Quantifying Complexity to Advance the Discovery and Design of Next Generation Smart Materials
Abstract
MandelbrotÕs ground breaking concept of a fractalÐa self-similar object that is scale-free, has been hypothesized as a design principle in physiology, information theory, and statistical physics, but much less emphasis has been placed on how it may advance materials. One example is cerebral Blood Flow (CBF) which has advanced auto-regulation to provide the right amount of oxygen and nutrients to the brain in the presence of variations in blood pressure and heart beats. It has been shown that the rates of fluctuation of CBF follow a multifractal time seriesÐnot a regular, Gaussian, or monofractal distribution about some mean flow. This is fascinating because healthy people that exhibit this multifractal distribution have low susceptibility to migraines while those who follow a CBF monofractal series often suffer from severe migraines. The origins of these differences are believed to be associated with superior adaptation to different flows and fluctuations in blood pressure. This observation raises interesting questions about similar behavior that the PI has recently been investigating in multifunctional materials and adaptive structures. Whether the system is based on biology, information, physics, or materials they all can be described by a complex web that often has interactions that follow a power law. In these complex systems, power law behavior is much more prevalent than Gaussian processes. In mechanics, power law constitutive models are often very good at predicting hyperelasticity in elastomers and strain hardening plasticity in metals. These power law relations have not been rigorously evaluated to fundamentally understand structure-function relationships like in biology. Examples including building multiscale relations between phase, domain, grain structure distributions and properties such as modulus, strength, piezoelectricity, and photostriction. The PI has recently demonstrated this connection in dielectric elastomers where a fractal polymer structure was related to fractional viscoelasticity. Other cases are believed to occur in hard ferroic materials (e.g., ferroelectrics, ferromagnetics, SMAs). For example, complex ferroic domain structures evolve at complicated rates and prior observations have hinted at fractal domain patterns but have not connected fractal geometry to fractional material properties. Making these connections plays an important role in both property prediction and guidelines for material processing and additive manufacturing. We propose to understand structure-property connections in a unified manner across a broad spectrum of multifunctional materials and structures. New concepts are envisioned that build upon fractional mechanics, fractional/fractal dynamics, and uncertainty quantification that will push the frontier beyond our conventional thinking of multifunctional materials and structures. The connections between fractional properties and the underlying fractal structure is expected to open up a new design paradigm that embraces complexity to create new classes of smart materials that can efficiently operate, auto-regulate, and maximize structural reliability through novel adaptations. Whereas we will investigate a broad spectrum of materials in the literature, we will also conduct experiments on select multifunctional materials to validate the theory. We plan to validate the theory and computations on a new class of photoresponsive nanocomposites that take advantage of complex photochemical transport between sensitizer molecules, semiconducting quantum dots, and photoresponsive chromophores within a stilbene-quantum dot polymer network. These materials offer a prototypical material to study complex multiphysics energy transport associated with photochemical singlet and triplet excitations, triplet energy transfer that drives photoisomerization, heat generation, photostriction, and viscoelasticity.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 31, 2020
- Source ID
- W911NF2010299
Entities
People
- William S Oates
Organizations
- Army Contracting Command
- Florida A&M University
- Office of the Secretary of Defense