The heterogenization technique, recently developed by the authors, is applied to the problem, in antiplane elastostatics, of two circular inclusions of arbitrary radii and of different shear moduli, and perfectly bonded to a matrix, of infinite extent, subjected to arbitrary loading. The solution is formulated in a manner which leads to some exact results. Universal formulae are derived for the stress field at the point of contact between two elastic inclusions. It is also discovered that the difference in the displacement field, at the limit points of the Apollonius family of circles to which the boundaries of the inclusions belong, is the same for the heterogeneous problem as for the corresponding homogeneous one. This discovery leads to a universal formula for the average stress between two circular holes or rigid inclusions. Moreover, the asymptotic behavior of the stress field at the closest points of two circular holes or rigid inclusions approaching each other is also studied and given by universal formulae, i.e., formulae which are independent of the loading being considered.
Further Aspects of the Elastic Field for Two Circular Inclusions in Antiplane Elastostatics
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Honein, E., Honein, T., and Herrmann, G. (December 1, 1992). "Further Aspects of the Elastic Field for Two Circular Inclusions in Antiplane Elastostatics." ASME. J. Appl. Mech. December 1992; 59(4): 774–779. https://doi.org/10.1115/1.2894041
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