Journal
COMPUTATIONAL MATERIALS SCIENCE
Volume 45, Issue 4, Pages 1073-1080Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.commatsci.2009.02.025
Keywords
Asymptotic expansion homogenisation; Formal mathematics; Composite materials; Periodic microstructure; Localisation; Finite element method
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The asymptotic expansion homogenisation method is an excellent methodology to model physical phenomena on media with periodic microstructure and a useful technique to study the mechanical behaviour of structural components built with composite materials. In the first part of this work the authors present a detailed form of the mathematical formulation of the asymptotic expansion homogenisation for linear elasticity problems, as well the explicit mathematical equations that characterise the microstructural stress and strain fields associated with a given macrostructural equilibrium state - the localisation procedure. From this mathematical basis, the authors also present the numerical equations resulting from the finite element modelling of the asymptotic expansion homogenisation method in linear elasticity. (C) 2009 Elsevier B.V. All rights reserved.
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