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Eshelby showed that the pointwise force F on and normal to the interface between a transformed inclusion and its surrounding matrix is the jump in the normal component of the elastic energy-momentum tensor across the interface. Gavazza later showed, using an entirely different approach, that this thermodynamic driving force F has a much simpler form involving only the average of the stress tensors at adjacent points on opposite sides of the interface and the “transformation strain” tensor. The equivalence of and connection between the two formulae was apparently first shown by Eshelby in a personal letter to Gavazza (attached as an appendix to this paper), although the brevity of the letter makes following Eshelby’s proof a little difficult. Here we expand Eshelby’s hitherto unpublished proof of the equivalence of the two expressions in what we believe is a clearer fashion. [ABSTRACT FROM AUTHOR]

A two-dimensional plane strain elastic solution is determined for the Cottrell solute atmosphere around an edge dislocation in an infinitely long cylinder of finite radius (the matrix), in which rows of solutes are represented by cylindrical rods with in-plane hydrostatic misfit (axial misfit is also considered). The periphery of the matrix is traction-free, thus introducing an image solute field which generates a solute-solute interaction energy that has not been considered previously. The relevant energy for the field of any distribution of solutes coexistent with a single edge dislocation along the (matrix) cylinder axis is determined, and coherency effects are discussed and studied. Monte Carlo simulations accounting for all pertinent interactions over a range of temperatures are found to yield solute distributions different from classical results, namely, (1) Fermi-Dirac condensations at low temperatures at the free surface, (2) the majority of the atmosphere lying within an unexpectedly large non-linear interaction region near the dislocation core, and (3) temperature-dependent asymmetrical solute arrangements that promote bending. The solute distributions at intermediate temperatures show a 1/r dependence in agreement with previous linearized approximations. With a standard state of solute corresponding to a mean concentration, c 0 , the relevant interaction energy expression presented in this work is valid when extended to large concentrations for which Henry's Law and Vegard's Law do not apply. [ABSTRACT FROM AUTHOR]

Kelvin probe force microscopy (KPFM) is designed for measuring the tip-sample contact potential differences by probing the sample surface, measuring the electrostatic interaction, and adjusting a feedback circuit. However, for the case of a dielectric (insulating) sample, the contact potential difference may be ill defined, and the KPFM probe may be sensing electrostatic interactions with a certain distribution of sample trapped charges or dipoles, leading to difficulty in interpreting the images. We have proposed a general framework based on boundary integral equations for simulating the KPFM image based on the knowledge about the sample charge distributions (forward problem) and a deconvolution algorithm solving for the trapped charges on the surface from an image (inverse problem). The forward problem is a classical potential problem, which can be efficiently solved using the boundary element method. Nevertheless, the inverse problem is ill posed due to data incompleteness. For some special cases, we have developed deconvolution algorithms based on the forward problem solution. As an example, this algorithm is applied to process the KPFM image of a gadolinia-doped ceria thin film to solve for its surface charge density, which is a more relevant quantity for samples of this kind than the contact potential difference (normally only defined for conductive samples) values contained in the raw image. [ABSTRACT FROM AUTHOR]

Presents the thermal management options which have been evaluated in the development of the multifunctional structure (MFS) designs for miniature spacecraft. MFS thermal control aspects; Thermal analysis and vacuum testing of MFS panels; MFS panel configuration.

The capacitance system of a hyperboloidal tip and a rough surface is usually encountered in analyzing electrostatic force microscopy images. In this letter, a perturbation approach has been applied to solve for the electric potential of this system, in which the rough surface is treated as perturbation from a flat one. For the first-variation solution, the boundary value problem is represented in the prolate-spheroidal coordinate system and solved in terms of a generalized Fourier series involving conical functions. Based on this solution, the tip-surface Coulombic interaction can be computed. Sample calculations have been applied to sinusoidal surface profiles. [ABSTRACT FROM AUTHOR]

A preface to this special issue of "Mathematics and Mechanics of Solids," which is devoted to topical problems in the theory and applications of linear elasticity, is presented.

The existence of Eshelby’s equivalent inclusion solution is proved for a non-degenerate ‘transformed’ ellipsoidal inhomogeneity in an infinite anisotropic linear elastic matrix. We prove the invertibility of the fourth rank tensor expression, C′SE+C(I−SE), where C is the stiffness tensor of the matrix, C′ is the stiffness tensor of the inhomogeneity, I is the Eshelby tensor, and SE is the symmetric identity tensor. Taking advantage of the positive definiteness of certain tensor expressions, a proof-by-contradiction using energy arguments is posited that eliminates the possibility that the above expression is singular. Because the tensor expression is non-singular, it can always be inverted and Eshelby’s equivalent ellipsoidal inclusion method can be used to find the stress and strain fields in both the matrix and inhomogeneity. [ABSTRACT FROM PUBLISHER]