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Nano to Micro – Perspectives for Homogenization in Crystalline Solids
Author(s) -
Schröder Jörg,
Eidel Bernhard,
Brands Dominik,
Balzani Daniel
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210006
Subject(s) - microscale chemistry , homogenization (climate) , macro , nanoscopic scale , micro level , nano , continuum mechanics , nanotechnology , perspective (graphical) , computer science , finite element method , materials science , statistical physics , physics , mathematics , mechanics , engineering , artificial intelligence , thermodynamics , biodiversity , ecology , mathematics education , civil engineering , economic impact analysis , composite material , biology , programming language
This paper communicates perspectives and ideas for lengthscale‐transitions for metallic materials from nano over micro to macro. For micro‐macro transitions, the FE 2 ‐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)