On the dyadic Green's functions for Beltrami fields

A simple derivation of the Green's functions for Beltrami fields is presented for use with time-harmonic electromagnetism in homogeneous biisotropic media.     

Viktor Trkal,Beltrami fields,and Trkalian flows

A 1919 contribution of Viktor Trkal on Beltrami fields is contextualized and shown to be of significance in fluid mechanics, time-harmonic electromagnetism and astrophysics.This paper introduces the English translation of an article by V. Trkal from 1919 — see next paper in this issue, p. 97.I gratefully acknowledge the assistance of Drs. Per Lindstrom (Bergen, Norway), Avadh B. Saxena (Los Alamos, New Mexico), Chandra S. Vikrarn (Huntsville, Alabama) and Miloslav Znojil (Prague) in locating old publications. I also thank the editors of this journal for asking me to write this introductory piece as well as for readily agreeing to publish an English translation of Trkal's paper.     

Influence of elastic stress fields on the diffusional redistribution of impurities in silicon

The redistribution of boron in silicon under the action of elastic stress fields created by the diffusion of various impurities is investigated experimentally. It is shown that the diffusion of boron slows down in the elastic compression interval. The slowing effect intensifies with increasing absolute stress values. A model is proposed to account qualitatively for the experimental results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 124–127, June, 1977.     

Interaction of a gravitational wave with an elastic body

The problem concerning the interaction of a weak gravitational wave with an elastic body in the general theory of relativity is solved by the use of the theory of elasticity composed earlier by the author on the basis of a gravitoinertial system of reference (GISR).Translated from Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 67–73, July, 1976.In conclusion, we thank V. I. Rodichev and D. D. Ivanenko for interest in the project and for valuable critical comments.     

Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress

The concept of eigenstrain is adopted to derive a general analytical framework to solve the elastic field for 3D anisotropic solids with general defects by considering the surface stress. The formulation shows the elastic constants and geometrical features of the surface play an important role in determining the elastic fields of the solid. As an application, the analytical close-form solutions to the stress fields of an infinite isotropic circular nanowire are obtained. The stress fields are compared with the classical solutions and those of complex variable method. The stress fields from this work demonstrate the impact from the surface stress when the size of the nanowire shrinks but becomes negligible in macroscopic scale. Compared with the power series solutions of complex variable method, the analytical solutions in this work provide a better platform and they are more flexible in various applications. More importantly, the proposed analytical framework profoundly improves the studies of general 3D anisotropic materials with surface effects.     

Effect of elastic stress fields generated by ion-implanted helium layers on changes in carbon steel microstructure

Microstructure and phase composition of iron-based alloys with 0.1 to 0.7% carbon are studied upon irradiation of the latter by α-particles followed by annealing at temperatures higher than those of the polymorphic α-γ-transformation. This treatment is shown to bring about irreversible phase and structural changes of the ferrite-pearlite structural components and grain size resulting in a higher microhardness in the areas saturated with helium. Based on calculations by the theory of elasticity of stress fields generated by the implanted helium atoms, it is shown that these microstructural changes are caused by deformations induced by helium present in the region of α-particle deceleration. Nuclear Physics Institute of the National Nuclear Center, the Republic of Kazakhstan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 14–18, June, 1999.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

Adhesion between an elastic body and a randomly rough hard surface

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macro-asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment. Received 3 April 2002     

Asymptotic representations of elastic wave fields in permeable strata

An analytical method has been developed for studying filtration wave fields in oil-gas collectors, which makes it possible to reduce wave conjugation problems to simple problems for the aymptotic expansion coefficients. Simple analytic dependences have been found to calculate the fields in inhomogeneous anisotropic layers for the zero and first coefficients. Such dependences can serve as the basis for a fundamentally new and more complete study of wave fields as applied to acoustic logging and seismic surveying. The reliability of this method is substantiated by comparing the obtained asymptotic solutions with the expansion coefficients of an exact solution to the parameterized problem expanded into a Maclaurin series for the formal parameter.     

Dislocation stress fields in α-Fe

The stress components based on anisotropic elasticity are found for edge and screw dislocations in α-Fe. The method of Eshelby, Read and Shockley is used.     

