This brief note presents a rigorous proof of the general solutions obtained by Aderogba [1977, “On Eigenstresses in Dissimilar Media,” Philos. Mag., 35, pp. 281–292] for a defect in elastic bimaterial solids. The derivation is based on the fact that some derivative and integral forms of the biharmonic functions are also biharmonic. The associated solutions can be expressed as the linear combinations of these biharmonic functions and their unknown coefficients can be determined by the interface conditions. It is found that the coefficients only depend on the contrasts of material constants across the interface.
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A Note on the Derivation of Plane-Strain Elastic Green’s Functions for Bimaterial Solids
Zhang, X. (July 27, 2009). "A Note on the Derivation of Plane-Strain Elastic Green’s Functions for Bimaterial Solids." ASME. J. Appl. Mech. November 2009; 76(6): 064503. https://doi.org/10.1115/1.3112746
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