Uniformity of anti-plane stresses inside a nonlinear elastic elliptical or parabolic inhomogeneity.

We study the anti-plane strain problem associated with a p-Laplacian nonlinear elastic elliptical inhomogeneity embedded in an infinite linear elastic matrix subjected to uniform remote anti-plane stresses. A full-field exact solution is derived using complex variable techniques. It is proved that the stress field inside the elliptical inhomogeneity is nevertheless uniform. The uniformity of stresses is also observed inside a p-Laplacian nonlinear elastic parabolic inhomogeneity.

Interaction between an edge dislocation and a circular incompressible liquid inclusion.

We use Muskhelishvili's complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson's ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation.

Effect of Inevitable Heat Leap on the Conversion Efficiency of Thermoelectric Generators.

Discrepancies between experimental and theoretical results in the study of thermoelectric generators (TEGs) have been a major long-standing problem in thermoelectric technology. In this Letter, we report that, besides interfacial resistance, the inevitable heat leap caused by the Peltier effect is the main factor affecting the conversion efficiency of TEGs. In fact, the heat leap is proven to have an impact of approximately 10% on the conversion efficiency of common TEGs. In addition, we enhance the formula for maximum conversion efficiency with heat leap from the classical expression to allow for the prediction of the performance of advanced materials in TEGs. For the first time, the experimental data from conversion efficiency corresponds exactly to that obtained theoretically by considering both the heat leap and interfacial resistivity.

Clarification of Faber series and related applications to complex variable methods in two-dimensional elasticity.

Faber series are used extensively in the application of complex variable methods to two-dimensional elasticity theory, for example, in the mechanical analysis of composite materials where Faber series representations of complex potentials lead to convenient expressions for the corresponding displacement and stress distributions. In many cases, the use of the Faber series is combined with conformal mapping techniques which "transfer" a boundary value problem defined in the elastic body (physical plane) to a simpler problem posed in an imaginary plane characterized by the conformal mapping. In several instances in the literature, however, little attention has been paid to the domain of definition of the Faber series in the imaginary plane leading often to misunderstandings and erroneous conclusions regarding the concept and feasibility of the use of the Faber series. In this paper, we present a thorough and rigorous examination of the representation of the Faber series in both the physical (occupied by the material) and imaginary (defined by the conformal mapping) plane. In addition, we show that replacing a truncated Faber series by a truncated Taylor series does not induce any additional errors in the numerical analysis of the corresponding boundary value problem. We anticipate that the discussion in this paper will help clarify any existing misinterpretations regarding the application of the Faber series and help further extend their use to a range of problems in composite mechanics.

Interaction between an edge dislocation and a circular elastic inhomogeneity with Steigmann-Ogden interface.

We propose an effective method for the solution of the plane problem of an edge dislocation in the vicinity of a circular inhomogeneity with Steigmann-Ogden interface. Using analytic continuation, the pair of analytic functions defined in the infinite matrix surrounding the inhomogeneity can be expressed in terms of the pair of analytic functions defined inside the circular inhomogeneity. Once the two analytic functions defined in the circular inhomogeneity are expanded in Taylor series with unknown complex coefficients, the Steigmann-Ogden interface condition can be written explicitly in complex form. Consequently, all of the complex coefficients appearing in the Taylor series can be uniquely determined so that the two pairs of analytic functions are then completely determined. An explicit and general expression of the image force acting on the edge dislocation is derived using the Peach-Koehler formula.

An elliptical inhomogeneity under nonuniform heat flux.

We use complex variable techniques to study the decoupled two-dimensional steady-state heat conduction and thermoelastic problems associated with an elliptical elastic inhomogeneity perfectly bonded to an infinite matrix subjected to a nonuniform heat flux at infinity. Specifically, the nonuniform remote heat flux takes the form of a linear distribution. It is found that the internal temperature and thermal stresses inside the elliptical inhomogeneity are quadratic functions of the two in-plane coordinates. Explicit closed-form expressions of the analytic functions characterizing the temperature and thermoelastic field in the matrix are derived.

