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Uniform stress field inside a non-parabolic open inhomogeneity interacting with a mode III crack

Wang X., Schiavone P.

Archives of Mechanics

2021

Vol. 73, nr 1

67--81

Using conformal mapping techniques, analytic continuation and the theory of Cauchy singular integral equations, we prove that a non-parabolic open inhomogeneity embedded in an elastic matrix subjected to a uniform remote anti-plane stress nevertheless admits an internal uniform stress field despite the presence of a finite mode III crack in its vicinity. Our analysis indicates that: (i) the internal uniform stress field is independent of the specific shape of the inhomogeneity and the presence of the finite crack; (ii) the existence of the finite crack plays a key role in the non-parabolic open shape of the inhomogeneity and in the non-uniform stresses in the surrounding matrix; (iii) the two-term asymptotic expansion at infinity of the stress field in the matrix is independent of the presence of the finite crack. Detailed numerical results are presented to demonstrate the proposed theory.

Two imperfectly bonded half-planes with an arbitrary inclusion subject to linear eigenstrains in anti-plane shear

Sudak L. J.

Archives of Mechanics

2019

Vol. 71, nr 6

615--631

An analytic solution to the anti-plane problem of an arbitrary inclusion within an elastic bimaterial under the premise of linear eigenstrains is developed. The bonding along the bimaterial interface is considered to be homogeneously imperfect. The boundary value problem is reduced to a single nonhomogeneous first order differential equation for an analytic function prescribed in the lower half-plane where the inclusion is located. The general solution is given in terms of the imperfect interface parameter and an auxiliary function constructed from the conformal mapping function. In particular, the solution obtained for a circular inclusion demonstrates that the imperfect interface together with the prescribed linear eigenstrains have a pronounced effect on the induced stress field within the inclusion and show a strong non-uniform behaviour especially when the inclusion is near the imperfect interface. Specific solutions are derived in a closed form and verified with existing solutions.