The objective of this investigation is to develop a rigorous method for the stress analysis of composite structures. It is anticipated that the results of this project will provide the necessary link between failure criteria related to stress fluctuations at the micro-scale and the averaged or macroscopic stress and strain that can be measured using strain gauges placed on the boundary of a composite structural component. The analysis will be carried out for periodic microstructures, random microstructures, and microstructures associated with G or H convergent sequences of solution operators to linear and nonlinear elliptic boundary value problems. In this project a ladder of increasingly sophisticated continuum models incorporating pre-stress and nonlinear elastic and elastic-plastic behavior will be incorporated into the stress assessment methodology. This is crucial as engineering and naturally occurring bio-composite structures are pre-stressed and often exhibit nonlinear elastic behavior near regions of high stress.
Composite materials are increasingly becoming the materials of choice for structural applications that require materials with high specific strength and stiffness. Modern design practice increasingly incorporates the use of load bearing components made up of composite substructures that are connected through bonded or bolted joints. This trend can be seen in the latest aircraft, ships and automobiles. Examples include the Airbus A300-600R and the Boeing 777 that feature a composite vertical tail. Components of the tail are bolted together and secured to the fuselage through clevises. It is of central interest to be able to understand and anticipate the modes of failure initiation in these structures. This requires fundamental understanding of how the mechanical loads are distributed across the hierarchy of scales seen in a typical composite structure. In this project the investigator and his colleagues will work on new rigorous and systematic methods for accurate stress assessment across length scales. These methods will be employed in novel computational methods for the design of hierarchical composite structures that hedge against failure. Here the opportunity for failure will be minimized through optimal tailoring of the composite microstructure.
