Geodesic
Griffith's Formula and Cherepanov--Rice's Integral for a Plate with a Rigid Inclusion and a Crack
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 2, pp. 98-117

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The model problem for a plate with rigid inclusion, describing a biharmonic equation, is considered. There is a crack between the inclusion and an elastic part of the plate. The derivative of the energy functional with respect to a small perturbation of the crack length is found. Moreover such derivative can be represented by an invariant integral. The derivative and the invariant integral are corresponding analogues of Griffith's formula and Cherepanov–Rice's integral in the brittle fracture theory.
Keywords: plate, crack, rigid inclusion, Griffith's criteria, derivative of the energy functional, nonsmooth domain. 
@article{VNGU_2010_10_2_a8,
     author = {E. M. Rudoy},
     title = {Griffith's {Formula} and {Cherepanov--Rice's} {Integral} for a {Plate} with a {Rigid} {Inclusion} and a {Crack}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {98--117},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_2_a8/}
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E. M. Rudoy. Griffith's Formula and Cherepanov--Rice's Integral for a Plate with a Rigid Inclusion and a Crack. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 2, pp. 98-117. http://geodesic.mathdoc.fr/item/VNGU_2010_10_2_a8/