Anisotropic Ellipsoidal Inclusions Research Articles

Two-sided estimate of effective thermal conductivity coefficients of a textured composite with anisotropic ellipsoidal inclusions

Two-sided estimate of effective thermal conductivity coefficients of a textured composite with anisotropic ellipsoidal inclusions

Estimates for the Thermoelastic Properties of a Composite with Ellipsoidal Anisotropic Inclusions

A mathematical model describing the thermoelastic characteristics of a composite reinforced by anisotropic ellipsoidal inclusions is proposed. The model is applied to estimating the thermoelastic properties in the case of strengthening the material with single-walled carbon nanotubes. The estimates obtained by the self-consistent method and dual variational formulation of a thermoelasticity problem for an inhomogeneous solid body are compared.

Anisotropic ellipsoidal inclusion with an anisotropic shell in an isotropic medium subjected to a uniform electric field

An electrostatic problem has been solved for a dielectric inclusion that consists of an anisotropic core and an anisotropic shell. The inclusion is immersed in a uniform isotropic medium (matrix) subjected to a uniform electric field. It is assumed that the outer boundaries of the core and shell are ellipsoidal and become confocal after a linear nonorthogonal transformation that removes the anisotropy of the dielectric properties of the shell. Analytical expressions have been derived for the potential and strength of the electric field in the matrix and also in the shell and core of the inclusion, and an expression for the polarizability tensor of the inclusion has been deduced. It has been shown that the results agree with the well-known solutions in partial (limiting) cases.

Effective elastic properties of a composite containing multiple types of anisotropic ellipsoidal inclusions, with application to the attachment of tendon to bone

Estimates of the effective stiffness of a composite containing multiple types of inclusions are needed for the design and study of a range of material systems in engineering and physiology. While excellent estimates and tight bounds exist for composite systems containing specific classes and distributions of identical inclusions, these are not easily generalized to systems with multiple types of inclusions. The best estimate available for a composite containing multiple classes of inclusions arises from the Kanaun–Jeulin approach. However, this method is analogous to a generalized Benveniste approach, and therefore suffers from the same limitations: while excellent for low volume fractions of inclusions, the Kanaun–Jeullin and Benveniste estimates liebelow three-point bounds at higher volume fractions. Here, we present an estimate for composites containing multiple classes of aligned ellipsoidal inclusions that lies within known three-point bounds at relatively higher volume fractions of inclusions and that is applicable to many engineering and biological composites. The approach involves replacing the averaged strains used in the Kanaun-Jeulin method with an effective strain measure. We demonstrate application of the constitutive model to the graded tissue system at the attachment of tendon to bone.

Теплопроводность текстурированного композита с анизотропными эллипсоидальными включениями

Теплопроводность текстурированного композита с анизотропными эллипсоидальными включениями

An inclusion problem

An inclusion is a special region in a material, and this region experiences a transformation of the following nature. If the inclusion were free, then it would acquire a certain deformation with no stress arising in it; but since the inclusion is “pasted” into the material, this prevents free deformations and causes stresses arising in the inclusion itself and in the environment. Three systems of equations describing the problem are derived. For a space with a homogeneous isotropic matrix, an equivalent system of integral equations is obtained whose solution, for a homogeneous anisotropic ellipsoidal inclusion, is reduced to a system of linear algebraic equations. For the case where the moduli of elasticity in the inclusion and the homogeneous matrix coincide, an explicit solution for an inclusion of arbitrary shape is obtained.

A micromechanical model for the elastic properties of semicrystalline thermoplastic polymers

AbstractThis paper presents a micromechanical analysis of the elastic properties of semicrystalline thermoplastic materials. A lamellar stack aggregate model reported in the literature is used to derive tighter bounds and a self‐consistent scheme for the elastic modulus, and it is shown that the existing geometric models of the microstructures are not effective in predicting experimentally measured modulus of semicrystalline materials. Toward addressing this limitation, a model based on Mori‐Tanaka's mean field theory is developed by treating the semicrystalline materials as short‐fiber reinforced composites, in which the lamella crystalline phase is modeled as randomly embedded anisotropic ellipsoidal inclusions, and the amorphous phase as an isotropic matrix. The lamellae are characterized by two independent aspect ratios from three distinct geometric axes in general. Existing morphological studies on polyethylene (PE) and a syndiotactic polystyrene (sPS) are used to deduce the corresponding lamella aspect ratios, based on which the theoretical model is applied to predict the elastic modulus of the two material systems. The model predictions are shown to compare well with the reported measurements on the elastic moduli of PE and sPS. Polym. Eng. Sci. 44:433–451, 2004. © 2004 Society of Plastics Engineers.

