Sitiro Minagawa

Propagation of harmonic waves in a layered elasto-piezoelectric composite

Abstract The exact analytical treatment of the propagation of harmonic waves in an infinitely extended, periodically layered, elastic and piezoelectric composite is presented. The general anisotropic constitutive equations including the terms of piezoelectric and anti-piezoelectric effects are used. The electric field is assumed as quasi-static. The continuity and the Floquet condition are assumed as boundary conditions on the field variables, leading to a dispersion equation of an 8 × 8 determinantal form. This dispersion equation is solved to investigate the dispersion characteristics of a composite. Numerical computations are made for a composite consisting of zinc oxide, gallium arsenide, and lithium tantalate. The influence of the piezoelectric effect of materials on the phase velocity of waves is investigated.

On the stress and electric field produced by dislocations in anisotropic piezoelectric crystals with special attention to the stress function

Abstract The author is concerned with the stress and electric field produced by dislocations in an anisotropic piezoelectric crystal, with a proposal on the way of choosing the best triad as stress functions from among the six components of Beltrami’s stress-function tensor. A pair of constitutive equations is assumed to connect the elastic strain and electric displacement with the stress and electric field. The fundamental equations governing the field of stress functions and electric scalar potential are presented, and solved by application of the method of Fourier transform. The stress and electric field are stated in terms of the dislocation density tensor, and by means of the convolution integrals throughout the region where there exist dislocations. The expressions are converted into those for the fields of an infinitely extended straight dislocation, as well as an elliptic dislocation, by Willis’ method. The choice of three stress functions is made on the way of numerical computations so that the line integrals can be achieved by application of Cauchy’s residue theorem. As example, the field of dislocations in a gallium arsenide is evaluated.

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional, anisotropic, elastic and piezoelectric media: elliptical Frank disclination

A statement is made on the theory of continuous distributions of dislocations and disclinations in anisotropic elastopiezoelectric media. The basic field equations governing the fields of stress functions, electric vector potential and incompatibility are presented and solved to give the fields of stress and electric displacement caused by a distribution of dislocations and disclinations. They are expressed in terms of the dislocation- and disclination-density tensors by means of the convolution integrals, extended throughout the medium, and the Fourier integrals. To treat the fields around discrete defects, that is dislocation and/or Frank disclination, the convolution integrals are replaced by the line integrals belonging to the loop of the defect. The fields of stress and electric displacement are given in terms of three quadruple integrals, which are converted into single integrals of explicitly given functions, in the case where the loop of the defect is elliptical. Numerical computations are carried...A statement is made on the theory of continuous distributions of dislocations and disclinations in anisotropic elastopiezoelectric media. The basic field equations governing the fields of stress functions, electric vector potential and incompatibility are presented and solved to give the fields of stress and electric displacement caused by a distribution of dislocations and disclinations. They are expressed in terms of the dislocation- and disclination-density tensors by means of the convolution integrals, extended throughout the medium, and the Fourier integrals. To treat the fields around discrete defects, that is dislocation and/or Frank disclination, the convolution integrals are replaced by the line integrals belonging to the loop of the defect. The fields of stress and electric displacement are given in terms of three quadruple integrals, which are converted into single integrals of explicitly given functions, in the case where the loop of the defect is elliptical. Numerical computations are carried out to estimate the fields in gallium arsenide. The values of those fields at a certain point of the body are presented. The contours and zero lines of the fields of dilatational stress and electric displacement in the plane placed parallel to and at a certain distance from the loop are illustrated.

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional, anisotropic, elastic, and piezoelectric media. II. Infinite straight dislocation and Frank disclination

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the authors statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchys theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the authors statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchys theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional, anisotropic, elastic, and piezoelectric media: III. Hexagonal crystal

The author is concerned with the fields of stress and electric displacement, in a piezoelectric hexagonal crystal, caused by infinite straight defects; dislocations and disclinations, that belong to its hexad axis. Computations are made for those fields in crystals of classes 6, 622, 6mm and m2. In the crystal of class 6, the complete analytical solutions are presented. In the absence of the piezoelectric effect, the expressions for the stress field become coincident with those given hitherto. In class m2, the complex solutions are presented; the expressions for the fields of defects are given as their imaginary part. Finally, the dilatational fields produced by the disclination-dipole are illustrated for caesium copper chloride, zinc oxide and gallium selenide, as well as the components of the electric-displacement field for zinc oxide and gallium selenide.

On the Basic Components of the Interaction Energy Between Two Infinitesimal Circular Defects in an Isotropic Elastic Body

The energy of interaction between two infinitesimal circular defects—dislocations and/or Frank disclinations—are given by the method of tensor analysis. The stress, incompatibility, and stress functions are expressed in terms of the dislocation and disclination density tensors. The interaction energy is given in terms of those tensors by means of the double-volume integrals with respect to the regions where there exist continuous distributions of defects. For discrete defects, the double-volume integrals are converted into the double-line integrals. The integrations are carried out for infinitesimal circular defects and the interaction energy between infinitesimal circular defects is given by a linear combination of certain basic components. Finally, the physical meaning of those components is given.

A trial of the gauge theory for the stress-function space

Following Golebiewska-Lasota and Edelen, a gauge structure existing in the field of the stress and the stress function is demonstrated, on the basis of an electromagnetic analogy given elsewhere. The four-tensors and four-vectors are used to state the set of fundamental equations, and the gauge condition and the gauge transformations are given in a similar way to electromagnetic theory.

Dislocation Dynamics in Anisotropic Piezoelectric Crystals: Influence of the Disturbance in the Electrical Field

The author’s theory for the mechanical and electrical fields produced by a continuous distribution of moving dislocations is reviewed with its application to the fields produced by a uniformly moving discrete dislocation-loop. Finally, the author is concerned with the mechanical and electrical fields which are brought about by the influence of the disturbance occured in the electrical field. Special attention is paid to the duality of the formulations for these fields to those given before.

Elastic interaction energies between dislocations and/or disclinations in an isotropic body

The elastic interactions between crystal defects, say dislocations and/or disclinations, are studied by means of the tensorial terminologies. The elastic interaction energies between two aggregates of continuously distributed defects are expressed in terms of the dislocation- and disclination-density tensors. The expressions are specialized into those for discrete defect loops. Finally, the dislocation-dislocation, dislocation-Frank disclination and Frank disclination-Frank disclination interaction energies are deduced for infinitesimal circular defect loops.