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Seminar-Nonlinear dispersive wave motion in continuous and atomistic metamaterials: Insights into extreme dynamics
February 17 @ 11:30 am
EB III Room 2201
Mahmoud I. Hussein
Associate Professor, H. Joseph Smead Faculty Fellow
Department of Aerospace Engineering Sciences, University of Colorado Boulder
Wave motion lies at the heart of many disciplines in the physical sciences and engineering.
For example, problems and applications involving light, sound, heat or fluid flow are all likely to
involve wave dynamics at some level. In this seminar, in Part A, I will present our recent work
on a class of problems involving intriguing nonlinear wave phenomena‒large-deformation elastic
waves in solids; that is, the “large-on-small” problem. In Part B, I will present our recent
research on a new class of nanostructured semiconductors that enables superior thermoelectric
energy conversion properties.
In Part A, I will examine the propagation of a large-amplitude wave in an elastic one-
dimensional medium that is undeformed at its nominal state. In this context, the focus is on the
effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the
thickness is small compared to the wavelength, I will present an exact formulation for the
treatment of a nonlinearity in the strain-displacement gradient relation. The derivation starts with
an implementation of Hamilton’s principle and terminates with an expression for the finite-strain
dispersion relation in closed form. The derived relation is then verified by direct time-domain
simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-
breaking dispersion (by Fourier transformations), as well as by perturbation theory. The results
establish a perfect match between theory and simulation and reveal that an otherwise linearly
nondispersive elastic solid may exhibit dispersion solely due to the presence of a nonlinearity.
Next, I will present a method for extending this analysis to a continuous thin rod with
periodically embedded local resonators, i.e., an elastic metamaterial. This work provides insights
into the fundamentals of nonlinear wave propagation in solids, both natural and engineereda
problem relevant to a range of disciplines including dislocation and crack dynamics, geophysical
and seismic waves, material nondestructive evaluation, biomedical imaging, elastic metamaterial
engineering, among others.
In Part B, I will discuss thermoelectric materials–these are materials that convert heat into
electricity or vice versa. One challenging condition for these materials to be competitive is the
need to simultaneously exhibit good electrical conductivity and poor thermal conductivity. This
mix of properties, however, is extremely hard to find in existing materials. In this context, I will
present the concept of a locally resonant nanophononic metamaterial (NPM) . The NPM is
based on a silicon membrane (thin film) with a periodic array of nanoscale pillars standing on a
free surface. Heat is transported in this nanostructured material as a succession of propagating
vibrational waves, known as phonons. The atoms making up the minuscule pillars on their part
generate stationary vibrational waves. These two types of waves linearly interact causing a
substantial slowdown of the heat carrying phonons in the base membrane. This is manifested in
the form of reductions in the phonon group velocities at, in principle, every coupling point in the
phonon band structure. This in turn leads to a profound reduction in the overall lattice thermal
conductivity along the plane of the membrane. This novel phenomenon is practically
independent of the mechanisms concerned with the generation and carrying of electrical charge
and thus is not expected to affect the electrical conductivity. Thus this concept promises to
impact a wide range of applications as a high performing thermoelectric device would be of
immediate use for harvesting wasted heat in power plants, cars, computers, and solar panels, to
name a few examples.
Mahmoud Hussein is an Associate Professor and H. Joseph Smead Fellow at the
Department of Aerospace Engineering Sciences at the University of Colorado Boulder.
He is also an affiliate faculty at the Department of Applied Mathematics. After receiving
a BS degree from the American University in Cairo in 1994, he went on to receive an MS
degree from Imperial College in mechanical engineering (1995), and MS degrees in
applied mechanics (1999) and mathematics (2002) and a PhD degree in mechanical
engineering (2004) from the University of Michigan-Ann Arbor. Shortly afterwards, he
spent two years as a research associate at the University of Cambridge’s Department of
Engineering. His research focuses on the dynamics of materials and structures,
especially phononic crystals and locally resonant phononic metamaterials, at both the
continuum and atomistic scales. He is interested in physical phenomena governing these
systems, including the interplay between dispersion, resonance, dissipation and
nonlinearity, and works towards the development of relevant theoretical, mathematical
and computational treatments. Dr. Hussein is a recipient of a DARPA Young Faculty
Award in 2011 and an NSF CAREER Award in 2013. In 2011, he co-established the
Phononics conference series, which has since been serving as the world’s premier event
in the emerging field of phononics.