Interaction of anisotropic ellipsoidal inclusions in an isotropic medium under mechanical loads and uniform heating

Eshelby's equivalent-inclusion method is extended to a finite number of arbitrarily oriented anisotropic ellipsoidal inclusions in an elastic isotropic matrix under polynomial mechanical loading and heating. The interaction of two identical and two different triaxial ellipsoidal inclusions in an elastic medium is studied as numerical examples. In special cases, the results are compared with those obtained by other authors

Residual thermal stresses in MoSi2–Mo5Si3 in-situ composites

Residual thermal stresses in MoSi 2 –Mo 5 Si 3 in-situ composites are calculated for a dilute concentration of particles of one phase embedded in a matrix of the other, using the fields of anisotropic ellipsoidal inclusions. Additionally, the eutectic interfaces are modeled as boundaries between two anisotropic half-spaces. The misorientation between MoSi 2 –Mo 5 Si 3 is obtained from the literature for Mo 5 Si 3 precipitates in MoSi 2 and by electron diffraction in the scanning electron microscope (SEM) for the opposite case. Tensile stresses of up to 3 GPa can develop after cooling from the eutectic temperature due to the thermal expansion mismatch between the phases. Electron microscopy of arc-melted Si-rich Mo 5 Si 3 shows that stresses are relieved by intergranular fracture in Mo 5 Si 3 and either dislocation plasticity or transgranular cracks in MoSi 2 , in a manner consistent with the calculations.

Effective elastic properties of composites with disoriented anisotropic ellipsoidal inclusions

Effective elastic properties of composites with disoriented anisotropic ellipsoidal inclusions

Thermoelastic state of an isotropic medium containing an anisotropic ellipsoidal inclusion, for ideal mechanical and thermal contact

Thermoelastic state of an isotropic medium containing an anisotropic ellipsoidal inclusion, for ideal mechanical and thermal contact

Effect of macroscopic inclusions on the electrical constants of solids

The problem of streamline current flow in an anisotropic medium with an ellipsoidally shaped macroscopic inclusion having a conductivity tensor different from that of the medium is solved. The solution obtained allowed us to find an expression for the effective conductivity tensor of the anisotropic medium with anisotropic ellipsoidal inclusions in a magnetic field. The problem of the effective values of the magnetoresistance coefficients of a medium with spherical dielectric inclusions is examined as a special case of the application of the general formula. It is shown how one may analyze galvanomagnetic effects in composites with the aid of the results obtained.

Form and intrinsic birefringence*

We consider a base medium with index of refraction n containing aligned anisotropic ellipsoidal inclusions having coincident optical and geometrical axes, specified by three indices of refraction ni and depolarization factors Qi (with i = a,b,c). From Maxwell–Clausius forms for the bulk dielectric constants, we construct the difference of two indices of refraction ηa − ηb = τ (to third order in ni − n) for comparison with birefringence measurements. We obtain simple explicit expressions for τ(n) (showing both intrinsic and form birefringence) and for the special value n = nˆ corresponding to an extremum of τ. The dependence of nˆ on na and nb, and on Qa and Qb is emphasized.

The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion

T he problem of an anisotropic ellipsoidal inclusion which undergoes a stress-free transformation strain (in the sense of J.D. Eshelby) is considered, and the following theorem is proved: If an ellipsoidal region in an infinite anisotropic linear elastic medium undergoes, in the absence of its surroundings, a stress-free transformation strain which is a polynomial of degree M in the position coordinates x t , then the final stress and strain state in the transformed inclusion, when constrained by its surroundings, is also a polynomial of degree M in x t .