable parameters (interface stress and material mismatch). The influence of the core–shell nanowire and the interface stresses on the interaction between two screw dislocations is also considered. The results show that the impact of the interface stresses on the motion and the equilibrium position of the dislocation near the core–shell nanowire is very significant when the radius of the nanowire is reduced to nanometer scale.     

Mechanisms of morphological evolution on faceted core–shell nanowire surfaces

Core-shell nanowires with radial heterostructures hold great promise in photonic and electronic applications and controlling the formation of these heterostructures in the core-shell configuration remains a challenge. Recently, GaAs nanowires have been used as substrates to create AlGaAs shells. The deposition of the AlGaAs layer leads to the spontaneous formation of Al-rich stripes along certain crystallographic directions and quantum dots/wires near the apexes of the shell. A general two-dimensional model has been developed for the motion of the faceted solid-vapor interfaces for pure materials that accounts for capillarity and deposition. With this model, the growth processes and morphological evolution of shells of nanowires around hexagonal cores (six small facets {112} in the corners of six equivalent facets {110}) are investigated in detail both analytically and numerically. It is found that deposition can yield facets that are not present on the Wulff shape. These small facets can have slowly time-varying sizes that can lead to stripe structures and quantum dots/wires depending on the balances between diffusion and deposition. The effects of deposition rates and polarity (or asymmetry) on planes {112} on the development of the configurations of nanowires are discussed. The numerical results are compared with experimental results giving almost quantitative agreement, despite the fact that only pure materials are treated herein whereas the experiments deal with alloys.     

A consistent equilibrium in a cross-section of an elastic–plastic beam

A phenomenon of inequality of equilibrium and constitutive internal forces in a cross-section of elastic–plastic beams is common to many finite element formulations. It is here discussed in a rate-independent, elastic–plastic beam context, and a possible treatment is presented. The starting point of our discussion is Reissners finite-strain beam theory, and its finite element implementation. The questions of the consistency of interpolations for displacements and rotations, and the related locking phenomena are fully avoided by considering the rotation function of the centroid axis of a beam as the only unknown function of the problem. Approximate equilibrium equations are derived by the use of the distribution theory in conjunction with the collocation method. The novelty of our formulation is an inclusion of a balance function that measures the error between the equilibrium and constitutive bending moments in a cross-section. An advantage of the present approach is that the locations, where the balance of equilibrium and constitutive moments should be satisfied, can be prescribed in advance. In order to minimize the error, explicit analytical expressions are used for the constitutive forces; for a rectangular cross-section and bilinear constitutive law, they are given in Appendix A. The comparison between the results of the two finite element formulations, the one using consistent, and the other inconsistent equilibrium in a cross-section, is shown for a cantilever beam subjected to a point load. The problem of high curvature gradients in a plastified region is also discussed and solved by using an adapted collocation method, in which the coordinate system is transformed such to follow high gradients of curvature.     

Effect of strain hardening in elastic–plastic transition behavior in a hemisphere in contact with a rigid flat

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic–plastic material on the lines of the Kogut–Etsion Model (KE Model) and the Jackson–Green Model (JG Model). The present work extends the previous KE and JG works, accounting for the effect of realistic material behavior in terms of the varying yield strengths and the isotropic strain hardening behavior. The predicted results show that the transition behavior of the materials from the elastic–plastic to the fully plastic case is influenced by the yield strength and the tangent modulus (E_t) and such transition do not take place at specific values of interference ratios as suggested by the KE model. New empirical relations are proposed to determine the contact load and the contact area based on the analysis. Numerical results from the finite element modeling are also validated with an experimental ball on flat configuration approach.     

The effect of concrete slab–rockfill interface behavior on the earthquake performance of a CFR dam

Earthquake response of the concrete slab is mostly depended upon its conjunction with rockfill. This study aims to reveal the effect of concrete slab–rockfill interface behavior on the earthquake performance of a concrete-faced rockfill dam considering friction contact and welded contact. Friction contact is provided by using interface elements with five numbers of shear stiffness values. 2D finite element model of Torul concrete-faced rockfill dam is used for this purpose. Linear and materially non-linear time-history analyses considering dam–reservoir interaction are performed using ANSYS. Reservoir water is modeled using fluid finite elements by the Lagrangian approach. The Drucker–Prager model is preferred for concrete slab and rockfill in non-linear analyses. Horizontal component of 1992 Erzincan earthquake with peak ground acceleration of 0.515g is used in analyses. The maximum and minimum displacements and principal stresses are shown by the height of the concrete slab and earthquake performance of the dam is investigated considering different joint conditions for empty and full reservoir cases. In addition, potential damage situations of concrete slab are evaluated.     

