Geodesic
On homogenization of a~variational inequality for an~elastic body with periodically distributed fissures
Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 291-306

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We study the problem of small deformations of an elastic body with periodically distributed fissures, where one-sided constraints are imposed on the sides of the fissures; this problem is equivalent to a variational inequality. We prove that if the linear size of the period of the distribution of the fissures tends to zero, then the solutions of this problem converge in the $L^2$-norm to the solution of the homogenized problem, which is a non-linear boundary-value problem of elasticity theory for a domain without fissures. 
@article{SM_2000_191_2_a5,
     author = {S. E. Pastukhova},
     title = {On homogenization of a~variational inequality for an~elastic body with periodically distributed fissures},
     journal = {Sbornik. Mathematics},
     pages = {291--306},
     publisher = {mathdoc},
     volume = {191},
     number = {2},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_2_a5/}
}
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S. E. Pastukhova. On homogenization of a~variational inequality for an~elastic body with periodically distributed fissures. Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 291-306. http://geodesic.mathdoc.fr/item/SM_2000_191_2_a5/