Abstract
AbstractBased on the idea of the Cosserats at the beginning of the 20th century, Mindlin, Tiersten, Toupin, Rivlin, Green, Trostel et al. developed theories for generalized continua in the 1960s. Currently, such theories for continua with microstructure are extended in micromechanics, fluid mechanics, etc. by various scientists. All such theories follow the same purpose of a more precise material description embedded in a continuum theory. In the following article the well‐known Cosseratcontinuum is used for the calulation of strains and stresses in Representative Volume Elements (RVEs) with arbitrary stiffness distribution and periodic boundary conditions. Restricting the problem to small displacements and linear elasticity results in linear equations of motion, that can be solved iteratively by means of Fourier series. It is pointed out that other types of generalized continua can be analyzed in the same manner. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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