Periodic intermittent regime of a boundary flow

Melting of an ultrathin lubricant film during friction between two atomically smooth surfaces is investigated using the Lorentz model for approximating the viscoelastic medium. Second-order differential equations describing damped harmonic oscillations are derived for three boundary relations between the shear stresses, strain, and temperature relaxation times. In all cases, phase portraits and time dependences of stresses are constructed. It is found that under the action of a random force (additive uncorrelated noise), an undamped oscillation mode corresponding to a periodic intermittent regime sets in, which conforms to a periodic stick-slip regime of friction that is mainly responsible for fracture of rubbing parts. The conditions in which the periodic intermittent regime is manifested most clearly are determined, as well as parameters for which this regime does not set in the entire range of the friction surface temperature.     

Numerical simulation of flow in a screw-type blood pump

This study presents a numerical investigation of the flow field in a screw pump designed to circulate biological fluid such as blood. A simplified channel flow model is used to allow analysis using a Cartesian set of coordinates. Finite analytic (FA) numerical simulation of the flow field inside the channel was performed to study the influence of Reynolds number and pressure gradient on velocity distribution and shear stresses across the channel cross-section. Simulation results were used to predict flow rates, circulatory flow and the shear stresses, which are known to be related to the level of red blood cell damage (hemolysis) caused by the pump. The study shows that high shear levels are confined to small regions within the channel cross-section, but the circulatory nature of the flow causes an increased percentage of blood elements to pass through the high shear regions, and increases the likelihood of cell damage.     

Residual stresses deriving from holographic interferometry data on a base of inverse problem solution

A transition model, which is capable of obtaining both membrane and bending residual stress components from initial experimental information, is developed for thin-walled plane structures. The determination of residual stresses is based on the combined implementing of the hole-drilling method and reflection hologram interferometry. Required input data are obtained by simultaneous measurements on through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Superimposed residual stresses field, which consists of both membrane and bending components, is a reason for the various deviations of each specific fringe pattern from an ideal form. This fact is a clear experimental indication of the bending stress contribution in a total stress field. Two ways of decomposition of superimposed residual stresses field are proposed and analysed in detail. Emphasis is laid on a careful quantitative formulation of the inverse problem needed for an accurate deriving both membrane and bending residual stress components. It is shown that an availability of two-side initial data is both an essential and necessary condition of such a formulation. Detailed analysis of an accuracy of the results obtained is performed. This analysis is based on a wide set of both actual interferograms and analogous reference fringe patterns related to superimposed residual stress field under study. Comparing residual stress values obtained proceeding from one-side and two-side data are presented for different types of superimposed field of interest.     

Generic theory of active polar gels: a paradigm for cytoskeletal dynamics

We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel leads to a non equilibrium state characterized by the generation of flows and stresses. Our theory can be applied to experiments in which cytoskeletal patterns are set in motion by active processes such as those which are at work in cells.     

Wave field localization in a prestressed functionally graded layer

Characteristic features of wave field formation caused by a surface source of harmonic vibration in a prestressed functionally graded layer are investigated. It is assumed that the elastic moduli and the density of the material vary with depth according to arbitrary laws. The initial material of the medium is represented by a model hyperelastic material with third-order elastic moduli. The boundary-value problem for a set of Lamè equations is reduced to a set of Cauchy problems with initial conditions, which is solved by the Runge–Kutta–Merson method modified to fit the specific problem under study. Considering shear vibrations of a functionally graded layer as an example, effects of the type of its inhomogeneity, variations in its properties, and nature of its initial stressed state on the displacement distribution in depth are investigated. Special attention is paid to characteristic features of displacement localization in a layer with an interface-type inclusion near critical frequencies. A direct relation between the inhomogeneous layer structure and the type of displacement localization in depth is demonstrated. It is found that the role of initial stresses and variations in material parameters considerably increases in the vicinities of critical frequencies.     

Local instability of a plate with a circular nanohole under uniaxial tension

The problem of the influence of surface tension on the local instability of a plate under tension is investigated by the example of an infinite plate with a circular nanohole. The method for solving the problem under consideration is based on a previously developed approach for solving problems on local buckling of a thin uniaxially stretched elastic sheet with variously shaped macroholes. The critical (Euler) load, at which the instability occurs, is sought by the Ritz method in framework of the linearized Karman set of equations based on the principle of virtual motions as the smallest positive load giving the minimum of the potential energy of the plate deformation. The generalized plane stress state of the plate with a nanohole is found for its application taking into account surface stresses. The linearized Gurtin-Murdoch relationships for the surface elasticity, the generalized Young-Laplace law, and the Goursat-Kolosov complex potentials are used when deriving analytical dependences for the stress in this plane problem. The deflection of the plate is represented by a double row satisfying the damping condition at infinity and ensuring freedom of motion of hole edges. Numerical calculations are performed for the aluminum plate. Two variants of the elastic properties of a circular hole are considered. Zones of compressing circumferential tensions near the edges of the circular hole with radii 1, 2, and 4 nm under uniaxial tension are constructed. It is shown that the account of the surface stresses decreases the critical load, which has a tendency to decrease in both cases with a decrease in the cut radius in a nanometer variation range.     

