Isotropic Inclusions Research Articles

Numerical solution for elastic half-plane inclusion problems by different integral equation approaches

The boundary integral equation approach, also known as the boundary element method, the displacement domain integral equation approach and the strain domain integral equation approach are applied to calculate the elastostatic field of an isotropic elastic half-plane containing possibly isotropic, orthotropic and anisotropic inclusions. Numerical examples are given to show the characteristics of these three integral equation approaches.

On the use of Somigliana's formula and Fourier series for elasticity problems with circular boundaries

AbstractThis paper considers the problem of an infinite, isotropic elastic plane containing an arbitrary number of non‐overlapping circular holes and isotropic elastic inclusions. The holes and inclusions are of arbitrary size and the elastic properties of all of the inclusions can, if desired, be different. The analysis is based on the two‐dimensional version of Somigliana's formula, which gives the displacements at a point inside a region V in terms of integrals of the tractions and displacements over the boundary S of this region. We take V to be the infinite plane, and S to be an arbitrary number of circular holes within this plane. Any (or all) of the holes can contain an elastic inclusion, and we assume for simplicity that all inclusions are perfectly bonded to the material matrix. The displacements and tractions on each circular boundary are represented as truncated Fourier series, and all of the integrals involved in Somigliana's formula are evaluated analytically. An iterative solution algorithm is used to solve the resulting system of linear algebraic equations. Several examples are given to demonstrate the accuracy and efficiency of the numerical method. Copyright © 2003 John Wiley & Sons, Ltd.

Elastic interaction between "hard" or "soft" pointwise inclusions on biological membranes.

We calculate the induced elastic interaction between pointwise membrane inclusions that locally interact up to quadratic order with the membrane curvature tensor. For isotropic inclusions, we recover the usual interaction proportional to the inverse fourth power of the separation, however with a prefactor showing a non-trivial dependence on the rigidity Gamma of the quadratic potential. In the large-Gamma limit, corresponding to "hard" inclusions, we recover the standard prefactor first obtained by Goulian et al. (Europhys. Lett. 22, 145 (1993)). In the small-Gamma limit, corresponding to "soft" inclusions, we recover the recent result of Marchenko and Misbah (Eur. Phys. J. E 8, 477 (2002)). This shows that the latter result bears no fundamental discrepancy with previous works, but simply corresponds to the limit of soft inclusions. We discuss how the same inclusion can be depicted as hard or soft according to the degree of coarse-graining of the pointwise description. Finally, we argue that conical transmembrane proteins should be fundamentally considered as hard inclusions.

A Real Coded Genetic Algorithm Approach for Detection of Subsurface Isotropic and Anisotropic Inclusions

An inverse problem is considered to identify the geometry of discontinuities in a conductive material with anisotropic conductivity from Cauchy data measurements taken on the boundary. In this study we propose a real coded genetic algorithm in conjunction with a boundary element method to detect an anisotropic inclusion, such as a circle, by a single boundary measurement. Numerical results are presented for both isotropic and anisotropic inclusions. The genetic algorithms based method developed in this article is found to be a robust, efficient method for detecting the size and location of subsurface inclusions.

820 異方性球状介在物中に生ずる瞬間相変態ひずみに伴う応力焦点化現象

820 異方性球状介在物中に生ずる瞬間相変態ひずみに伴う応力焦点化現象

Elastic interaction of point defects on biological membranes.

The interaction between inclusions mediated by biological membranes undulations is analyzed. The interaction law is interpreted in terms of symmetries associated with inclusions. We show, in particular, that for a C3 and C3v symmetries the interaction law falls as 1/r3. We show that for completely isotropic inclusions, the dominant interaction vanishes to all orders, and the first contribution stems from the induced interaction which behaves as 1/r4. The same law holds for any other symmetry which is higher than C4. We introduce a straightforward method to compute these interactions. We point out important differences with results in the literature and explain the discrepancies.

THERMAL STRESS-FOCUSING EFFECT IN A TRANSVERSELY ISOTROPIC SPHERICAL INCLUSION EMBEDDED IN AN ISOTROPIC INFINITE ELASTIC MEDIUM

When an isotropic infinite elastic medium with a transversely isotropic spherical inclusion is suddenly subjected to a uniform temperature rise, stress waves occur at the interface of spherical inclusion at the moment thermal impact is applied. The stress wave in a transversely isotropic inclusion proceeds radially inward to the center of the inclusion. The wave may accumulate at the center and cause very large stress magnitudes even though the initial thermal stress should be relatively small. This phenomenon is called the stress-focusing effect. The stress wave in an infinite elastic medium proceeds radially to infinity. This paper analyzes, in an exact manner, the effects of these waves using the ray integrals. The results give a clear indication of the mechanism of the thermal stress-focusing effect in a transversely isotropic inclusion embedded in the isotropic infinite elastic medium.

