Geodesic
Asymptotics of anisotropic weakly curved inclusions in an elastic body
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 93-104

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We study boundary value problems that describeg the equilibrium for two-dimensional elastic bodies with thin weakly curved anisotropic inclusions. The presence of an inclusion means the existence of a crack between the inclusion and the elastic matrix. Nonlinear boundary conditions in the form of inequalities are imposed on the crack faces to prevent their mutual penetration, which leads to formulating the problems as problems with unknown contact domain. Limit passages are investigated over the rigidity parameters of the thin inclusions. In particular, we construct the models obtained by letting the rigidity parameters tend to infinity and analyze their properties.
Keywords: thin inclusion, elastic body, crack, nonlinear boundary condition, limit model. 
@article{SJIM_2017_20_1_a9,
     author = {A. M. Khludnev},
     title = {Asymptotics of anisotropic weakly curved inclusions in an elastic body},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {93--104},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a9/}
}
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A. M. Khludnev. Asymptotics of anisotropic weakly curved inclusions in an elastic body. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 93-104. http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a9/