Covariantising the Beltrami equation in W-gravity

Recently, certain higher-dimensional complex manifolds were obtained by S. Govindarajan [1] by associating a higher dimensional uniformisation to the generalised Teichmüller spaces of Hitchin. The extra dimensions are provided by the times of the generalised KdV hierarchy. In this Letter, we complete the proof that these manifolds provide the analog of superspace for W-gravity and that W-symmetry linearises on these spaces. This is done by explicitly constructing the relationship between the Beltrami differentials which naturally occur in the higher-dimensional manifolds and the Beltrami differentials which occur in W-gravity. This also resolves an old puzzle regarding the relationship between KdV flow. and W-diffeomorphisms.Dedicated to the memory of Claude Itzykson.     

Hydrogen diffusion in the elastic fields of dislocations in iron

The effect of dislocation stress fields on the sink efficiency thereof is studied for hydrogen interstitial atoms at temperatures of 293 and 600 K and at a dislocation density of 3 × 10¹⁴ m^–2 in bcc iron crystal. Rectilinear full screw and edge dislocations in basic slip systems 〈111〉{110}, 〈111〉{112}, 〈100〉{100}, and 〈100〉{110} are considered. Diffusion of defects is simulated by means of the object kinetic Monte Carlo method. The energy of interaction between defects and dislocations is calculated using the anisotropic theory of elasticity. The elastic fields of dislocations result in a less than 25% change of the sink efficiency as compared to the noninteracting linear sink efficiency at a room temperature. The elastic fields of edge dislocations increase the dislocation sink efficiency, whereas the elastic fields of screw dislocations either decrease this parameter (in the case of dislocations with the Burgers vector being 1/2〈111〉) or do not affect it (in the case of dislocations with the Burgers vector being 〈100〉). At temperatures above 600 K, the dislocations affect the behavior of hydrogen in bcc iron mainly owing to a high binding energy between the hydrogen atom and dislocation cores.     

Role of elastic stress in statistical and scaling properties of elastic turbulence

The role of elastic stress in statistical and scaling properties of elastic turbulence in a polymer solution flow between two disks is discussed. The analogy with a small-scale magnetodynamics and a passive scalar turbulent advection in the Batchelor regime is used to explain the experimentally observed statistical properties, the flow structure, and the scaling of elastic turbulence. The emergence of a new length scale, namely, the boundary layer thickness, is observed and studied.     

Modelling of the stiffness of elastic body

It is necessary for designing vibration-isolation systems to know the components’ static stiffness, dynamic stiffness and shock stiffness, which are obtained through experiment at present. If the stiffness model of (viscous) elastic body is set-up, the essence of stiffness will be clearer and the experiment simpler. This paper presents a new method for modelling the stiffness of elastic body with viscoelastic theory. The parameters of the model set-up by using this method can be determined easily and present the characteristics of the elastic body's static stiffness, dynamic stiffness and shock stiffness.     

Quasi-Hamiltonian principle of liquid-filled elastic body dynamics

Liquid-filled elastic body dynamics is an important branch of fluid-solid coupling mechanics. It deals with the study of motion of a body and the liquid contained in the body under the interaction between the two,for example,a liquid-filled satellite,a fuel tank of an airplane,etc. The research on liquid-filled elastic body dynamics is usually done by the variational method since the method has a feature of treating things as a whole. Considering the elastic motion of the liquid-filled body and the surface tension effect on the liquid-gas interface,liquid-solid interface and gas-solid interface,the present paper establishes a quasi-Hamiltonian variational principle for the above-mentioned system. After finding the stationary-value conditions of its functional obtained,a complete system of governing equations consisting of the stationary value conditions,preconditions and constraint conditions is established,and then the equations are reduced into some known ones in a special case.     

Reflection of plane Beltrami waves from a plane interface in an isotropic chiral medium

The reflection of plane electromagnetic waves of circular polatization from a flat, ideally conducting screen limiting an isotropic chiral-medium half-space is examined. The equations relating the reflection coefficients with the common angle of incidence and material parameters of the medium are discussed.__________This revised version was published online in May 2005 with a correction on affiliation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 23–26, November, 2004.