#### Vol. 10, No. 3, 2015

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Interaction between a circular inclusion and a circular void under plane strain conditions

Vol. 10 (2015), No. 3, 317–330
DOI: 10.2140/jomms.2015.10.317
##### Abstract

The interaction force between a circular inclusion characterized by uniform eigenstrain and a nearby circular void is determined by evaluating the $J$-integral around the void. The Kienzler–Zhuping formula was used to determine the hoop stress along the boundary of the void in terms of the infinite-medium solution to the inclusion problem. Specific results are given for the inclusion with dilatational eigenstrain. The $M$-integrals around the void and inclusion are then evaluated, the former being proportional to the energy release rates associated with a self-similar expansion of the void. The energy rate associated with an isotropic expansion of the inclusion differs from the $M$-integral around the inclusion. The relationship between the two is derived. It is shown that the greater the distance from the void, the greater the energy associated with the presence of the inclusion and the greater the energy rate associated with its growth, which suggests that the presence of nearby free surfaces facilitates the eigenstrain transformations. The attraction exerted on a circular inclusion with a uniform shear eigenstrain by the free surface of a half-space is also evaluated. Peculiar variation of this configurational force with the distance between the inclusion and the free surface is noted and discussed.

##### Keywords
configurational force, conservation integrals, dilatation, eigenstrain, half-space, inclusion, plane strain, shear, void