Mathematical Sciences: The Overall Elastic Properties of Transversely Isotropic Composites

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8907658 Lipton This project will apply recent advances in the mathematical analysis of composite materials to obtain the effective elastic properties of transversely isotropic composite materials. The goal is to obtain new bounds that correlate the six elastic moduli for transverse isotropic composites made from two isotropic elastic materials in prescribed proportions. The overall plan of attack is twofold: the set of all finite rank laminates exhibiting transverse isotropy will be characterized. Then bounds will be derived using the fact that laminates are extremal in the set of composites. The behavior of composite materials is of fundamental technological importance. Composites have been widely used in structural optimization to design strong but lightweight components for use in aerospace and aviation.