Periodic Stress Field Research Articles

An FFT‐based Galerkin method for the effective permeability of porous material

AbstractA numerical scheme which is a combination of FFT and Galerkin methods is proposed for calculating the effective permeability of periodic porous material. First, a periodic stress field whose divergence is equal to the subtraction of body force from prescribed pressure gradient is introduced to reformulate the governing equations. Then, an auxiliary problem is established to replace the prescribed pressure gradient with the resulting initial prescribed stress. An FFT‐based Galerkin method of stress control type, the associated projection operator for zero divergence condition and the treatment of composite pixels/voxels are presented for solving the viscous flow in periodic porous material. Finally, numerical examples of viscous flows in 2D parallel fissured medium, 2D medium with regularly packed squares, 2D medium with regularly packed and rotated squares, 3D medium with regularly packed ellipsoids, and 3D medium with randomly packed ellipsoids are implemented. Numerical results calculated by FFT‐based Galerkin method agree well with analytical solutions and finite element results. The proposed FFT‐based Galerkin method is effective for predicting the macro permeability of porous material with complex meso structures.

Mixed boundary value problems in power-law functionally graded circular annulus

The present work proposes a semi-analytical technique for solution of mixed boundary value problem in functionally graded circular annulus wherein shear modulus varies radially in power-law form while Poisson’s ratio is constant. The technique relies on two main steps. In the first step, corresponding to terms in periodic Fourier series applied individually as traction along the annulus surface, stress and displacement field in the annulus is computed harnessing Airy stress functions approach. In the second step, leveraging the strain–displacement relations in polar co-ordinates, mixed boundary conditions are rendered in terms of displacement all along the annulus surface. Assuming the unknown traction along the annulus surface in terms of periodic Fourier series with finite terms, the modified displacement boundary condition, family of solution from the first step and orthogonality of sine and cosine functions is used to generate a system of simultaneous linear equations for the series coefficients. Knowing the coefficients of periodic Fourier series, stress and displacement field can be computed everywhere in the annulus. The first step is digitized in terms of MAPLE functions, exhaustively validated through traction distribution comprising of normal, shear traction on part of the boundary and pair of equal and diametrically opposite point load along the boundary. The second step is corroborated through a problem where the inner surface is subjected to a specified traction distribution and mixed boundary conditions exist along the outer surface in the form of complete constraint along a part and traction-free condition elsewhere.

Microstructure and Mechanical Properties of Zirconia (3Y-TZP)/Zr Composites Prepared by Wet Processing and Subsequent Spark Plasma Sintering

ZrO2 (3Y-TZP) matrix composites with 30 vol % Zr metallic particles were obtained by spark plasma sintering (SPS) using a colloidal processing method. The microstructure and mechanical properties of this novel ceramic–metal composite have been studied. The fracture toughness of composites is slightly higher than the values corresponding to monolithic zirconia. Scanning electron microscope (SEM) observations of the crack path show that the major contributions to toughening are the resulting crack blunting and branching that occurs at crack tips in the metallic particles before the onset of crack propagation. Plastic deformation of the metallic particles is strongly influenced by the constraint induced by the different phase arrangements. This system can be considered as a particulate composite with a periodic residual stress field, in which the metal phase is under strong compression due to the residual thermal stresses as a consequence of the coefficient of thermal expansion mismatch. Therefore, the plastic deformation of the metallic particles in this composite is likely to be reduced to a large extent.

Structural colour using organized microfibrillation in glassy polymer films

The formation of microscopic cavities and microfibrils at stress hotspots in polymers is typically undesirable and is a contributor to material failure. This type of stress crazing is accelerated by solvents that are typically weak enough not to dissolve the polymer substantially, but which permeate and plasticize the polymer to facilitate the cavity and microfibril formation process1-3. Here we show that microfibril and cavity formation in polymer films can be controlled and harnessed using standing-wave optics to design a periodic stress field within the film4. We can then develop the periodic stress field with a weak solvent to create alternating layers of cavity and microfibril-filled polymers, in a process that we call organized stress microfibrillation. These multi-layered porous structures show structural colour across the full visible spectrum, and the colour can be tuned by varying the temperature and solvent conditions under which the films are developed. By further use of standard lithographic and masking tools, the organized stress microfibrillation process becomes an inkless, large-scale colour printing process generating images at resolutions of up to 14,000 dots per inch on a number of flexible and transparent formats5,6.

