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Series: GT-MAP Seminars

Robotic locomotive mechanisms designed to mimic those of their biological counterparts differ from traditionally engineered systems. Though both require overcoming non-holonomic properties of the interaction dynamics, the nature of their non-holonomy differs. Traditionally engineered systems have more direct actuation, in the sense that control signals directly lead to generated forces or torques, as in the case of rotors, wheels, motors, jets/ducted fans, etc. In contrast, the body/environment interactions that animals exploit induce forces or torque that may not always align with their intended direction vector.Through periodic shape change animals are able to effect an overall force or torque in the desired direction. Deriving control equations for this class of robotic systems requires modelling the periodic interaction forces, then applying averaging theory to arrive at autonomous nonlinear control models whose form and structure resembles that of traditionally engineered systems. Once obtained, classical nonlinear control methods may be applied, though some attention is required since the control can no longer apply at arbitrary time scales.The talk will cover the fundamentals of averaging theory and efforts to identify a generalized averaging strategy capable of recovering the desired control equations. Importantly, the strategy reverses the typical approach to averaged expansions, which significantly simplifies the procedure. Doing so provides insights into feedback control strategies available for systems controlled through time-periodic signals.

Series: GT-MAP Seminars

The first part of this talk will review our
recent efforts on the electroelastodynamics of smart structures for
various applications ranging from nonlinear energy harvesting,
bio-inspired actuation, and acoustic power transfer to elastic wave
guiding and vibration attenuation via metamaterials. We will discuss
how to exploit nonlinear dynamic phenomena for frequency bandwidth
enhancement to outperform narrowband linear-resonant devices in
applications such as vibration energy harvesting for wireless
electronic components. We will also cover inherent nonlinearities
(material and internal/external dissipative), and their interactions
with intentionally designed nonlinearities, as well as electrical
circuit nonlinearities. Electromechanical modeling efforts will be
presented, and approximate analysis results using the method of
harmonic balance will be compared with experimental measurements. Our
recent efforts on phononic crystal-enhanced elastic wave guiding and
harvesting, wideband vibration attenuation via locally resonant
metamaterials, contactless acoustic power transfer, bifurcation
suppression using nonlinear circuits, and exploiting size effects via
strain-gradient induced polarization (flexoelectricity) in
centrosymmetric elastic dielectrics will be summarized.
The second part of the talk, which will be given by Chris Sugino (Research Assistant and PhD Student), will be
centered on low-frequency vibration attenuation in finite structures
by means of locally resonant elastic and electroelastic
metamaterials. Locally
resonant metamaterials are characterized by bandgaps at wavelengths
that are much larger than the lattice size, enabling low-frequency
vibration/sound attenuation. Typically, bandgap analyses and
predictions rely on the assumption of waves traveling in an infinite
medium, and do not take advantage of modal representations commonly
used for the analysis of the dynamic behavior of finite structures.
We will present a novel argument for estimating the locally resonant
bandgap in metamaterial-based finite structures (i.e. meta-structures
with prescribed boundary conditions) using modal analysis, yielding a
simple closed-form expression for the bandgap frequency and size. A
method for understanding the importance of the resonator locations
and mass distribution will be discussed in the context of a Riemann
sum approximation of an integral. Numerical
and experimental results will be presented regarding the effects of
mass ratio, non-uniform spacing of resonators, and parameter
variations among the resonators. Electromechanical
counterpart of the problem will also be summarized for piezoelectric
structures.