On axisymmetric/diamond-like mode transitions in axially compressed core–shell cylinders

Recent interests in curvature- and stress-induced pattern formation and pattern selection motivate the present study. Surface morphological wrinkling of a cylindrical shell supported by a soft core subjected to axial compression is investigated based on a nonlinear 3D finite element model. The post-buckling behavior of core–shell cylinders beyond the first bifurcation often leads to complicated responses with surface mode transitions. The proposed finite element framework allows predicting and tracing these bifurcation portraits from a quantitative standpoint. The occurrence and evolution of 3D instability modes including sinusoidally deformed axisymmetric patterns and non-axisymmetric diamond-like modes will be highlighted according to critical dimensionless parameters. Besides, the phase diagram obtained from dimensional analyses and numerical results could be used to guide the design of core–shell cylindrical systems to achieve the desired instability patterns.     

Simulation of an optically induced asymmetric deformation of a liquid–liquid interface

Deformations of liquid interfaces by the optical radiation pressure of a focused laser wave were generally expected to display similar behavior, whatever the direction of propagation of the incident beam. Recent experiments showed that the invariance of interface deformations with respect to the direction of propagation of the incident wave is broken at high laser intensities. In the case of a beam propagating from the liquid of smaller refractive index to that of larger one, the interface remains stable, forming a nipple-like shape, while for the opposite direction of propagation, an instability occurs, leading to a long needle-like deformation emitting micro-droplets. While an analytical model successfully predicts the equilibrium shape of weakly deformed interface, very few work has been accomplished in the regime of large interface deformations. In this work, we use the Boundary Integral Element Method (BIEM) to compute the evolution of the shape of a fluid–fluid interface under the effect of a continuous laser wave, and we compare our numerical simulations to experimental data in the regime of large deformations for both upward and downward beam propagation. We confirm the invariance breakdown observed experimentally and find good agreement between predicted and experimental interface hump heights below the instability threshold.     

β-Cyclodextrin carbon-based nanoparticles with a core–shell–shell structure for efficient adsorption of crystal violet and bisphenol A

Textile wastewater contains highly toxic, nondegradable, carcinogenic organic pollutants, causing severe damage to the ecological environment. In this work, β-cyclodextrin carbon-sphere-based nanocomposite (CS/SiO₂@β-CD) with a core–shell–shell configuration was prepared by hydrothermal synthesis and subsequent sedimentation-azeotropic distillation with SiO₂ as intermediate layer for the removal of crystal violet (CV) and bisphenol A (BPA). The chemical structure and morphology of the CS/SiO₂@β-CD were characterized by FT-IR, SEM and TEM. The effects of contact time, pH, temperature and initial concentration of the absorbates on the adsorption property were explored. The CS/SiO₂@β-CD showed excellent adsorption capacity on CV and BPA, and the maximum adsorption capacity was 87.873 mg g^–1 and 165.095 mg g^–1, respectively. Their adsorption process was in line with the pseudo-second-order and pseudo-first-order kinetic models, respectively. The adsorption thermodynamics could be better fitted by Langmuir model than by Freundlich model. The calculated thermodynamic parameters (–ΔG₀, ΔS₀ and ΔH₀) illustrated the adsorption of CV was endothermic, in contrast, the adsorption of BPA was exothermic process. Furthermore, the CS/SiO₂@β-CD showed excellent recovery performance, making it a potential adsorbent for the practical treatment of textile wastewater.     

Nonlinear elastic wave propagation in a phononic material with periodic solid–solid contact interface

Phononic materials enable enhanced dynamic properties, and offer the ability to engineer the material response. In this work we study the wave propagation in such a structure when introduced with nonlinearity. Our system is comprised of pre-compressed material with periodic solid–solid contacts, which exhibit a quadratic nonlinearity for small displacements. We suggest a new approach to modeling this system, where we discretize the unit cell in order to derive an approximate analytical solution using a perturbation method, which we are then able to easily validate numerically. With these methods, we study the band structure in the system and the second harmonic generation originating from the nonlinearity. We qualitatively analyze the second harmonic response of the system in terms of the single-crack response with linear band structure considerations. Significant band structure manipulation by changing system parameters is demonstrated, including possible in-situ tuning. The system also exhibits effective frequency doubling, i.e. the transmitted wave is primarily comprised of the second harmonic wave, for a certain range of frequencies. We demonstrate very high robustness to disorder in the system, in terms of band structure and second harmonic generation. These results have possible applications as frequency-converting devices, tunable engineered materials, and in non-destructive evaluation.     

