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We analyze the thermo-elastic behavior of an elliptical nano-inclusion incorporating interface conduction and interface stress effects when embedded in an infinite matrix under plane deformation. The effect of interface conduction is represented by a highly conductive interface model, while that of interface stress is described via the complete version of the Gurtin–Murdoch model with the residual interface tension. Based on the complex variable method, we obtain, for the case of a constant heat flux applied remotely on the matrix, the uncoupled steady-state temperature field and thermal stress field using conformal mapping and series expansion techniques. We present also a group of numerical examples to illustrate the influence of interface conduction and interface effects on the stress field around the inclusion relative to the aspect ratio and relative stiffness of the inclusion. [ABSTRACT FROM AUTHOR]

In the mechanical analysis of a structure/composite with periodic holes/inhomogeneities based on analytic techniques, the holes/inhomogeneities are usually assumed to be circular. In this paper, we develop an efficient method (based on complex variable techniques) to calculate the surface tension-induced stress field in a porous material containing a periodic array of unidirectional holes of arbitrary shape. In this method, we use conformal mapping and Faber series techniques to address a finite representative unit cell (RUC) consisting of a single arbitrarily-shaped hole with a constant surface tension imposed on the hole’s boundary and periodic deformations imposed on the edge of the RUC. Several numerical examples are presented to verify the accuracy of our method and to study the influence of the shape and volume fraction of the periodic holes on the stress concentration in the structure. We show that the maximum hoop stress around periodic holes of some shapes (such as triangle, pentagon or hexagon) may appear exactly at the point(s) of maximum curvature when the hole volume fraction exceeds a certain value. Moreover, when the hole volume fraction falls below about 7%, it is found that the surface tension-induced stress concentration around periodic holes can be treated approximately as that around a single hole with the same hole shape and size in an infinite plane. [ABSTRACT FROM AUTHOR]

Harmonic holes are designed to leave undisturbed the mean stress in an uncut body subjected to a system of prescribed remote loadings. The role of residual surface tension in the design of harmonic holes is an important consideration, which is usually neglected at the macroscale but remains a significant factor in the design of such holes at the nanoscale. We consider the identification of the geometry of a single harmonic hole in an elastic plane subjected to uniform remote loading when residual surface tension is incorporated into the model of deformation. The geometry of the hole is defined by a conformal mapping with certain unknown coefficients determined from a system of non-linear equations. We illustrate our results with several examples. In particular, we show that for a given remote loading and surface tension, the shapes obtained exhibit strong size-dependency. Moreover, we find that the incorporation of the effect of surface tension greatly extends the range of admissible uniform remote loadings that guarantee the existence of harmonic holes. [ABSTRACT FROM AUTHOR]

We propose an innovative numerical scheme (based on complex variable techniques) for the calculation of the effective properties of a composite containing unidirectional periodic fibers in which we additionally incorporate the separate contribution of the 'interface effect' between the fibers and the surrounding material. The incorporation of interface effect into the model of deformation allows our model to accommodate the general class of nanocomposite materials, a fast growing area of research and our primary focus in this paper. The composite is loaded by a constant normal strain along the direction parallel to the fibers and by a uniform remote loading in the plane perpendicular to the fibers. Our method is based on the analysis of a representative unit cell with periodic boundary conditions imposed on its edge. Several examples are presented to study the influence of the interface and the volume fraction of the fibers on the effective properties of the composite and the interfacial stress field. We show that when the volume fraction falls below roughly 9%, the interfacial stress distribution recovers effectively to that corresponding to a single fiber with the same interface parameters embedded within an infinite matrix. We find also that if the shear modulus of the fibers exceeds approximately two and a half times that of the matrix, the interface effect is negligible in the determination of the effective properties of the corresponding nanocomposites. Finally, we show that the use of traditional effective medium theories may induce significant errors in the determination of transverse effective properties (in the plane perpendicular to the fibers) of the composite, in particular when the fibers are significantly softer than the matrix. [ABSTRACT FROM AUTHOR]