Series: GT-MAP Seminars

This talk contains two parts. First I will discuss our work related
to causal modeling in hybrid systems. The idea is to model jump
conditions as caused by impulsive inputs. While this is well defined for
linear systems, the notion of impulsive inputs poses problems in the
nonlinear case. We demonstrate a viable approach based on nonstandard
analysis.
The second part deals with dynamical systems with delays. First I will
show an application of the maximum principle to a delayed resource
allocation problem in population dynamics solving a problem in the model
of a bee colony cycle. Next I discuss some problems regarding causality
in systems with varying delays. These problems relate to the
well-posedness (existence and uniqueness) and causality of the
mathematical models for physical phenomena, and illustrate why one
should consider the physics first and then the mathematics. Finally, I
consider the post Newtonian problem as a problem with state dependent
delay.
Einstein’s field equations relate space time geometry to matter and
energy distribution. These tensorial equations are so unwieldy that
solutions are only known in some very specific cases. A
semi-relativistic approximation is desirable: One where space-time may
still be considered as flat, but where Newton’s equations (where gravity
acts instantaneously) are replaced by a post-Newtonian theory,
involving propagation of gravity at the speed of light. As this
retardation depends on the geometry of the point masses, a dynamical
system with state dependent delay results, where delay and state are
implicitly related. We investigate several problems with the
Lagrange-Bürman inversion technique and perturbation expansions.
Interesting phenomena (entrainment, dynamic friction, fission and
orbital speeds) not explainable by the Newtonian theory emerge.
Further details on aspects of impulsive systems and delay systems will
be elaborated on by Nak-seung (Patrick) Hyun and Aftab Ahmed
respectively.

Series: GT-MAP Seminars

Talk by Shuozhi Xu,

Title: Algorithms and Implementation for the Concurrent Atomistic-Continuum Method.

Abstract: Unlikemany other multiscale methods, the concurrent atomistic-continuum

(CAC) method admits the migration of dislocations and intrinsic

stacking faults through a lattice while employing an underlying

interatomic potential as the only constitutive relation. Here, we

build algorithms and develop a new CAC code which runs in parallel

using MPI with a domain decomposition algorithm. New features of the

code include, but are not limited to: (i) both dynamic and

quasistatic CAC simulations are available, (ii) mesh refinement

schemes for both dynamic fracture and curved dislocation migration

are implemented, and (iii) integration points in individual finite

elements are shared among multiple processors to minimize the amount

of data communication. The CAC program is then employed to study a

series of metal plasticity problems in which both dislocation core

effects at the nanoscale and the long range stress field of

dislocations at the submicron scales are preserved. Applications

using the new code include dislocation multiplication from Frank-Read

sources, dislocation/void interactions, and dislocation/grain

boundary interactions.

Crystal
plasticity modeling is useful for considering the influence of
anisotropy of elastic and plastic deformation on local and global
responses in crystals and polycrystals. Modern crystal plasticity
has numerous manifestations, including bottom-up models based on
adaptive quasi-continuum and concurrent atomistic-continuum methods
in addition to discrete dislocation dynamics and continuum crystal
plasticity. Some key gaps in mesoscale crystal plasticity models will
be discussed, including interface slip transfer, grain subdivision in
large deformation, shock wave propagation in heterogeneous
polycrystals, and dislocation dynamics with explicit treatment of
waves. Given the mesoscopic character of these phenomena, contrasts
are drawn between bottom-up (e.g., atomistic and discrete dislocation
simulations and in situ experimental observations) and top-down
(e.g., experimental) information in assembling mesoscale constitutive
relations and informing their parameters.

Series: GT-MAP Seminars

This is an information session about research opportunities related to GT MAP activities. If you are a math graduate student, please join for free pizza as well.

Series: GT-MAP Seminars

Most available techniques for the design of tensegrity structures can be grouped in two categories. On the one hand, methods that rely on the systematic application of topological and geometric rules to regular polyhedrons have been applied to the generation of tensegrity elementary cells. On the other hand, efforts have been made to either combine elementary cells or apply rules of self-similarity in order to generate complex structures of engineering interest, for example, columns, beams and plates. However, perhaps due to the lack of adequate symmetries on traditional tensegrity elementary cells, the design of three-dimensional tensegrity lattices has remained an elusive goal. In this work, we first develop a method to construct three-dimensional tensegrity lattices from truncated octahedron elementary cells. The required space-tiling translational symmetry is achieved by performing recursive reflection operations on the elementary cells. We then analyze the mechanical response of the resulting lattices in the fully nonlinear regime via two distinctive approaches: we first adopt a discrete reduced-order model that explicitly accounts for the deformation of individual tensegrity members, and we then utilize this model as the basis for the development of a continuum approximation for the tensegrity lattices. Using this homogenization method, we study tensegrity lattices under a wide range of loading conditions and prestressed configurations. We present Ashby charts for yield strength to density ratio to illustrate how our tensegrity lattices can potentially achieve superior performance when compared to other lattices available in the literature. Finally, using the discrete model, we analyze wave propagation on a finite tensegrity lattice impacting a rigid wall.

