Journal
MECHANICS OF MATERIALS
Volume 80, Issue -, Pages 136-144Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.mechmat.2014.10.007
Keywords
Multiscale; Inertia; Body forces; RVE; Hill-Mandel Principle; Homogenisation
Categories
Funding
- Brazilian agency CNPq
- Brazilian agency FAPERJ
- CONICET, Argentina [PIP 2013-2015 631]
- European Research Council under the FP7 programme (ERC) [320815]
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A multiscale theory of solids based on the concept of representative volume element (RVE) and accounting for micro-scale inertia and body forces is proposed. A simple extension of the classical Hill-Mandel Principle together with suitable kinematical constraints on the micro-scale displacements provide the variational framework within which the theory is devised. In this context, the micro-scale equilibrium equation and the homogenisation relations among the relevant macro-and micro-scale quantities are rigorously derived by means of straightforward variational arguments. In particular, it is shown that only the fluctuations of micro-scale inertia and body forces about their RVE volume averages may affect the micro-scale equilibrium problem and the resulting homogenised stress. The volume average themselves are mechanically relevant only to the macro-scale. (C) 2014 Elsevier Ltd. All rights reserved.
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