Tunable surface configuration of skyrmion lattices in cubic helimagnets

In bulk helimagnets, the presence of magnetic skyrmion lattices is always accompanied by a periodic stress field due to the intrinsic magnetoelastic coupling. The release of this nontrivial stress field at the surface causes a periodic displacement field, which characterizes a novel particle-like property of skyrmion: its surface configuration. Here, we derive the analytical solution of this displacement field for semi-infinite cubic helimagnet with the skyrmion magnetization approximated by the triple-Q representation. For MnSi, we show that the skyrmion lattices have a bumpy surface configuration characterized by periodically arranged peaks with a characteristic height of about 10−13 m. The pattern of the peaks can be controlled by varying the strength of the applied magnetic field. Moreover, we prove that the surface configuration varies together with the motion and deformation of the skyrmion lattices. As a result, the surface configuration can be tuned by application of electric current, mechanical loads, as well as any other effective external fields for skyrmion lattices.

Periodic Mechanical Stress Induces Extracellular Matrix Expression and Migration of Rat Nucleus Pulposus Cells Through Src-GIT1-ERK1/2 Signaling Pathway

Background/Aims: Periodic mechanical stress has been shown to promote extracellular matrix (ECM) synthesis and cell migration of nucleus pulposus (NP) cells, however, the mechanisms need to be fully elucidated. The present study aimed to investigate the signal transduction pathway in the regulation of NP cells under periodic mechanical stress. Methods: Primary rat NP cells were isolated and seeded on glass slides, and then treated in our self-developed periodic stress field culture system. To further explore the mechanisms, data were analyzed by scratch-healing assay, quantitative reverse transcription polymerase chain reaction (RT-qPCR) analysis, western blotting, and co-immunoprecipitation assay. Results: Under periodic mechanical stress, the mRNA expression of ECM collagen 2A1 (Col2A1) and aggrecan, and migration of NP cells were significantly increased (P < 0.05 for each), associating with increases in the phosphorylation of Src, GIT1, and ERK1/2 (P < 0.05 for each). Pretreatment with the Src inhibitor PP2 reduced periodic mechanical stress-induced ECM synthesis and cell migration of NP cells (P < 0.05 for each), while the phosphorylation of GIT1 and ERK1/2 were inhibited. ECM synthesis, cell migration, and phosphorylation of ERK1/2 were inhibited after pretreatment with the small interfering RNA for GIT1 in NP cells under periodic mechanical stress (P < 0.05 for each), whereas the phosphorylation of Src was not affected. Pretreatment with the ERK1/2 inhibitor PD98059 reduced periodic mechanical stress-induced ECM synthesis and cell migration of NP cells (P < 0.05 for each). Co-immunoprecipitation assay showed that there was a direct interaction between Src and GIT1 and between GIT1 and ERK1/2. Conclusion: In conclusion, periodic mechanical stress induced ECM expression and migration of NP cells via Src-GIT1-ERK1/2 signaling pathway, playing an important role in regulation of NP cells.

