Inhomogeneity Of Arbitrary Shape Research Articles

Semi-analytical solution for temperature rise in a heterogeneous half plane containing arbitrarily shaped inhomogeneities subjected to surface heating

Temperature rise caused by surface heating is responsible for thermal-related failures of heterogeneous material, such as composites and alloys, in manufacturing processes and tribology. This study presents a semi-analytical method (SAM) for temperature rise in a half plane involving dispersed inhomogeneities of arbitrary shape undergoing external heat load. Green functions and frequency response functions (FRFs) for subsurface heat flux induced by the applied heat load, as well as a set of formulas for influence coefficients correlating disturbed temperature rise and uniform eigen-temperature gradients inside a rectangular inclusion in a full plane, are derived. The rectangular inclusion solution in a full plane is treated as an elementary solution to solve disturbed temperature rise in a heterogeneous half plane involving arbitrarily shaped inhomogeneities, through implementing the equivalent inclusion method (EIM), the method of images and discretizing the total computation area into a good many rectangular elements with the same size. Results obtained by the SAM are consistent with those of the finite element method (FEM). Effects of inhomogeneity numbers, material properties, volume fractions, and velocities of the moving heat load on temperature rise are discussed in detail. HIGHLIGHTS Green functions and frequency response functions for heat flux in a half plane subjected to surface heating are obtained. Influence coefficients relating disturbed temperature rise and uniform rectangular inclusion in a full plane are derived. The elementary rectangular inclusion method is utilized to cope with problems for inhomogeneities of arbitrary shapes and distributions. Effects of inhomogeneity numbers, material properties, volume fractions, and velocities of the moving heat load on temperature rise are discussed.

Debonding of an elastic inhomogeneity of arbitrary shape in anti-plane shear

We investigate the anti-plane shear problem of a curvilinear crack lying along the interface of an arbitrarily shaped elastic inhomogeneity embedded in an infinite matrix subjected to uniform stresses at infinity. Complex variable and conformal mapping techniques are used to derive an analytical solution in series form. The problem is first reduced to a non-homogeneous Riemann–Hilbert problem, the solution of which can be obtained by evaluating the associated Cauchy integral. A set of linear algebraic equations is obtained from the compatibility condition imposed on the resulting analytic function defined in the inhomogeneity and its Faber series expansion. Each of the unknown coefficients in the corresponding analytic functions can then be uniquely determined by solving the linear algebraic equations, which are written concisely in matrix form. The resulting analytical solution is then used to quantify the displacement jump across the debonded section of the interface as well as the traction distribution along the bonded section of the interface. In addition, our solution allows us to obtain mode-III stress intensity factors at the two crack tips. The solution to the anti-plane problem of a partially debonded elliptical inhomogeneity containing a confocal crack is also derived using a similar method.

Using the Monte Carlo method to model radiation propagation and absorption in optically inhomogeneous biological media

The proposed model is based on the solution of the radiation-transport equation by the Monte Carlo method. A multilayer biological medium with included inhomogeneities of arbitrary shape is considered, to which a photon flux is directed. The proposed model makes it possible to calculate the absorbed density distribution of laser-radiation energy in multilayer materials.

The interaction of an edge dislocation with an inhomogeneity of arbitrary shape in an applied stress field

A general, approximate solution is presented for an edge dislocation interacting with an inhomogeneity of arbitrary shape under combined dislocation and applied stress fields. The solution shows that the contributions of the dislocation stress field and the applied stress field to the interaction follow a simple superposition principle. The dislocation stress field has a short range effect, while the applied stress field has a long range effect. As special cases, explicit solutions for some common inhomogeneity shapes are obtained for the interaction induced by the applied stress field.

Size-dependent interaction between a screw dislocation and an inhomogeneity of arbitrary shape in an applied stress field

We present a general approximate solution for a screw dislocation interacting with an inhomogeneity of arbitrary shape in an applied stress field. The analysis is based on the Eshelby inhomogeneity theory. As special cases, explicit solutions for some common inhomogeneity shapes are obtained, from which size-dependent effects of dislocation stress field and the applied stress field on the interaction can be identified.