We develop a new method to construct periodic inclusions with uniform internal hydrostatic stress in an elastic plane subjected to uniform remote in-plane loading. The method is based on two particular conformal mappings which lead to a system of nonlinear equations from which the inclusion shapes are determined. We illustrate our results with several examples. In particular, we show that the ratio of the inclusion size to the period of the inclusion-matrix system changes with the inclusion aspect ratio and, in the specific case of uniform remote shear loading, the orientation of the inclusions is also altered. Finally, we show that if the period of the inclusion-matrix system exceeds roughly six times the inclusion size, such periodic inclusions can be treated approximately as periodic elliptical inclusions with specific aspect ratio and orientation determined by the corresponding elastic constants and uniform remote loading. [ABSTRACT FROM AUTHOR]

On the crack problem of ferromagnetic solids, almost all studies in previous literatures used two simple crack models, e.g., permeable and impermeable crack models. This means that a crack is always assumed to be a slit without thickness (mathematical crack). In fact, when a ferromagnetic solid with a crack is placed in magnetic fields, the mechanical/or magnetic loadings will make the crack opening and the high magnetic fields will be induced inside the deformed crack. Thus, the crack should be modeled as a semi-permeable cavity. In the present work, the semi-permeable crack model is adopted to study the fracture problems of a soft ferromagnetic solid. The general solutions are derived for complex potential functions and the intensity factors of fields. For some special cases, more explicit solutions are given and compared with those in literature. Numerical results are also presented to discuss the effects of magnetic fields inside the crack on fracture behavior of the ferromagnetic solid, and it is found that the model of semi-permeable crack is more reasonable than that of permeable crack or impermeable crack. [ABSTRACT FROM AUTHOR]

Abstract: Based on the complex variable method, this paper studies the effects of electric fields on the fracture of an electrostrictive solid under combined mechanical and electrical loads at infinity. The electric field inside a deformed crack is first determined by using the semi-permeable crack model. Then, the complex potentials and the intensity factors of stresses are presented, respectively, in concise and closed forms. Numerical results are also obtained to discuss the effects of applied electric and/or mechanical loads on the induced electric fields inside the crack and the stress intensity factors when the interior of the deformed crack and the surrounding space at infinity are filled with different gases. [Copyright &y& Elsevier]

This paper reports on the analysis of the strip dielectric breakdown (DB) model for an electrically impermeable crack in a piezoelectric medium based on the general linear constitutive equations. The DB model assumes that the electric field in a strip ahead of the crack tip is equal to the dielectric breakdown strength, which is in analogy with the classical Dugdale model for plastic yielding. Using the Stroh formalism and the dislocation modeling of a crack, we derived the relationship between the DB strip size and applied mechanical and electrical loads, the intensity factors of stresses and electric displacement, and the local energy release rate. Based on the results, we discussed the effect of electric fields on fracture of a transversely isotropic piezoelectric ceramic by applying the local energy release rate as a failure criterion. It is shown that for an impermeable crack perpendicular to the poling direction, a positive electric field will assist an applied mechanical stress to propagate the crack, while a negative electric field will retard crack propagation. However, for an impermeable crack parallel to the poling direction, it is found that the applied electric field does not change the mode I stress intensity factor and the local energy release rate, i.e., the applied electric field has no effect on the crack growth. [ABSTRACT FROM AUTHOR]

A simple method is proposed to analyze asymmetric indentation of a supported elastic beam by a rigid cylinder placed at an arbitrary position on the beam. A key advantage of our method over existing methods is that a single governing Kerr-type differential equation, which gives the relation between contact pressure and the normal deflection of the pressured surface of the beam, is applied both inside and outside the contact zone. With the present method, the two ends of contact zone will be determined as part of the solution, in contrast to the existing related studies which were all based on a simplifying assumption that the contact zone is geometrically symmetric about the tip of the indenter. Indeed, our results confirm that the contact zone is generally geometrically non-symmetric about the indenter tip, and even the whole contact zone can locate on one side of the indenter tip in some cases. Asymmetric indentation behaviors are demonstrated with numerical examples, with an emphasis on asymmetric contact pressure distribution inside the contact zone. Explicit formulas for the contact-zone width-displacement, force-displacement and moment-displacement relations are derived and illustrated with numerical examples. In particular, the present model predicts that as the indentation displacement exceeds a critical value, the indenter will lose contact with the beam inside the contact zone, which implies that the actual contact zone becomes two separate contact strips. Validity and accuracy of the present method are demonstrated by comparing its predictions with known results for some special cases. New features of asymmetric indentation as compared to symmetric indentation are summarized at the end of the paper. [ABSTRACT FROM AUTHOR]