Periodic mechanical stress activates EGFR-dependent Rac1 mitogenic signals in rat nucleus pulpous cells via ERK1/2

The mitogenic effects of periodic mechanical stress on nucleus pulpous cells have been studied extensively but the mechanisms whereby nucleus pulpous cells sense and respond to mechanical stimulation remain a matter of debate. We explored this question by performing cell culture experiments in our self-developed periodic stress field and perfusion culture system. Under periodic mechanical stress, rat nucleus pulpous cell proliferation was significantly increased (p < 0.05 for each) and was associated with increases in the phosphorylation and activation of EGFR, Rac1, and ERK1/2 (p < 0.05 for each). Pretreatment with the ERK1/2 selective inhibitor PD98059 reduced periodic mechanical stress-induced nucleus pulpous cell proliferation (p < 0.05 for each), while the activation levels of EGFR and Rac1 were not inhibited. Proliferation and phosphorylation of ERK1/2 were inhibited after pretreatment with the Rac1 inhibitor NSC23766 in nucleus pulpous cells in response to periodic mechanical stress (p < 0.05 for each), while the phosphorylation site of EGFR was not affected. Inhibition of EGFR activity with AG1478 abrogated nucleus pulpous cell proliferation (p < 0.05 for each) and attenuated Rac1 and ERK1/2 activation in nucleus pulpous cells subjected to periodic mechanical stress (p < 0.05 for each). These findings suggest that periodic mechanical stress promotes nucleus pulpous cell proliferation in part through the EGFR-Rac1-ERK1/2 signaling pathway, which links these three important signaling molecules into a mitogenic cascade.

Fracture-based model of periodic-arrayed indentation for rock cutting

Periodic singular stress fields and K-dominant regions arise adjacent to sharp 90° indenter edges if an elastic substrate is subject to indentation with rigid, flat-ended and periodic indenters. The concept of indentation stress intensity factor Kind is convenient to describe such a singular indentation stress field, which is mathematically similar to that of a Mode-I crack. The singular indentation stress field is sufficient to induce surface cracking even if the substrate surface is free of any micro-cracks. This surface cracking mechanism generated from the flat-ended indentation potentially can play a significant role in damage analysis of rock cutting. During the rock-cutting processing, those periodic singular-stress fields will move along the rock surface, leading to continuous rock surface fracture. In this study, a fracture mechanics model is proposed for rock breakage by using an energy-based approach. The indentation stress intensity factor Kind and indentation cracking equation for rock-cutting/breakage have thus been formulated analytically.

Experimental investigation of the vortex breakdown in a lean premixing prevaporizing burner

The spiral vortex breakdown has been experimentally studied in the flow field generated by a lean premixing prevaporizing (LPP) combustor model. The vortex breakdown structures are characterized by a solid-body rotation. Hence, phase-locked laser Doppler velocimeter measurements, performed in a meridional plane, have allowed reconstruction of the periodic velocity and Reynolds stress fields within a time period and in a relative cylindrical frame of reference. Then, the turbulent kinetic energy (TKE) production term has been computed. The velocity distribution analysis indicates that a spiral vortex core wraps around an inner reverse flow zone. Both are characterized by a precessing motion. Then, the main contributions to the TKE production have been identified together with their spatial locations. Their distribution indicates that the maxima are placed in two regions: one located between the inner reverse flow and the spiral vortex and the second between the spiral vortex core and the external nearly quiescent fluid. In the latter, the TKE production term distributions have the features of a Kelvin–Helmholtz-like instability. In the former, the TKE production seems to be related to a Kelvin–Helmholtz-like instability only at the interface between the bubble and the spiral vortex core.

Selected Topics on Material Strength and Thermally Activated Deformation Processes

Thermally activated deformation processes are discussed with reference to the studies done by the present author and his coworkers. First, dislocation motion in one- and two-dimensional periodic stress fields is analyzed to understand the deformation mechanisms of bcc metals and spinodally decomposed alloys. The role of the thermally activated kink-pair formation on the temperature and strain-rate dependence of strength is also discussed. Secondly, diffusion-controlled processes pertinent to high-temperature deformation are discussed by applying a unified and fundamental rate equation derived previously. Thirdly, mechanisms for the temperature and strain-rate dependence of polycrystals and ultrafinegrained and nanocrystalline materials are introduced. A proposed model taking into account the thermally activated dislocation depinning at grain boundaries is discussed. [doi:10.2320/matertrans.M2014386]

Opening-mode fractures of a brittle coating bonded to an elasto-plastic substrate

