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Multi-scale computational homogenization: trends and challenges. (English) Zbl 1402.74107
Summary: In the past decades, considerable progress had been made in bridging the mechanics of materials to other disciplines, e.g. downscaling to the field of materials science or upscaling to the field of structural engineering. Within this wide context, this paper reviews the state-of-the-art of a particular, yet powerful, method, i.e. computational homogenization. The paper discusses the main trends since the early developments of this approach up to the ongoing contributions and upcoming challenges in the field.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74Q99 Homogenization, determination of effective properties in solid mechanics
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