We use conformal mapping techniques to derive a semi-analytical solution to the problem of a (straight) screw dislocation embedded in a thin solid film. The surfaces of the film are assumed to incorporate surface effects which result in deformation-dependent tractions imposed on the surfaces of the film. A number of examples are used to illustrate the stress distribution in the film and the image force acting on the dislocation. We show that in the absence of surface effects significant errors are induced in the determination of both the stress field in the film and the mobility of the dislocation, in particular as the dislocation approaches each of the film's surfaces or as the film becomes thinner. In fact, we demonstrate that the incorporation of surface effects with either positive or negative (surface) shear modulus can either relieve or intensify the stress concentration on the surfaces of the film. We find also that the dislocation tends to move towards a surface which possesses a smaller surface shear modulus and a smaller distance to the dislocation. Moreover, we show that when the thickness of the film exceeds ten times the (smaller) distance between the film's surfaces and the dislocation, the film can be treated essentially as a half-space without inducing large errors in the determination of the stress field in the film and the image force imposed on the dislocation. [ABSTRACT FROM AUTHOR]

We examine the existence of neutral nano-inhomogeneities in a hyperelastic inhomogeneity-matrix system subjected to finite plane deformations when uniform (in-plane) external loading is imposed on the matrix. We incorporate nanoscale interface effects by representing the material interface as a separate hyperelastic membrane, perfectly bonded to the surrounding bulk material. We show that for any type of hyperelastic bulk material and practically any type of hyperelastic membrane representing the interface, neutral nano-inhomogeneities do exist but are necessarily circular in shape. We show further that the radius of the circular neutral nano-inhomogeneity is determined by the (uniform) external loading (which must be hydrostatic) and the respective strain energy density functions associated with the hyperelastic bulk and interface materials. [ABSTRACT FROM AUTHOR]

We present a rigorous treatment of the problem of collinear periodic cracks in an infinite electrostrictive plane subjected to plane strain deformation in the presence of a uniform remote in-plane electric field. Using complex variable methods, exact electric and stress fields in the electrostrictive plane are obtained for both permeable and impermeable cracks. We show that the ratio of the mode-I stress intensity factors for periodic cracks to those for a single crack is determined by only the ratio of the period of the periodic crack-system to the crack length. Additionally, we find that the stress intensity factors for periodic cracks and the stress field in the proximity of periodic cracks can be treated essentially as those for a single crack when the period exceeds four times the crack length. [ABSTRACT FROM AUTHOR]

An extended analysis for the single-fiber pull-out process is presented based on Part I of this paper (Qing, 2013). The whole process of fiber pull-out contains three stages: elastic deformation with fully bonded interface, partially debonded interface and fully debonded interface with frictional sliding. Stress required to debond the fiber-matrix interface and pull-out a fiber is expressed as a function of the model length, fiber volume content and the radial residual thermal stress. The influence of fiber pull-out rate on interfacial frictional coefficient and shear strength is also taken into account. The calculation results show that the initial debonding stress is independent on the radial residual thermal stress, decreases with the increase of the pull-out rate, while increases and reaches a plateau with the increase of model length. The applied stress to cause further debonding increases with the increase of the radial residual thermal stress, while decrease with the increase of fiber pull-out rate. There is a drop for the applied stress and displacement of fiber end when the interface debonds to further close to the model length. [ABSTRACT FROM AUTHOR]