An elasto-plastic fracture model is presented to study the opening-mode fractures for an alumina coating fully bonded to an aluminum substrate undergoing large tensile deformation. The periodic stress field in the coating layer is described by one section between two adjacent cracks. The coating material is brittle and elastic; whereas the substrate exhibits elasto-plastic behavior that is characterized with a bi-linear hardening plastic function. For simplicity, a one-dimensional elasto-plastic model is employed to the substrate; an elasto-plastic shear lag model is used to describe the stress transfer from the substrate to the coating; and a plane strain formulation is derived for stress analysis in the coating. Explicit solutions have been derived for the coating-substrate system under different loading stages. When the applied load is in the linear elastic state, the elastic field in the coating is verified with the finite element results. When the substrate yields, the fracture energy release rate can be calculated and the corresponding elasto-plastic fracture analysis is conducted. Experimental characterization has been further conducted to validate the present model, which in overall predicts the fracture initiation, infilling and saturation in the coating successfully. The present formulation is general and can be applicable to other types of coating – ductile substrate systems.

材料強度と熱活性化変形過程に関する若干の考察

Thermally activated deformation processes are discussed with reference to the studies done by the present author and his coworkers. First, dislocation motion in one- and two-dimensional periodic stress fields is analyzed to understand the deformation mechanisms of bcc metals and spinodally decomposed alloys. The role of the thermally activated kink-pair formation on the temperature and strain-rate dependence of strength is also discussed. Secondly, diffusion-controlled processes pertinent to high-temperature deformation are discussed by applying a unified and fundamental rate equation derived previously. Thirdly, mechanisms for the temperature and strain-rate dependence of polycrystals and ultrafinegrained and nanocrystalline materials are introduced. A proposed model taking into account the thermally activated dislocation depinning at grain boundaries is discussed. [doi:10.2320/matertrans.M2014386]

Conditional convergence in two-dimensional dislocation dynamics

For two-dimensional dislocation dynamics simulations under periodic boundary conditions in both directions, the summation of the periodic image stress fields is found to be conditionally convergent. For example, different stress fields are obtained depending on whether the summation in the x-direction is performed before or after the summation in the y-direction. This problem arises because the stress field of a 1D periodic array of dislocations does not necessarily go to zero far away from the dislocation array. The spurious stress fields caused by conditional convergence in the 2D sum are shown to consist of only a linear term and a constant term with no higher order terms. Absolute convergence, and hence self-consistency, is restored by subtracting the spurious stress fields, whose expressions are derived in both isotropic and anisotropic elasticity.

An Analysis of Collinear Periodic Crack-Tip Stress Field of an Infinite Plate Subjected to Concentrated Force

The Stress field of collinear periodic cracks in an infinite orthotropic composite plate subjected to the concentrated force is studied. The mechanical problem is turned into partial differential boundary value problem. The solution of partial differential equations can be obtained by the complex function methods, which contains unknown coefficients. Using undetermined coefficients method and with the help of boundary conditions, the partial differential boundary value problem is solved. The expressions for stress and displacements near crack tip are derived. Since the distribution of periodic cracks, the stress intensity factor is related to crack shape. Finally, a numerical example shows that the stress changes with the polar angle.

Periodic mechanical stress enhances rat chondrocyte area expansion and migration through Src-PLCγ1-ERK1/2 signaling

The signal transduction pathways of chondrocyte area expansion and migration under periodic mechanical stress remain a matter of debate. We explore this question by performing cell culture experiments in our self-developed periodic stress field and perfusion culture system. Under periodic mechanical stress, we find that both rat chondrocyte area and migration are significantly amplified. These changes are associated with increases in the phosphorylation of Src, PLCgamma1 and ERK1/2. Area expansion, migration and phosphorylation of PLCgamma1-Tyr(783) and ERK1/2-Thr(202)/Tyr(204) are inhibited (p<0.05) after pretreatment with Src inhibitor (PP2). We further demonstrate that area expansion, migration and phosphorylation of ERK1/2-Thr(202)/Tyr(204) are significantly inhibited (p<0.05) after pretreatment with PLCgamma1 inhibitor (U73122); the phosphorylation site of Src-Tyr(418) is not affected. After pretreatment with an ERK1/2 inhibitor (PD98059), area expansion and migration are inhibited (p<0.05), while the phosphorylation sites of Src-Tyr(418) and PLCgamma1-Tyr(783) are not affected. These findings suggest that periodic mechanical stress promotes chondrocyte area expansion and migration in part through the Src-PLCgamma1-ERK1/2 signaling pathway.