Prediction of Energy Barriers due to Nucleation in Solid‐to‐Solid Phase–Transitions

AbstractThis contribution generally aims at the application of the multiscale‐FEM to problems arising from inhomogeneities of arbitrary shape within a solid matrix material. In the context of our work, the inhomogeneity represents a nucleus of a new solid phase. According to the theory of homogeneous nucleation, the model predicts whether it is energetically preferable to initiate the growth of the nucleus or not. The implementation of this procedure into a micromechanical model for shape‐memory alloys is assumed to be suitable to reconstruct the so‐called stress‐drop after the initiation of phase‐transformation as observed in experiments. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Stress disturbances caused by the inhomogeneity in an elastic half-space subjected to contact loading

Inhomogeneities can increase localized stress and cause microstructural alterations to initiate fatigue failures in rolling elements under cyclic contact loading. To study the stress disturbances created by the inhomogeneity, a two-dimensional contact stress analysis is presented for a cylindrical indenter sliding on an elastic half-space containing an inhomogeneity of arbitrary shape. The boundary element method is used to analyze the contact problem, where actual contact boundary, contact pressure as well as tractions and displacements at inhomogeneity–substrate interface are determined by solving a set of integral equations numerically. Numerical results are presented to investigate effects and the stress disturbances caused by the inhomogeneity with various locations, sizes and material properties of inhomogeneity. The results also show that hard inclusions are more detrimental than soft deformable particles in rolling contact elements.

On the uniformity of stresses inside an inhomogeneity of arbitrary shape

We consider an inhomogeneity of 'arbitrary' shape embedded within an infinite isotropic elastic medium (matrix) subjected to antiplane shear deformations under the assumption of uniform remote loading. The inhomogeneity-matrix interface is assumed to be imperfect, characterized by a single interface function. Under these assumptions, we present a novel method leading to the solution of the problem concerned with identifying the shape of the inhomogeneity and the form of the corresponding interface function which leads to a uniform interior stress field. The analysis is based on complex variable methods. Specific solutions are derived in closed form and verified by comparison with existing solutions. As a consequence of our analysis, we present an interesting result on the uniqueness (within a certain class of smooth curves) of the circular inhomogeneity as the only inhomogeneity which, under the given conditions, leads to a uniform interior stress field when the interface function is constant (homogeneously imperfect interface).

The lowest order solution of the crack–inhomogeneity interaction for mode I crack

The lowest order solution to crack–inhomogeneity interaction is derived for mode I crack. The basic solution evaluates the variation of near-tip stress intensity factors induced by an inhomogeneity of arbitrary shape. A set of simplified forms of the basic solution is also obtained for several special inhomogeneity shapes. As validated by numerical examples, the approximate solutions have good accuracy.

Uniform Asymptotic Solutions for Lamellar Inhomogeneities in Anisotropic Elastic Solids

We consider the problem of a lamellar anisotropic inhomogeneity of arbitrary shape embedded in a different anisotropic matrix of infinite extent. Uniform asymptotic solutions for the equations of elastostatics on this configuration are obtained. The first order terms, in the inhomogeneity thickness, are explicitly determined for elastic inclusions, rigid inclusions, or cracks. We give real-form expressions for displacements and stresses at the interface and on the inhomogeneity axis. For the particular case of an elliptic inclusion or crack, our solution agrees with the asymptotic form of the exact solution. We also calculate the first order solution for lemon-shaped inhomogeneities and the corresponding expressions of the displacements and stresses on the interface and the inhomogeneity axis, and we find that, whereas for elliptic inclusions these stresses become unbounded at the inclusion's ends, for a lemon-shaped inclusion they remain bounded.

Elastic inhomogeneous inclusion and inhomogeneity in bimaterials

A method is presented for obtaining the elastic field due to an inhomogeneous inclusion or an inhomogeneity of any shape in two joined semi-infinite isotropic solids (bimaterials) which are either perfectly bonded or in frictionless contact at the planar interface. Eshelby’s equivalent inclusion method and the Galerkin vectors for double forces and double forces with moment in bimaterials are used to obtain the solution. The expression for the equivalent eigenstrains for an inhomogeneous inclusion or an inhomogeneity of arbitrary shape is obtained in terms of a system of singular integral equations which can then be solved numerically. The elastic fields for inhomogeneous inclusions and inhomogeneities are then obtained by treating the problem as a homogeneous inclusion.

A General Computer Program to Determine the Perturbation of Alternating Electric Currents in a Two-Dimensional Model of a Region of Uniform Conductivity with an Embedded Inhomogeneity

Summary A computer program to calculate the perturbation of alternating electric currents in a two-dimensional Earth model with a conductivity inhomogeneity is presented. The program provides for an inhomogeneity of arbitrary shape surrounded by a region of different conductivity. The equations and boundary conditions are solved by a numerical method for both E-polarization and H-polarization. The computer program allows for the solution over a grid of variable mesh dimensions and for a general model which consists of several conductivities. The program is given in detail and an example for a particular model is illustrated.