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On the strong closure of strains and stresses in linear elasticity

  • Markku Miettinen (a1) and Uldis Raitums (a2)


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.



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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), 675699.
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), 839878.
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), 11791218.
4Ball, J. M. and James, R. D.. Fine phase mixtures as minimizers of energy. Arch. Ration. Mech. Analysis 100 (1987), 1352.
5Bhattacharya, K., Firoozye, N. B., James, R. D. and Kohn, R. V.. Restrictions on microstructure. Proc. R. Soc. Edmb. A 124 (1994), 843878.


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