Composite properties and microstructure

Monday, February 7, 2005 - 11:00am - 12:00pm
EE/CS 3-180
Robert Lipton (Louisiana State University)
We begin with an overview of composite materials and their effective properties. Most often only a statistical description of the microstructure is available and one must assess the effective behavior in terms of this limited information. To this end approximation schemes such as effective medium schemes and differential schemes are discussed. Variational methods for obtaining tight bounds on effective properties for statistically defined microgeometries are reviewed. Formulas for the effective properties of extremal microgeometries are presented. Such microgeometries include layered materials and sphere and ellipsoid assemblages.

Next we focus on physical situations where the interface between component materials play an important role in determining effective transport properties. This is relevant to the study of nanostructured materials in which the interface or interphase between materials can have a profound effect on overall transport properties. Variational methods and bounds are presented that illuminate the effect of particle size and shape distribution inside random composites with coupled heat and mass transport on the interface.

We conclude by introducing methods for quantifying load transfer between length scales. 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 physical examples are provided illustrating how these quantities can be used to quantify the stress and strain distribution inside multi-scale composite structures.