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A partially debonded rigid hypotrochoidal inhomogeneity under uniform remote in-plane stresses

Xu Wang and Peter Schiavone
Vol. 20 (2025), No. 1, 95–106
DOI: 10.2140/jomms.2025.20.95
Abstract

We study the plane linear elasticity problem associated with a partially debonded rigid hypotrochoidal inhomogeneity embedded in an infinite isotropic elastic matrix subjected to uniform remote in-plane stresses. Using conformal mapping and analytic continuation, the original boundary value problem is reduced to a standard Riemann–Hilbert problem with discontinuous coefficients to which we derive an analytical solution. All the unknown constants appearing in the analytical solution are uniquely determined by solving a set of linear algebraic equations. We find elementary expressions for the displacement jumps across the debonded portion of the hypotrochoidal interface and the complex stress intensity factors at the two tips of the debonded portion. The two far-field constants related to the effective elastic moduli of composite materials containing partially debonded rigid hypotrochoidal inhomogeneities are also obtained.

Keywords
rigid hypotrochoidal inhomogeneity, interface curvilinear crack, complex stress intensity factor, conformal mapping, analytic continuation, Riemann–Hilbert problem, plane elasticity
Milestones
Received: 3 November 2024
Revised: 1 February 2025
Accepted: 11 February 2025
Published: 9 March 2025
Authors
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Shanghai 200237
China
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
Edmonton AB  T6G 1H9
Canada
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