Geodesic
Problems on thin inclusions in a~two-dimensional viscoelastic body
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 2, pp. 66-78

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Under study are the equilibrium problems for a two-dimensional viscoelastic body with delaminated thin inclusions in the cases of elastic and rigid inclusions. Both variational and differential formulations of the problems with nonlinear boundary conditions are presented; their unique solvability is substantiated. For the case of a thin elastic inclusion modelled as a Bernoulli–Euler beam, we consider the passage to the limit as the rigidity parameter of the inclusion tends to infinity. In the limit it is the problem about a thin rigid inclusion. Relationship is established between the problems about thin rigid inclusions and the previously considered problems about volume rigid inclusions. The corresponding passage to the limit is justified in the case of inclusions without delamination.
Keywords: variational inequality, viscoelasticity, nonpenetration conditions, elastic inclusion, rigid inclusion, thin inclusion, nonlinear boundary conditions. 
@article{SJIM_2018_21_2_a5,
     author = {T. S. Popova},
     title = {Problems on thin inclusions in a~two-dimensional viscoelastic body},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {66--78},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_2_a5/}
}
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T. S. Popova. Problems on thin inclusions in a~two-dimensional viscoelastic body. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 2, pp. 66-78. http://geodesic.mathdoc.fr/item/SJIM_2018_21_2_a5/