Surface deformation induced by a variation in surface stresses in anisotropic half-regions

The deformations and the stresses in anisotropic half-regions taking into account surface stresses originating from surface energy, which exists originally at surfaces and interfaces dividing phases, are analysed theoretically. In the present paper, the equilibrium equation of force considering surface stresses is used to calculate the inelastic deformation induced by a variation in surface stresses. The problem of varying surface stresses in a half-surface of a half-infinite anisotropic domain is analysed using the theory of elasticity. This problem is related to the occurrence of cracks in contaminated, oxidized or chemisorbed surfaces. Stress analysis on the basis of continuum mechanics is performed precisely under the boundary condition taking into account surface stresses. The Fourier transform technique is applied to perform the analysis, and the components of stress and displacement are expressed in an explicit form. The shear component of bulk stress attains infinity at the edge of discontinuity of the surface stresses, and the free surface deforms like an edge dislocation. This result suggests that cracking in a chemically contaminant surface is easier than in a clean surface.     

Comparison of growth stress measurements with modelling in thin iron oxide films

High temperature oxidation of metals leads to residual stresses both in the metal and in the growing oxide. In this work, the evolution of this residual stresses is theoretically predicted in the growing oxide layers. The origin of these stresses is based on a microstructural model. Using experimental results providing from the oxidation kinetics, and an analysis proposed to describe the growth strain occurring in the thin layers, a set of equations is established allowing determining the stresses evolution with oxidation time. Then, the model is compared with experimental results obtained on both α-Fe and phosphated α-Fe, oxidised at different temperatures. Numerical data are extracted from experiments either with an asymptotic formulation or with an inverse method. These two methods give good agreement with experiments and allow extracting the model parameters.     

Tuning natural modes of vibration by prestress in the design of a harmonic gong

Prestresses are purposefully added to an object to improve its performance, such as tuning a guitar string by adding tension. This paper reports how the normal modes of a sheet metal component can be tuned through the prestresses generated by cold-forging small dimples. Finite element analysis showed that the frequencies of specific mode shapes were differentially affected by the location of residual stress fields due to dimple formation in relation to modal stress fields. The frequencies of overtones were most sensitive to the depth of the dimples located near the maxima of modal stresses. Using this approach a series of musical gongs were designed with up to the first five overtones tuned to within 5% of the harmonic series. The balance of harmonic and inharmonic overtones in these gongs that are well resolved by the human cochlea may constitute a set of recognizable musical timbres with sufficient harmonicity to produce an unambiguous pitch for most listeners. Since many other mechanical properties of sheet metal components are affected by residual stresses this manufacturing technique may have broader application in design engineering.     

Generation of elastic waves in a laminated solid by a moving photothermal source

The steady state response of an elastic layered plate (laminate) which is subjected to a moving laser source illumination is studied. The response of the laminate is obtained using the transfer matrix approach. The application of the photo-thermal source (laser) to the upper surface of the laminate is formulated as equivalent stresses applied at the illuminated boundary. The equivalent stresses are derived with the use of the causality principle. It is shown that the generated displacement field is sensitive to the variations of the laminate inner structure and also to the variations of the elastic properties of a bonded elastic half-space.     

Computer stability test for aluminum films heated on a graphene sheet

The behavior of single- and double-sided monatomic aluminum films on graphene heated from 300 to 3300 K is studied by the molecular dynamics method. Atoms of single-sided coating are preserved on graphene up to 3300 K, while atoms of double-sided coating leave graphene even at 1800 K; upon a further increase in temperature, this leads to an increase in the horizontal and vertical components of the self-diffusion coefficient. The stresses produced by vertical forces are found to be most significant in metallic films; these stresses almost disappear when temperature reaches 2300 K. The stresses in graphene, the highest of which are concentrated in the zone of formation of the metal film, substantially decrease upon heating.     

Holographic interferometry for measuring residual stresses by using probing holes

An original method of determining residual stresses by using probing holes and measuring the difference in the holographic interference fringe orders for two sets of pairs of points taken on the principal strain axes is suggested. The optical scheme of the interferometer is based on the use of reflection holograms. The principal residual strains are found by solving an overdetermined set of linear equations. The effect of rigid displacement on the fringe pattern is taken into account. The method is experimentally verified by measuring elastic stresses in uniaxially and biaxially strained specimens.     