혼합 체적-경계 적분방정식법을 이용한 탄성해석 방법 개발

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of elastic wave scattering problems and plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green`s function for anisotropic inclusions to solve this class of problems since only Green`s function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. In the formulation of this method, the continuity condition at each interface is automatically satisfied, and in contrast to finite element methods, where the full domain needs to be discretized, this method requires discretization of the inclusions only. Finally, this method takes full advantage of the pre- and post-processing capabilities developed in FEM and BIEM. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, and the analysis of plane wave scattering problems in unbounded isotropic matrix with isotropic inclusions and voids, it will be established that this new method is very accurate and effective for solving plane wave scattering problems and plane elastic problems in unbounded solids containing general anisotropic inclusions and voids/cracks or isotropic inclusions.

円形介在物内の任意点に特異荷重が作用する面外弾性体問題の解析

In this paper, the theoretical solutions are shown for the cases of a two-dimensional isotropic elastic medium containing an isotropic elastic circular inclusion loaded in singular disturbances at a finite point inside and having different isotropic elastic circular inclusions, under the anti-plane loading. It is assumed that the boundary conditions among the matrix and the elastic inclusion are perfectly bonded. This analysis is based on the complex variable method using the Mebius Transformation. Using these techniques, several examples are shown by graphical representation.

Method of Normal Modes for Modeling of the Electromagnetic Processes in Waveguide Structures Filled with Bi-Isotropic Media

A problem of normal electromagnetic oscillation modes in a rectangular waveguide with bi-isotropic inclusions having rectangular cross sections is formulated and solved. Analytical expressions for virtual currents caused by the presence of inclusions are derived by the method of natural modes. For isotropic inclusions, the convergence of the propagation constant of the principal mode, calculated by the method of normal modes, to its exact value is demonstrated with increasing number of basic functions.

Thermal and thermoelastic behaviour of multiply coated inclusion-reinforced composites

This work is devoted first to the derivation of the temperature field in an infinite medium constituted of an n-layered isotropic spherical inclusion, embedded in a matrix subjected to a uniform temperature gradient at infinity, under assumptions of no coupling between mechanical and thermal effects and of steady state conditions. These results lead to an estimate of the effective thermal conductivity coefficient of an n-layered inclusion-reinforced material. The second objective of this work is the derivation of the thermoelastic stress and strain fields in the same basic configuration but now, a coupling between stress and thermal properties is considered and the infinite matrix is stress free and subjected to a uniform change of temperature. These results and the solution of the same problem with a hydrostatic loading are used to estimate the effective thermal expansion coefficient and the specific heats for heterogeneous inclusion-reinforced materials.

Elastic effects on growth processes

Phase transformations in and on elastic substrates are affected by long-range elastic forces. Two examples are discussed. Fractal growth of adsorbed clusters and coarsening of isotropic inclusions inside a solid matrix are described by selfconsistent scaling methods.

A micromechanical damage model for effective elastoplastic behavior of partially debonded ductile matrix composites

A micromechanical damage model considering progressive partial debonding is presented to investigate the effective elastoplastic-damage behavior of partially debonded particle reinforced ductile matrix composites (PRDMCs). The effective, evolutionary elastoplastic-damage responses of three-phase composites, consisting of perfectly bonded spherical particles, partially debonded particles and a ductile matrix, are micromechanically derived on the basis of the ensemble-volume averaging procedure and the first-order effects of eigenstrains. The effects of random dispersion of particles are accommodated. Further, the evolutionary partial debonding mechanism is governed by the internal stresses of spherical particles and the statistical behavior of the interfacial strength. Specifically, following Zhao and Weng (1996), a partially debonded elastic spherical isotropic inclusion is replaced by an equivalent, transversely isotropic yet perfectly bonded elastic spherical inclusion. The Weibull's probabilistic function is employed to describe the varying probability of progressive partial particle debonding. The proposed effective yield criterion, together with the assumed overall associative plastic flow rule and the hardening law, forms the analytical framework for the estimation of the effective elastoplastic-damage behavior of ductile matrix composites. Finally, the present predictions are compared with the predictions based on Ju and Lee's (2000) complete particle debonding model, other existing numerical predictions, and available experimental data. It is observed that the effects of partially debonded particles on the stress–strain responses are significant when the damage evolution becomes rapid.

