Introduction to Homogenization Analysis

We outline the essential features of a multiscale homogenization analysis. A problem of a one-dimensional elastic bar is given as an example. 

The topic of homogenization has been extensively discussed in the literature in the context of multiphase components and heterogeneous media that are either microscopically periodic or non-periodic (Sanchez-Palencia 1980 Bakhvalov Panasenko 1984 Ene and Polisevski 1987 Hornung 1997 Milton 2002 Torquato 2002 Dormieux et al. 2006). 

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