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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2000 Volume 191, Number 2, Pages 149–164 (Mi sm456)

This article is cited in 7 papers

On homogenization of a variational inequality for an elastic body with periodically distributed fissures

S. E. Pastukhova

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: 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.

UDC: 517.953

MSC: Primary 35B27; Secondary 35B40, 35C20, 73B27

Received: 06.07.1999

DOI: 10.4213/sm456


 English version:
Sbornik: Mathematics, 2000, 191:2, 291–306

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