MATHEMATICS COLLOQUIUM
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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