Fractals in Mechanics of Bio-, Geo-, and Technological Materials
Research in materials and structures continually seeks more accurate methods of assessment. The usual approach has been to generalize conventional continuum mechanics to describe static and dynamic responses of constitutive behaviors (e.g., heat conduction, thermo-viscoelasticity, elasto-plasticity, various coupled-field phenomena). Volumes of research on fracture mechanics, fatigue, and reliability have been carried out to assess states of growth, inelasticity, and damage.
During his Center appointment, Professor Ostoja-Starzewski will adopt a new approach to this area, focusing on why fractal patterns are displayed by a great many materials and how these patterns can be linked with material parameters. He will address two main questions: (a) How and why do fractal patterns form in living and inanimate materials? and (b) What methods of solution can be brought to bear on initial/boundary-value problems?
The project involves a number of components and challenges. Professor Ostoja-Starzewski will seek a deeper understanding of the characteristics and behavior of fractal patterns in materials at elastic-inelastic transition states. He will also seek to generalize the current toolbox of solution methods for initial/boundary-value problems to materials with fractal patterns; and to connect fractal material structures to fractional derivatives in viscoelastic materials and to anomalous heat conduction.
There is potential here, for example, for rapidly assessing the damage state in a wall of concrete through inspection of the fractal dimension of its crack pattern. Indeed, the research results should have broad application to many kinds of bio-, geo-, and technological materials.