Geodesic
Invariant integrals in the plane elasticity problem for bodies with rigid inclusions and cracks
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 99-109

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We consider the plane elasticity problem for a body with a rigid inclusion and a crack along the boundary between the elastic matrix and rigid inclusion. We show that this problem possesses $J$- and $M$-invariant integrals. In particular, we construct an invariant integral of Cherepanov–Rice type for straight cracks.
Keywords: invariant integrals, rigid inclusion, crack, derivative of the energy functional, Cherepanov–Rice integral. 
@article{SJIM_2012_15_1_a9,
     author = {E. M. Rudoǐ},
     title = {Invariant integrals in the plane elasticity problem for bodies with rigid inclusions and cracks},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {99--109},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a9/}
}
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E. M. Rudoǐ. Invariant integrals in the plane elasticity problem for bodies with rigid inclusions and cracks. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 99-109. http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a9/