Skip navigation
Please use this identifier to cite or link to this item:
Title: Multipoles, symmetry representations and thermal fluctuations in elastic systems
Authors: Sarkar, Siddhartha
Advisors: Kosmrlj, Andrej
Contributors: Electrical Engineering Department
Keywords: Elasticity
soft condensed matter
Statistical mechanics
topological mechanics
Subjects: Applied physics
Statistical physics
Mechanical engineering
Issue Date: 2021
Publisher: Princeton, NJ : Princeton University
Abstract: In recent years, we have seen exciting new developments in research on mechanical metamaterials, topological phononics, and mechanics of atomically thin 2D materials. In this thesis, I present how methods from physics can help us in understanding the mechanical properties of these systems as well as gaining further intuition. First, we develop a multipole expansion method to describe the deformation of infinite as well as finite solid structures with cylindrical holes and inclusions by borrowing concepts from electrostatics, such as induction and method of image charges. Our method shows excellent agreement with finite element simulations and experiments. Next, using representation theory, I show how symmetries of phononic crystals affect the degeneracies in their phononic band structures. Deformation of phononic crystals under external load that causes breaking of some symmetries can lead to the lifting of degeneracies for bands and creating gaps such that waves of certain frequencies become disallowed. Finally, using methods from statistical physics, I present how the mechanical properties of atomically thin 2D sheets and shells get modified due to thermal fluctuations. Freely suspended sheets subject to such fluctuations are much harder to bend, but easier to stretch, compress and shear, beyond a characteristic thermal length scale, which is on the order of nanometers for graphene at room temperatures. Just like in critical phenomena, these renormalized elastic constants become scale dependent with universal power-law exponents. In nanotubes, competition between stretching and bending costs associated with radial fluctuations introduces another characteristic elastic length scale, which is proportional to the geometric mean of the radius and effective thickness. Beyond this elastic length scale, bending rigidities and in-plane elastic constants of nanotubes become anisotropic.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Electrical Engineering

Files in This Item:
File Description SizeFormat 
Sarkar_princeton_0181D_13796.pdf27.85 MBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.