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Homogenisation of a class of fourth order equations with application to incompressible elasticity

Published online by Cambridge University Press:  14 November 2011

G. A. Francfort
G. A. Francfort
Affiliation:
Laboratoire Central des Ponts et Chaussees, 58 Boulevard Lefebvre, 75732 Cedex 15, France
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Synopsis

Upon formalising an analogy between two-dimensional Stokes flow and two-dimensional isotropic conductivity, we exhibit a class of fourth order equations which behave “isomorphically” like isotropic conductivity from the standpoint of homogenisation and from that of corresponding bounding methods on possible effective behaviours. In particular, Lipton's result on the G-closure problem for mixtures of two incompressible elastic materials is recovered in the two-dimensional case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 25 - 46
Copyright
Copyright © Royal Society of Edinburgh 1992

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