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Abstract
The object of discussion of this article is the fourth-order tensor d introduced as a set of macro coefficients associated with fine periodic structures. Focus of attention is its variation on laminated microstructures. Complete bounds are obtained on its quartic form along with the corresponding optimal structures. Differences with corresponding results for the homogenized matrix are pointed out. Using Blossoming Principle, it is shown that d is not negative in the sense of Legendre–Hadamard, even though its quartic form is negative.
Acknowledgements
The authors thank the anonymous referee for his/her comments on our work. Their suggestions are noted and will be addressed in a future work. C. Conca thanks the MICDB for partial support through Grant ICM P05-001-F, Fondap-Basal-Conicyt. J. San Martín was partially supported by Grant Fondecyt 1090239 and BASAL-CMM Project. L. Smaranda was partially supported by Grant PN-II-RU-TE-2011-3-0059 of CNCS-UEFISCDI. M. Vanninathan thanks French CNRS and Institut de Mathématiques de Toulouse for hospitality and support for his stay in France during which this work was carried out.