Analysis of a line defect in a multilayered smart structure by the image method

Force on a screw dislocation in a multiphase laminated structure

“…For an arbitrary position of the screw dislocation, the force acting on it depends on six combinations of the seven shear moduli, the thicknesses of the surface layers, and the distances of the dislocation and its infinity of images from the various interfaces. In view of the fact that a nine-layer piezoelectric actuator has been fabricated [14], an extension of this study to a general n -phase structure deserves consideration.…”

“…This will be necessary whenever the observation point is very close to the specified singularity, as in the general case of the determination of the forces acting on elastic singularities. By substituting for A 1 from equation (10) and applying the expansion formula (14) we obtain the series representation where…”

“…Choi and Earmme [13] used the alternating technique and the method of analytic continuation to study the singularities in an isotopic material. Wen and Wu [14] developed a generalized image method and used it to obtain solutions for a generalized dislocation in a multilayered solid consisting of three finite layers and a semi-infinite substrate. More recently, Zhou and Wu [15] used the method of image dislocations to obtain analytical solutions for the elastic fields due to an edge dislocation in a linearly elastic isotropic film-substrate, while Wang [16] employed the method of analytic continuation to solve the problem of an edge dislocation in a general n -phase laminated composite when the phases have the same shear modulus but different Poisson’s ratios.…”

On screw dislocation in a multiphase lamellar inclusion

“…His classical solution for the force on a screw dislocation in an isotropic half space on which there is a surface film paved the way for similar investigations for a variety of configurations of layered materials (see, for example, [3][4][5]). More recently, variants of the image method have been used to study the interaction of dislocations with boundaries for some two-dimensional anti-plane configurations (see, for example, [6][7][8][9][10]). In [7], the technique of Mellin transform was used in conjunction with the image method to analyze the problem of two-dimensional dissimilar isotropic composite annular wedges subjected to anti-plane concentrated forces and screw dislocations.…”

“…In [7], the technique of Mellin transform was used in conjunction with the image method to analyze the problem of two-dimensional dissimilar isotropic composite annular wedges subjected to anti-plane concentrated forces and screw dislocations. In [8], a generalized image method was developed and used to obtain solutions for a generalized dislocation in a solid consisting of three finite layers on a semi-infinite substrate. In [9], the method of image dislocations was used to obtain analytical solutions for the elastic fields due to an edge dislocation in a linearly elastic isotropic film-substrate, while in [10] a complex potential approach was employed in conjunction with the image method to study the interaction between an edge dislocation and an elastic thin layered semi-infinite matrix.…”