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On the strong closure of strains and stresses in linear elasticity

Published online by Cambridge University Press:  14 November 2011

Markku Miettinen  and
Uldis Raitums
Markku Miettinen
Affiliation:
Department of Mathematics, University of Jyvaskyla PO Box 35 FIN-40351 Jyväskylä, Finland
Uldis Raitums
Affiliation:
Institute of Mathematics and Computer Science, University of Latvia, LV-1459 Riga, Latvia
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Abstract

We consider the following special problem related to the optimal layout problems of materials: given two linear elastic materials, the elasticity tensors of which are C1 and C2, and a force f, find the strong closure of strains and stresses as the distribution of the materials varies, or, alternatively, find the sets of elasticity tensors which generate these strong closures. In this paper, it is shown that the local incompatibility conditions depending on C1, C2 and the local properties of strains or stresses completely characterize these sets. A connection to multiple-well problems is established.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 5 , 1999 , pp. 987 - 1009
Copyright
Copyright © Royal Society of Edinburgh 1999

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References

1Allaire, G. and Kohn, R. V.. Explicit optimal bounds on the elastic energy of a two-phase composite in two space dimensions. Q. Appl. Math. 51 (1993), 675–699.CrossRefGoogle Scholar
2Allaire, G. and Kohn, R. V.. Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Eur. J. Mech. A 12 (1993), 839–878.Google Scholar
3Avellaneda, M., Cherkaev, A. V., Gibiansky, L. V., Milton, G. W. and Rudelson, M.. A complete characterization of the possible bulk and shear moduli of planar polycrystals. J. Mech. Phys. Solids 44 (1996), 1179–1218.CrossRefGoogle Scholar
4Ball, J. M. and James, R. D.. Fine phase mixtures as minimizers of energy. Arch. Ration. Mech. Analysis 100 (1987), 13–52.CrossRefGoogle Scholar
5Bhattacharya, K., Firoozye, N. B., James, R. D. and Kohn, R. V.. Restrictions on microstructure. Proc. R. Soc. Edmb. A 124 (1994), 843–878.CrossRefGoogle Scholar