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There are now books available which contain excellent expositions of the theory of homogenization and its applications to the natural sciences and engineering. An exposition of the mathematical aspects of the homogenization theory can be found in Bensoussan et al. (1978), Jikov et al. (1994), Cioranescu and Donato (2000). Applications of the homogenization theory to problems in mechanics and physics can be found in Kalamkarov and Kolpakov (1997), Milton (2002). The homogenization method is applied to the design of materials with new and unusual properties Bendsøe and Sigmund (2004). The books Sanchez-Palencia (2025), Oleinik et al. (1962), Lewinski and Telega (2000), Gluzman et al. (2018), Drygas et al. (2019) present a combination of mathematical theory with the study of applied problems. There exist review papers on the subject, see, e.g., Sanchez-Palencia (1986), Kanout et al. (2009), Allaire et al. (2019), Charalambakis (2010), Gloria (2012), Nandakumaran (2007).

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Homogenization Method in the Linear Elasticity. Basic Approaches

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  • 发表日期：

    2026年

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  • Alexander Kolpakov

摘要

There are now books available which contain excellent expositions of the theory of homogenization and its applications to the natural sciences and engineering. An exposition of the mathematical aspects of the homogenization theory can be found in Bensoussan et al. (1978), Jikov et al. (1994), Cioranescu and Donato (2000). Applications of the homogenization theory to problems in mechanics and physics can be found in Kalamkarov and Kolpakov (1997), Milton (2002). The homogenization method is applied to the design of materials with new and unusual properties Bendsøe and Sigmund (2004). The books Sanchez-Palencia (2025), Oleinik et al. (1962), Lewinski and Telega (2000), Gluzman et al. (2018), Drygas et al. (2019) present a combination of mathematical theory with the study of applied problems. There exist review papers on the subject, see, e.g., Sanchez-Palencia (1986), Kanout et al. (2009), Allaire et al. (2019), Charalambakis (2010), Gloria (2012), Nandakumaran (2007).