Series: GT-MAP Seminars

Bio: Tomas Zegard is a postdoctoral fellow in the School of Civil and Environmental Engineering at Georgia Tech. He received a PhD in Structural Engineering from the University of Illinois at Urbana-Champaign in 2014. Afterwards, he took a position at SOM LLP in Chicago, an Architecture + Engineering firm specializing in skyscrapers. He has made significant contributions to the field of topology optimization through research papers and free open-source tools. Xiaojia Zhang is a doctoral candidate in the School of Civil and Environmental Engineering at Georgia Tech. She received her bachelor’s and master’s degrees in structural engineering from the University of Illinois at Urbana-Champaign. Her major research interests are structural topology optimization with material and geometric nonlinearity, stochastic programming, and additive manufacturing.

Topology optimization, an agnostic design method, proposes new and innovative solutions to structural problems. The previously established methodology of sizing a defined geometry and connectivity is not sufficient; in these lie the potential for big improvements. However, topology optimization is not without its problems, some of which can be controlled or mitigated. The seminar will introduce two topology optimization techniques: one targeted at continuum, and one targeted at discrete (lattice-like) solutions. Both will be presented using state-of-the-art formulations and implementations. The stress singularity problem (vanishing constraints), the ill-posedness of the problem, the large number of variables involved, and others, continue to challenge researchers and practitioners. The presented concepts find potential applications in super-tall building designs, aircrafts, and the human body. The issue of multiple load cases in a structure, a deterministic problem, will be addressed using probabilistic methodologies. The proposed solution is built around a suitable damping scheme based on simulated annealing. A randomized approach with stochastic sampling is proposed, which requires a fraction of the computational cost compared to the standard methodologies.

Series: GT-MAP Seminars

The workshop will launch the themetic semester on Material for GT-MAP activities.
This is a three day workshop: The first two days (Wed, Thurs) focusing on the theme of Material, and third day includes broad research topics, open to introducing your research.
See the complete Schedule.

Series: GT-MAP Seminars

Multiscale and multiphysics materials modeling addresses the challenging materials problems that involve multiple physical phenomena at multiple spatial and temporal scales. In this talk, I will present the multiscale and mulphysics models developed in my research group with a recent focus on energy storage materials and advanced structure materials. Our study of rechargeable lithium ion batteries for energy storage applications reveals a rich spectrum of electrochemically-induced mechanical degradation phenomena. The work involves a tight coupling between multiscale chemomechanical modeling and in situ nanobattery testing. Our study of nanostructured metals and alloys elucidates the effects of nanostructures on the size-dependent ultrahigh strengths and surface/interface mediated deformation mechanisms. Finally, I will present my perspectives on the multiscale and multiphysics modeling that requires a synergistic integration of engineering physics and applied mathematics, in order to design the advanced structural and functional materials to realize their potential to the full.

Series: GT-MAP Seminars

Recent breakthroughs in condensed matter physics are opening new
directions in band engineering and wave manipulation. Specifically,
challenging the notions of reciprocity, time-reversal symmetry and
sensitivity to defects in wave propagation may disrupt ways in which
mechanical and acoustic metamaterials are designed and employed, and may
enable totally new functionalities. Non-reciprocity and topologically
protected wave propagation will have profound implications on how
stimuli and information are transmitted within materials, or how energy
can be guided and steered so that its effects may be controlled or
mitigated. The seminar will briefly introduce the
state-of-the-art in this emerging field, and will present initial
investigations on concepts exploiting electro-mechanical coupling and
chiral and non-local interactions in mechanical lattices. Shunted
piezo-electric patches are exploited to achieve time-modulated
mechanical properties which lead to one-directional wave propagation in
one-dimensional mechanical waveguides. A framework to realize helical
edge states in two identical lattices with interlayer coupling is also
presented. The methodology systematically leads to mechanical lattices
that exhibit one-way, edge-bound, defect-immune, non-reciprocal wave
motion. The presented concepts find potential application in vibration
reduction, noise control or stress wave mitigation systems, and as part
of surface acoustic wave devices capable of isolator, gyrator and
circulator-like functions on compact acoustic platforms.