Evidence that newly synthesized esterified cholesterol is deposited in existing cytoplasmic lipid inclusions

Esterified cholesterol (EC) and triglyceride (TG) can be stored in cells as cytoplasmic inclusions. The physical state of the EC in these lipid droplets varies from liquid to liquid crystalline, depending on a number of factors, including the amount of TG co-deposited in the inclusion. The lipid in these droplets undergoes turnover via hydrolysis and resynthesis. We determined whether newly synthesized lipid is incorporated into existing cytoplasmic droplets, forms a discrete cytoplasmic droplet, or forms a small inclusion that fuses with an existing droplet. This was accomplished by monitoring the physical state of the lipid within the cytoplasmic inclusions following sequential deposition of TG and EC. Fu5AH cells were initially grown in media containing oleic acid to produce TG-rich, isotropic inclusions. The cells were then incubated with medium containing free cholesterol-phospholipid dispersions to promote synthesis and deposition of EC. To inhibit cytoplasmic TG hydrolysis, the lipase inhibitor, diethylumbelliferyl phosphate (UBP), was added at the time of cholesterol enrichment.The phase behavior of lipid droplets isolated from the lipid-rich cells was determined using polarizing light flow cytometry and microscopy. An anisotropic droplet population (EC-rich inclusions) was not detected, although there was an increase in cellular EC mass and no change in cellular TG mass. Therefore, under conditions where there is no turnover of cytoplasmic TG, newly synthesized EC is incorporated into existing TG inclusions.

An elastic singularity in a bounded region: volume change and related effects

When an equilibrated elastic field is induced in a homogeneous anisotropic bounded region by a point singularity, or by a finitely extended one, the evaluation of the various effects is deterred greatly by analytical difficulties associated firstly with the fundamental determination of the field of a point force in an unbounded anisotropic medium, and secondly with the determination of the image fields for practical shapes of the boundary, or for idealised ellipsoidal and spherical ones. We proceed in simple general terms nevertheless to certain overall evaluations, in particular, of the elastic increase or decrease in the total volume, without restrictions on the shape of the (traction-free) boundary, or on the anisotropy, or on the form of the singularity. We suppose secondly that the region in question is an inclusion of ellipsoidal shape, bonded to an unbounded matrix of another homogeneous anisotropic elastic phase. Formulae are found for the increase in volume of the ellipsoid and for the leading constant coefficients in the far field within the matrix, and evaluations are given for an arbitrary singularity in a spherical isotropic inclusion with an isotropic matrix.

Interfacial debonding of a spherical inclusion embedded in an infinite medium under remote stress

In the study of strength of particle reinforced composites, it is important to understand the energy release rate due to interfacial debonding between the particle and the matrix which is induced by manufacturing imperfection. This paper is aimed at the investigation of the critical condition for growth of the interfacial debonding and the corresponding volume increase due to void formation. The model used in the study is an isotropic elastic spherical inclusion embedded in an infinite isotropic elastic matrix under remote stress. Initial axisymmetrical interfacial debondings are assumed to exist in the vicinity of poles of the spherical inclusion. Axisymmetrical deformations of the matrix and the inclusion are analyzed based on the theory of three-dimensional elasticity in spherical coordinates. In order to avoid oscillatory stress singularity at the interfacial debonding front between two dissimilar materials, a condition of free slipping without friction at the interface is imposed. A Fredholm integral equation of the first kind is formulated based on the continuity conditions in the normal components of stress and displacement at the contact interface. The kernel function of the integral equation is expressed in terms of an infinite series of Legendre functions. Two types of remote stresses are considered in this study. The first type is the remote tension in the axial direction of the spherical inclusion and the second type is the remote compression in the transverse direction with respect to the axis of the spherical inclusion. Energy release rate is determined according to the rate of change of work done by remote stresses. In this paper, energy release rate and volume of the deformed void due to debonding are computed for any given size of initial interfacial debonding.

