Nano to Micro – Perspectives for Homogenization in Crystalline Solids

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Abstract

This paper communicates perspectives and ideas for lengthscale-transitions for metallic materials from nano over micro to macro. For micro-macro transitions, the FE2-method is described, where a top-down perspective manifests the need to introduce even finer-scaled information than typically considered on the microscale, such as e.g. atomistic details. In contrast, the description of the Quasi-Continuum method as an atomistic-continuum transition method naturally takes the perspective of a bottom-up approach, that starts at the nanoscale and aims at larger length scales by finite element techniques. We describe the main differences between the two multiscale frameworks referring to atomistics and those which pertain to continuum mechanics. Perspectives are proposed for combining and coupling the different frameworks in a consistent way. Finally we identify fields of applications, where nanoscale information is introduced to micro-models, either via sequential/hierarchical coupling or in concurrent frameworks. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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