Abstract
Homogenization is a procedure that allows one to replace a precise description of highly inhomogeneous media by an averaged one, an equivalent homogeneous media. The homogenization problem has a long and rich history which began in the first quarter of the nineteenth century. Relatively recently it was recognized that the homogenization problem has an asymptotic nature. This brought a complete understanding of the static behavior of periodic structures and a considerable insight for that of random structures. In this chapter the homogenization problems are considered in cases when they admit a variational formulation.
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© 2009 Springer-Verlag Berlin Heidelberg
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Berdichevsky, V.L. (2009). Homogenization. In: Variational Principles of Continuum Mechanics. Interaction of Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88469-9_4
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DOI: https://doi.org/10.1007/978-3-540-88469-9_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88468-2
Online ISBN: 978-3-540-88469-9
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