Periodically poled silicon

We propose a new class of photonic devices based on periodic stress fields in silicon that enable second-order nonlinearity as well as quasi-phase matching. Periodically poled silicon (PePSi) adds the periodic poling capability to silicon photonics and allows the excellent crystal quality and advanced manufacturing capabilities of silicon to be harnessed for devices based on second-order nonlinear effects. As an example of the utility of the PePSi technology, we present simulations showing that midwave infrared radiation can be efficiently generated through difference frequency generation from near-infrared with a conversion efficiency of 50%.

Structural characterization and stress-relaxation behavior of superlattice Cu 5Zr

A self-organized superlattice containing modulated layers in Cu5Zr was manufactured by casting a Cu–Zr system. Substitutional Zr atoms caused compressive stress in the superlattice so that periodic stress fields were formed with a long-range order along the 〈1 1 0〉 directions on {1 1 1} for stress relaxation. On the other hand, it was demonstrated theoretically by atomistic simulations that a superlattice could form easily due to the large negative enthalpy of formation in the structure (−12.890 kJ/mol of atoms).

On the nucleation of GaP/GaAs and the effect of buried stress fields

ABSTRACTWe have recently shown that spatial ordering for epitaxially grown InP dots can be obtained using the periodic stress field of compositional modulation on the InGaP buffer layer. The aim of this present work is to study the growth of films of GaP by Chemical Beam Epitaxy (CBE), with in-situ monitoring by Reflection High Energy Electron Diffraction (RHEED), on layers of unstressed and stressed GaAs. Complementary, we have studied the role of a buried InP dot array on GaP nucleation in order to obtain three-dimensional structures. In both cases, the topographical characteristics of the samples were investigated by Atomic Force Microscopy (AFM) in non-contact mode. Thus vertically-coupled quantum dots of different materials have been obtained keeping the in-place spatial ordering originated from the composition modulation.

Spinodal decomposition in a film with periodically distributed interfacial dislocations

Phase field approach is applied to modeling the spinodal decomposition process in a thin film with periodically distributed arrays of interfacial dislocations. The elastic stress field in the simultaneous presence of interfacial dislocations, substrate constraint, and compositional strains is obtained by solving the mechanical equilibrium equations using an iteration method. It is shown that the periodic stress field associated with the array of interfacial dislocations leads to a directional phase separation and the formation of ordered mesoscale microstructures. It is demonstrated that when the periodicity of the dislocation is small, the wavelength of the ordered microstructure tends to be the same periodicity as the dislocation array. The results have important practical implications that an ordered nanostructures could be produced by controlling the interfacial dislocation distribution.

Edge effects in angle-ply laminated hollow cylinders

The decay rates of stresses and displacements due to self-equilibrated loads acting on the end of angle-ply laminated hollow cylinders are found by using the theory of three-dimensional elasticity. The study assumes that the periodic displacement and stress fields used decay away exponentially from the end load region. The use of a recursive and successive approximation method leads to an eigenmatrix whose eigenvalues represent the decay rates of the problem. By this approach, the composite cylinders may be composed of an arbitrary number of anisotropic layers, each of which may have different material properties, thicknesses and lamination profiles. The decay rates for anti-symmetrically laminated cylinders are found and presented. The effects of material properties, thickness and laminate profiles of cylinders upon the decay rates are investigated for typical anti-symmetric angle-ply laminated cylinders.