Stabilization of growth of a pearlite colony because of interaction between carbon and lattice dilatations

The previously proposed model of pearlite transformation develops taking into account the possible interaction between carbon and lattice dilatations arising in austenite near the pearlite colony. The normal stresses caused by the colony stimulate autocatalysis of plates, and tangential stresses promote the stabilization of the transformation front. The mechanism of ferrite branching, which can play an important role in the kinetics of pearlite and bainite transformations, is discussed.     

Domain structure of a tetragonal antiferromagnet

A theory of the 90° and 180° domain structure in an easy-plane tetragonal antiferromagnet with nonuniform internal magnetostrictive and mechanical stresses has been developed. The reconstruction of domain structure in an external magnetic field was investigated. Dependencies of critical fields of stability loss of the 90° and 180° domain structures upon a directional external pressure, and magnetostrictive and nonuniform mechanical stresses have been determined. The dependence of the magnetization curve on mechanical stresses has also been determined.     

Experimental simulation and theoretical analysis of the thermal deformation of dielectric plates under submicrosecond radiation heating

The flexural deformation of dielectric plates subjected to submicrosecond thermal stresses generated by volume and surface sources is studied. The action of such stresses is simulated by laser irradiation of colored glass plates with different optical absorption factors. Such an approach to simulating the thermomechanical action of radiation on dielectric materials allows researchers to visualize the qualitative and quantitative thermoelastic response of the plates to the action of pulsed sources of thermal stresses with different spatial parameters. For volume sources of thermal stresses, it is shown that the thermal deformation of a dielectric plate can be viewed as a set of quasi-harmonic extension-compression wave processes combined with the quasi-static bend of the plate. Under the action of surface sources of submicrosecond thermal stresses, the deformation mechanism is a superposition of the thermal deformation of a thin surface layer and a pulse wave process resulting in the bend of the plate when the pulses reverberate between the surfaces of the plate. Approximate analytical models of thermal deformation due to pulsed thermal disturbances are suggested that make it possible to predict the extent of bend versus the absorbed energy dose under the action of both volume and surface sources of thermal stresses.     

Performance of a cantilever piezoelectric energy harvester impacting a bump stop

Piezoelectric cantilever beam energy harvesters are commonly used to convert ambient vibration into electrical energy. In practical applications, energy harvesters are subjected to large shocks which can shorten the service life by causing mechanical failure. In this work, a bump stop is introduced into the design of a piezoelectric cantilever beam energy harvester to limit the maximum displacement of the cantilever and prevent excessively high bending stresses developing as a result of shocks. In addition to limiting the maximum displacement of the beam, it is inevitable that the deflected shape of the beam and the electrical output are modified. A theoretical model for a piezoelectric cantilever beam harvester impacting against a stop is derived, which aims to develop an understanding of the vibration characteristics of the cantilever and quantify how the electrical output of the harvester is affected by the stop. An experiment is set up to measure the dynamics and the electrical output of a bimorph energy harvester and to validate the theoretical model. Numerical simulation results are presented for energy harvesters with different initial gaps and different stop locations, and it is found that the reduction in maximum bending stress is at the expense of the electrical power of the harvester.     

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.     

Mechanical stresses in an irradiated target with a disturbed surface

Mechanical stresses generated in a disturbed-surface solid target irradiated by intense fluxes of accelerated charged particles are studied numerically and analytically. The disturbed surface is needed to analyze the influence of microirregularities present on real surfaces on the stress pattern. Three basic components of the stress field are revealed: a shock wave; stresses localized in the energy liberation region; and disturbed stresses, which are due to the disturbed surface. The disturbed stresses are localized in a surface layer of width comparable to the disturbance wavelength and account for about 30% of the field stress energy. It is concluded that the disturbance of the surface and disturbance-induced stresses should be taken into account in analysis of structural transformations under irradiation.     

Destruction of defective conductors with a current in a magnetic field

A mechanism of destruction of conductors with a crack in an external magnetic field is proposed. In this case, ponderomotive forces form a complex strained state in the crack tip, which is estimated from the equations of the linear theory of elasticity. The critical ponderomotive forces are found, which depend on the current and magnetic field parameters and induce stresses in the defect top, which are comparable with the yield strength of the material.     

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

The electro-elastic interaction between a piezoelectric screw dislocation and an elliptical piezoelectric inhomogeneity, which contains an electrically conductive confocal elliptical rigid core under remote anti-plane shear stresses and in-plane electrical load is dealt with. The analytical solutions to the elastic field and the electric field, the interfacial stress fields of inhomogeneity and matrix under longitudinal shear and the image force acting on the dislocation are derived by means of complex method. The effect of material properties and geometric configurations of the rigid core on interfacial stresses generated by a remote uniform load, rigid core and material electroelastic properties on the image force is discussed.