Multilevel optimal design of composite structures including materials with negative Poisson's ratio

Multilevel iterative optimal design procedures, horrowed from the theory of structural optimization by means of homogenization, are used in this paper for the optimal material design of composite material structures. The method is quite general and includes materials with appropriate microstructure, which may lead eventually to phenomenological, overall negative Poisson's ratios. The benefits of optimal structural design gained by this approach, together with the first attempts to explain the taskoriented microstructure of natural structures, are investigated by means of numerical examples, and simulation of, among others, human bones.

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