The purpose of this "high-risk, high-payoff" research is to develop, and make known to the research community, a new approach to modeling aging, degradation and fracture of polymers. This will be accomplished by performing some preliminary research using novel tools of geometry and analysis that are evolving from the relatively new mathematical fields of fractals and fraction calculus. The PI will attempt to formulate a new, encompassing field theory, "fractal continuum mechanics," that can be used to bridge size scales in the study of the mechanics," that can be used to bridge size scales in the study of the mechanics of materials. This formulation will allow for the introduction of morphological features at scales finer than the usual macroscale at which ordinary machine and structural analysis and design takes place. It is necessary to take such "micro" features into account in order to more thoroughly understand (and, thereby, more precisely model) aging, degradation and fracture of materials.
