The interaction force between a circular inclusion characterized by uniform
eigenstrain and a nearby circular void is determined by evaluating the
-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
-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
-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.
Departments of NanoEngineering and
Mechanical and Aerospace Engineering
University of California, San Diego
9500 Gilman Drive
La Jolla, CA 92093-0411
United States
