We obtain an integral representation of an energy for structured deformations of continua in the space of functions of bounded variation, as a first step to the study of asymptotic models for thin defective crystalline structures, where phenomena as slips, vacancies and dislocations prevent the effectiveness of classical theories.

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AbstractΓ-convergence techniques combined with techniques of 2-scale convergence are used to give a characterization of the behavior as ε goes to zero of a family of integral functionals defined onZ Ω

The purpose of this article is to study the behavior of a heterogeneous thin film whose microstructure oscillates on a scale that is comparable to that of the thickness of the domain. The argument is based on a 3D-2D dimensional reduction through a Γ-convergence analysis, techniques of two-scale convergence and a decoupling procedure between the oscillating variable and the in-plane variable.

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In this work we briefly describe the theory of (first-order) structured deformations of continua as well as the variational problems arising from this theory.2000 Mathematics Subject Classification. 4E15, 49J45, 28A33, 46T30.