Session: 02-10: Design, Modeling, and Behavior of Functional and Shape Memory Materials and Composites

Paper Number: 111183

111183 - Multifractal Behavior and Material Complexity in Functional Materials 

Functional materials exhibit complexity in properties and structure which manifest across broad ranges of space and time scales leading to rich performance attributes.  These performance attributes are often difficult to predict requiring vast computing resources that span many time and length scales.  One methodology we propose to efficiently address material complexity is by applying fractal mathematics.  Fractals are known as geometric entities which repeat their structure over all scales in either space or time.  Classic examples include the Sierpinski triangle, the Koch curve, and the Menger sponge.  All of these cases describe geometries that have dimensions in-between the conventional integer 1D lines, 2D areas, or 3D solids.  We discuss how materials can often be approximated to have such fractal geometry which creates constraints on the flux of heat, chemical concentrations, electromagnetic fields and stresses.  However, real materials typically do not follow an exact fractal dimension nor do the properties map perfectly to a set of properties without uncertainty.  In this study, we discuss how the Renyi information entropy and associated entropy dimension help guide characterization of multifractal material structure and how this is related to fractional order properties.  We will describe developments using entropy dynamics to relate multifractal material constraints to thermodynamics and kinetics that govern a broad class of material properties applicable to functional materials.

Presenting Author: Mario Carvajal Florida A&M-Florida State University

Presenting Author Biography: Mario Carvajal is a PhD student studying the relationships between fractal structure and fractional order properties in materials.