An elastic half-plane with a fixed cycloid wavy boundary


We present a rigorous analysis of the plane problem of an elastic half-plane with a fixed cycloid wavy boundary under biaxial tension using Muskhelishvili’s complex variable method. A closed-form expression for the pair of analytic functions characterizing the stresses and displacements in the elastic body is derived by means of analytic continuation. Furthermore, elementary expressions for the interfacial and hoop stresses along the cycloid interface and stress distributions along the right of an interface valley are obtained. For a cusped cycloid interface, the stresses exhibit the square root singularity at the cusp tips. The mode I stress intensity factor at a cusp tip is expediently extracted from the resulting analytic functions. The interfacial normal stress and hoop stress are constant along a cusped cycloid interface except at the isolated cusp tips.

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This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN – 2017 - 03716115112).

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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Schiavone, P. An elastic half-plane with a fixed cycloid wavy boundary. Z. Angew. Math. Phys. 72, 82 (2021).

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  • Cycloid interface
  • Stress concentration
  • Stress intensity factor
  • Anticrack
  • Complex variable method
  • Conformal mapping
  • Analytic continuation

Mathematics Subject Classification

  • 30B40
  • 30C20
  • 30E25
  • 35Q74
  • 74-10
  • 74A60
  • 74B05
  • 74G70
  • 74M25
  • 74S70