Mechanical metamaterials are structures whose carefully constructed geometry allows for unusual mechanical response. It has been shown that local rigidity and softness in isostatic structures may...Show moreMechanical metamaterials are structures whose carefully constructed geometry allows for unusual mechanical response. It has been shown that local rigidity and softness in isostatic structures may be described by a topologically protected polarization field. Here we exhaustively characterize a class of 3D lattices based on the 2D kagome lattice. Our main finding is a 3D metamaterial at critical mechanical stability, whose bottom side is much floppier than its top side. We also derive a general formula describing rigidity and softness associated to line dislocations in 3D polarized latticesShow less
This thesis investigates acoustic phenomena associated with the presence of a synthetic gauge field in a mechanical metamaterial. Such fields minimally couple to the momentum of phonons in a low...Show moreThis thesis investigates acoustic phenomena associated with the presence of a synthetic gauge field in a mechanical metamaterial. Such fields minimally couple to the momentum of phonons in a low energy limit, which leads to acoustic analogs of some of the effects of a gauge field in an electronic system, such as Landau quantization. We develop two strategies for realizing a pseudo-magnetic field in a metamaterial based on the honeycomb lattice. In the first strategy, we consider deformations of the lattice that result from applied boundary stress. In the second strategy, we use nonuniform patterning of the local material stiffness. We then explore physical phenomena associated with a constant pseudo-magnetic field. We provide evidence for the existence of a mechanical Landau-level spectrum in this metamaterial. We then focus on the zeroth Landau level and show that the corresponding modes are localized in the bulk of the system and exist mostly on one sublattice. Following recent insights into similar physical systems, we investigate topologically robust sound modes along domain walls in the bulk of the metamaterial. Further, by introducing dissipation, we test selective enhancement of the domain-wall-bound topological sound mode, a feature that could potentially be exploited for the design of acoustic couplers, rectifiers, and sound amplification by stimulated emission of radiation (SASERs) -- mechanical devices analogs to lasers.Show less
Recent research has shown that it is possible to control the elastomechanical response of topological mechanical metamaterials via topologically localized and protected edge states. Topological...Show moreRecent research has shown that it is possible to control the elastomechanical response of topological mechanical metamaterials via topologically localized and protected edge states. Topological principles can in this sense be seen as a novel set of design guidelines that may aid us in the construction of mechanical metamaterials with controllable responses. In this thesis, we strive to investigate and expand the applicability of topological principles for the reliable, simple and response-oriented design of mechanical metamaterials consisting of central force springs, soft polymer beams, and rigid links with shearing constraints.Show less
Chiral phases of nematic structures in liquid crystals are generally produced by either chiral molecules or by doping a system of achiral LC molecules with chiral constituents. However, a chiral...Show moreChiral phases of nematic structures in liquid crystals are generally produced by either chiral molecules or by doping a system of achiral LC molecules with chiral constituents. However, a chiral nematic phase may also emerge in geometrically confined nematics with achiral constituents. It has recently been shown that spontaneous chirality emerges for a nematic in a torus with parallel anchoring for a particular choice of the aspect ratio. Experimental evidence suggests that a chiral phase can also be observed for perpendicular anchoring conditions, however, an analytical minimisation of the Frank free energy suggests otherwise. Nevertheless, analytical calculations show that a chiral vortex structure can be observed for very thin capillary lengths.Show less
