Explicit solutions for the elastic and thermoelastic fields with a rigid circular-arc inclusion

Abstract

A general solution to the elastic and thermoelastic problems with a rigid circular-arc inclusion is presented. The proposed analysis is based upon the complex variable theory dealing with sectionally holomorphic functions which is reduced to the solution of the Hilbert problem. It is indicated that both the stress and thermal stress fields near the inclusion tip possess a square-root singularity similar to that for the corresponding crack problem. In analogy to the stress intensity factors defined for crack problem, stress singularity coefficients are introduced in this paper to characterize the near tip fields. Complete stress fields and the corresponding stress singularity coefficients as the circular-arc inclusion are under uniform remote load, concentrated force and uniform heat flux are given. Failure initiation of an infinite plate embedded with a rigid arc inclusion under different loading conditions is also discussed.