Singularities Interacting With a Coated Circular Inhomogeneity Revisited

Singularities interacting with a coated circular inhomogeneity are analyzed with the method of analytic continuation and the Schwarz–Neumann’s alternating technique. It is shown that the solution for singularities in a homogeneous medium can be used as a building block of the solution for the same singularities interacting with a coated circular inclusion. The obtained solutions have series forms independent of any specific information about singularities, and thus they can be interpreted as general solutions for a variety of singularities.

Thermoelastic Interaction Between Singularities and Interfaces in an Anisotropic Trimaterial

The method of analytic continuation and Schwarz-Neumann’s alternating technique were applied to the thermoelastic interaction problems of singularities and interfaces in an anisotropic “trimaterial,” which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. It was assumed that the linear thermoelastic materials are under general plane deformations in which the plane of deformation is perpendicular to the planes of the two parallel interfaces. The author then showed that by alternately applying the method of analytic continuation across two parallel interfaces the solution for the thermoelastic singularities in an anisotropic trimaterial can be obtained in a series form from a solution for the same singularities in a homogeneous anisotropic medium.

Stress Analysis of a Elastic Cracked Layer Bonded to a Viscoelastic Substrate

The effect of a viscoelastic substrate on an elastic cracked layer under an in-plane concentrated load is solved and discussed in this study. Based on a correspondence principle, the viscoelastic solution is directly obtained from the corresponding elastic one. The elastic solution in an anisotropic trimaterial is solved as a rapidly convergent series in terms of complex potentials via the successive iterations of the alternating technique in order to satisfy the continuity condition along the interfaces between dissimilar media. This trimaterial solution is then applied to a problem of a thin layer bonded to a half-plane substrate. Using the standard solid model to formulate the viscoelastic constitutive equation, the real time stress intensity factors can be directly obtained by performing the numerical calculations. The results obtained in this paper are useful in studying the problem with defects where a crack is assumed to exist in an elastic body that is bonded to a viscoelastic substrate.