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.
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