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<p>Using Muskhelishvili’s complex variable formulation, we derive a closed-form solution to the two-dimensional Eshelby’s problem of a circular Eshelby inclusion undergoing uniform in-plane eigenstrains concentrically embedded in an isotropic elastic finite circular domain with a rigidly clamped or traction-free boundary. The interface between the inclusion and its surrounding material is assumed to be ‘spring-type imperfect’ with vanishing thickness permitting displacement jumps across the interface with the objective to simulate a damaged interface. Explicit expressions for the interior and exterior Eshelby tensors in the circular inclusion and in its supplement to the finite circular domain are obtained. A uniform elastic field of stresses and strains within the circular inclusion is achieved for a finite circular domain with a traction-free boundary.</p>

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A circular Eshelby inclusion with an imperfect interface in a finite domain

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Xu Wang,
  • Peter Schiavone

摘要

Using Muskhelishvili’s complex variable formulation, we derive a closed-form solution to the two-dimensional Eshelby’s problem of a circular Eshelby inclusion undergoing uniform in-plane eigenstrains concentrically embedded in an isotropic elastic finite circular domain with a rigidly clamped or traction-free boundary. The interface between the inclusion and its surrounding material is assumed to be ‘spring-type imperfect’ with vanishing thickness permitting displacement jumps across the interface with the objective to simulate a damaged interface. Explicit expressions for the interior and exterior Eshelby tensors in the circular inclusion and in its supplement to the finite circular domain are obtained. A uniform elastic field of stresses and strains within the circular inclusion is achieved for a finite circular domain with a traction-free boundary.