General solution to the hygrothermoelastic interface problem with discontinuity between dissimilar anisotropic media

Abstract

A general solution to the hygrothermoelastic problem associated with an interface discontinuity between dissimilar anisotropic media is presented. The complex variable representation of Lekhnitskii [Theory of Elasticity of an Anisotropic Elastic Body (Holden-Day, San Francisco, CA, 1963)] is extended into the hygrothermoelastic problem by means of five complex functions including three stress functions, one temperature function, and one moisture function. A special technique of analytical continuation is used to deal with the continuous conditions of dissimilar media. Based on the Hilbert problem formulation, the linear relation between the boundaries of discontinuity can be derived into a type of Cauchy integral, which makes the solution in a compact version. The result shows that the heat or moisture flux exhibits an inverse square-root singularity at the tips of discontinuity while the nature of singularity of the hygrothermal stresses possess the same trig-log character as those obtained for the elastic problem.