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An RVE-based multiscale theory of solids with micro-scale inertia and body force effects

E.A. de Souza Neto, P.J. Blanco, P.J. Sánchez, R.A. Feijóo, Eduardo de Souza Neto De Souza Neto Orcid Logo

Mechanics of Materials, Volume: 80, Pages: 136 - 144

Swansea University Author: Eduardo de Souza Neto De Souza Neto Orcid Logo

Abstract

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 prov...

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Published in: Mechanics of Materials
ISSN: 0167-6636
Published: 2015
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa22542
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Abstract: 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.
Keywords: Multiscale; Inertia; Body forces; RVE; Hill–Mandel Principle; Homogenisation
College: College of Engineering
Start Page: 136
End Page: 144