Abstract
In previous chapters, the assumption of scale separation was adopted. When this assumption does not hold, e.g., when the size of heterogeneities are not much smaller than local dimensions of the structures, classical homogenization methods fail to describe the local fields and up to a certain precision even the global response. More precisely, lack of scale separation occurs when the wavelength associated with the strain and stress fields at the microscale is of the same order of magnitude as the wavelength of the prescribed loads or the characteristic dimensions of the structure [1].
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Yvonnet, J. (2019). When Scales Cannot Be Separated: Direct Solving of Heterogeneous Structures with an Advanced Multiscale Method. In: Computational Homogenization of Heterogeneous Materials with Finite Elements. Solid Mechanics and Its Applications, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-030-18383-7_8
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