Some reflections on the Mori-Tanaka and Ponte Casta�eda-Willis methods with randomly oriented ellipsoidal inclusions

For a two-phase isotropic composite consisting of an isotropic matrix and oriented isotropic ellipsoidal inclusions, Mori-Tanaka's (MT) [6] method and the more recent Ponte Castaneda-Willis (PCW) [1] method are perhaps the only two methods that deliver explicit results for its effective moduli. An attractive feature of the MT method is that it always stays within the Hashin-Shtrikman [3] bounds, while the novel part of the PCW approach is that it has a well defined microstructure. In this paper, we made a comparative study on these two models, for both elasticity and their applications to plasticity. Over the entire range of inclusion shapes, the PCW estimates are found to be consistently stiffer than the MT estimates. An investigation of the possibility of a PCW microstructure for the MT model indicates that the MT moduli could be found from the PCW formulation, but this would require a spatial distribution that is identical to the oriented inclusion shape. Such a requirement implies that the underlying two-point joint probability density function is not symmetric, and thus it is not permissible. One is led to conclude that, unlike the aligned case, the MT model cannot be realized from the PCW microstructure with randomly oriented inclusions.

On a full-strength juncture between an isotropic matrix and an orthotropic inclusion under a triaxial load

The possibility exists for the full-strength state of the juncture between an isotropic medium and an orthotropic inclusion when the phases are in ideal contact and the stresses are tensile (compressive). It is found that an ellipsoid, whose semiaxes depend heavily on the elastic characteristics of the matrix and inclusion and the parameters of external loading, is such a form. A system of transcendental equations is obtained to search for the unknown semi-axes. Previous data confirm the results obtained. Numerical investigations are performed, and interrelations are established between geometrical parameters and loading conditions and the properties of the phases for transversally isotropic and orthotropic inclusions.

Lyotropic behaviour of liquid crystalline poly(ester amide) containing diamide links

The lyotropic behaviour of a poly(ester amide) (PEA), poly[bis (terephthalate butyramide) hexane] (PBTBH) containing aliphatic diamide links prepared through the amido diol route was studied by isothermal viscosity measurements at different shear rates and cross polarized light microscopic measurements in m-cresol, N-methyl pyrollidone (NMP) and concentrated sulphuric acid. The effects of polarity of solvent, shear rate and polydispersity on the threshold concentration were investigated. The viscosity values of the liquid crystalline (l.c.) PEA were found to increase with increase in concentration, reach a maximum and then decrease sharply. The critical concentration at which the viscosity–concentration curve shows a maximum and the threshold concentration where maximum anisotropy was observed did not coincide. The threshold concentrations in the viscosity-concentration curve obtained for the PEA are 56, 54 and 50 wt%, respectively, in m-cresol, NMP and concentrated sulphuric acid. The present experiments show that the threshold concentration depends on the polarity of the solvent, shear rate and polydispersity of the polymer. A narrow molecular weight distribution gives a sharper peak with a lower threshold concentration. PBTBH exhibited the typical shear thinning region under low shear rate peculiar to l.c. polymer solutions. The Newtonian plateau and the second shear thinning region under higher shear rate were also observed. Region I behaviour was confirmed by a number of observations, namely (a) the lack of scaling of transient viscosities during startup with strain and (b) the strong dependence of D 0 on concentration. In Region I, the viscosity showed a mild dependence on shear rate. This corresponds to a decrease of texture size with shear rate approximately as D −1/2, as in the Wissbrun model. The formation of the l.c. phase was confirmed by polarized light microscopy. Appearance of anisotropic inclusions in an isotropic phase started appearing prior to the occurrence of the critical concentration. As the concentration of anisotropic phase increased, the well known ‘phase inversion’ took place and isotropic inclusions in anisotropic phase started appearing as the system approached the threshold concentration. A fully anisotropic phase above the threshold concentration gave the typical nematic threaded texture under the polarized light microscope. A polydomain microstructure was observed in the shear thinning region under low shear rate, which tumbled down to a monodomain structure on application of higher stress.

The effective properties of piezoelectric composite materials with transversely isotropic spherical inclusions

The effective properties of piezoelectric composite materials are very important in engineering. In this paper, the closed-form solutions of the constraint-strain and the constraint-electric-field of a transversely isotropic spherical inclusion in an infinite non-piezoelectric matrix are obtained. The dilute solutions of piezoelectric composite materials with transversely isotropic spherical inclusions are also given. The solutions in the paper can be readily utilized in analysis and design of piezoelectric composite materials or smart materials and smart structures.