Grain–boundary interactions and orientation effects on crack behavior in polycrystalline aggregates

A dislocation-density grain–boundary interaction scheme has been developed to account for the interrelated dislocation-density interactions of emission, absorption and transmission in GB regions. The GB scheme is based on slip-system compatibility, local resolved shear stresses, and immobile and mobile dislocation-density accumulation at critical GB locations. To accurately represent dislocation-density evolution, a conservation law for dislocation-densities is used to balance dislocation-density absorption, transmission and emission from the GB. The behavior of f.c.c. polycrystalline copper, with different random low and high angle GBs, are investigated for different crack lengths. For aggregates with random low angle GBs, dislocation-density transmission dominates at the GBs, which can indicate that the low angle GB will not significantly change crack growth directions. For aggregates with random high angle GBs, extensive dislocation-density absorption and pile-ups occur. The high stresses associated with this behavior, along the GBs, can result in intergranular crack growth due to potential crack nucleation sites in the GB.     

Coriolis effects on the stability of pulsed flows in a Taylor–Couette geometry

Results steming from the linear stability of time-periodic flows in a Taylor–Couette geometry with cylinders oscillating in phase or out-of-phase are presented. Our analysis takes into account the gap size effects and investigates the influence of a superimposed mean angular rotation of the whole system.In case of no mean rotation, the finite gap geometry is found to affect the shape of the stability diagrams (critical Taylor number versus the frequency parameter) which consist of two distinct branches as opposed to being continuous in the narrow gap approximation. In particular, in the out-of-phase configuration a new branch for low frequencies was found, thus enabling better agreement with available experimental results.When cylinders are co-rotating and subject to rotation effects, our calculations provide the evolution of the critical Taylor number versus the rotation number for two values of the frequency. The stability curves are found to be in qualitative agreement with available experimental data revealing a maximum of instability for a rotation number of about 0.3.In the high rotation regime, enhancement of the critical Taylor number is investigated through an asymptotic analysis and the value of the rotation number at which restabilization occurs is found to depend on the frequency parameter.A restabilization of the flow also occurs when the rotation number and the gap size are of the same order, a phenomenon already pointed out in the case of steady flows and attributed to the near cancellation of Coriolis and centrifugal effects. Our investigation proves that the same mechanism still holds for time-periodic flows.     

Influence of conicity on the stress–strain state of a flexible orthotropic conical shell in a nonstationary magnetic field

A problem of magnetoelasticity for a flexible conical shell in a nonstationary magnetic field is solved. The effect of conicity on the stress–strain state of the shell is analyzed     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.     

Endoscopic effects on the peristaltic flow of an Eyring–Powell fluid

This study investigates the peristaltic flow of Eyring–Powell fluid in an endoscope. The governing equations for Eyring–Powell are modeled in cylindrical coordinates under the assumption of long wavelength and low Reynolds number approximation. The resulting nonlinear differential equations are solved analytically and numerically by employing perturbation method and shooting technique. Numerical integration have been done for pressure rise and frictional forces. Comparative study have been made for both the solutions to see the validity of the results. The effects of various emerging parameters are investigated for five different peristaltic waves. (Basically peristaltic phenomena is a natural phenomena so it is not necessary that peristaltic wave be always a sinusoidal wave it could be multisinusoidal, triangular, trapezoidal and square waves for example heartbeats.) Streamlines have been plotted at the end of the article.     

A chemo-mechanical model coupled with thermal effect on the hollow core–shell electrodes in lithium-ion batteries

Electrode is a key component to remain durability and safety of lithium-ion(Li-ion) batteries. Li-ion insertion/removal and thermal expansion mismatch may induce high stress in electrode during charging and discharging processes. In this paper, we present a continuum model based on COMSOL Multiphysics software, which involves thermal, chemical and mechanical behaviors of electrodes. The results show that,because of diffusion-induced stress and thermal mismatch, the electrode geometry plays an important role in diffusion kinetics of Li-ions. A higher local compressive stress results in a lower Li-ion concentration and thus a lower capacity when a particle is embedded another, which is in agreement with experimental observations.