Novel cloaking lamellar structures for a screw dislocation dipole, a circular Eshelby inclusion and a concentrated couple.

Using conformal mapping techniques, we design novel lamellar structures which cloak the influence of any one of a screw dislocation dipole, a circular Eshelby inclusion or a concentrated couple. The lamellar structure is composed of two half-planes bonded through a middle coating with a variable thickness within which is located either the dislocation dipole, the circular Eshelby inclusion or the concentrated couple. The Eshelby inclusion undergoes either uniform anti-plane eigenstrains or uniform in-plane volumetric eigenstrains. As a result, the influence of any one of the dislocation dipole, the circular Eshelby inclusion or the concentrated couple is cloaked in that their presence will not disturb the prescribed uniform stress fields in both surrounding half-planes.

Interaction of a screw dislocation with a nano-sized, arbitrarily shaped inhomogeneity with interface stresses under anti-plane deformations.

We propose an elegant and concise general method for the solution of a problem involving the interaction of a screw dislocation and a nano-sized, arbitrarily shaped, elastic inhomogeneity in which the contribution of interface/surface elasticity is incorporated using a version of the Gurtin-Murdoch model. The analytic function inside the arbitrarily shaped inhomogeneity is represented in the form of a Faber series. The real periodic function arising from the contribution of the surface mechanics is then expanded as a Fourier series. The resulting system of linear algebraic equations is solved through the use of simple matrix algebra. When the elastic inhomogeneity represents a hole, our solution method simplifies considerably. Furthermore, we undertake an analytical investigation of the challenging problem of a screw dislocation interacting with two closely spaced nano-sized holes of arbitrary shape in the presence of surface stresses. Our solutions quite clearly demonstrate that the induced elastic fields and image force acting on the dislocation are indeed size-dependent.

A model for carbon nanotube-DNA hybrid using one-dimensional density of states.

A model for a carbon nanotube (CNT)-DNA hybrid embedded in an electrolyte solution is developed. The DNA charges are smeared out uniformly onto a cylindrical surface covering the CNT and the response of the CNT to the DNA charges is captured using the one-dimensional density of states (1D DOS) proposed by Mintmire et al. Coupled with the Debye-Hückel equation for the electrolyte, the expressions for the electric potential of the hybrid are obtained for both metallic and semiconducting CNT cores. For the surface charge density of the cylinder corresponding to the physically measured wrapping angles of a single-stranded DNA around a CNT, the developed model predicts that the induced charges on a semiconducting CNT are about one order of magnitude smaller than the DNA charges, while the induced charges on a metallic CNT can be comparable in magnitude to the DNA charges. Because of this, the magnitude of the electric potential for a metallic CNT-DNA hybrid can be as much as approximately equal 30% smaller than that for a semiconducting one. This result can be used to explain the experiments on DNA-assisted CNT separation using ion exchange chromatography.

Adhesion between a charged particle in an electrolyte solution and a charged substrate: Electrostatic and van der Waals interactions.

The equilibrium separation between a charged particle in an electrolyte solution and a substrate with an initially uniform surface charge density is obtained using the classical Derjaguin-Landau-Verwey-Overbeek theory. The electrostatic free energy is obtained by coupling the electric response of the substrate with the electric potential obtained from the solution of the Debye-Hückel equation. The van der Waals free energy is calculated by integrating the 6-12 Lennard-Jones potential. Metallic, dielectric, and semiconducting substrates are considered in turn. At low ionic strength, our results demonstrate a distinct response to the charged particle in each case. For example, in the case of a metallic substrate, the attached state (corresponding to equilibrium separation at short range) is always close to the van der Waals energy minimum. In addition, the application of a surface charge of sign opposite to that of the particle facilitates the transition from the detached state (corresponding to large separation at which the interaction between the particle and the substrate is negligible) to the attached state but scarcely changes the equilibrium separation. In the case of a dielectric substrate, the attached state is located at a distance of around two orders of magnitude larger than that for a metallic substrate and this equilibrium separation decreases as the (opposing) surface charge increases. A semiconducting substrate can behave either like a metal or like a dielectric, depending on the ratio of its Debye length to that of the electrolyte solution.