Mathematics - Florida State University
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Robert P. Lipton



Speaker: Robert P. Lipton
Title: Microstructure and Properties of Composites
Affiliation: Louisiana State University
Date: Friday, March 24, 2006.
Place and Time: Room 101 - Love Building, 3:35-4:30 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.

Abstract. We introduce methods for quantifying load transfer between length scales inside composite structures. This is motivated by the fact that many composite structures are hierarchical in nature and are made up of substructures distributed across several length scales. Examples include aircraft wings made from fiber reinforced laminates and naturally occurring structures like bone. From the perspective of failure initiation it is crucial to quantify load transfer between length scales. The presence of geometrically induced stress or strain singularities at either the structural or substructural scale can have influence across length scales and initiate nonlinear phenomena that result in overall structural failure. We examine load transfer for statistically defined microstructures. New mathematical objects beyond the well known effective elastic tensor are presented that facilitate a quantitative description of the load transfer in hierarchical structures. Several concrete physical examples are provided illustrating how these quantities can be used to quantify the stress and strain distribution inside multi-scale composite structures


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Last modified: Friday March 10th, 2006